Archive

Tag Archives: trias politica

In The Guardian, 2018-12-13, historian Timothy Garton Ash asks the EU27:

“(…) all we need from you, my friends, is a clear, simple, positive message, without ifs or buts: “We want you to stay!””

The EU27 already said this, before this plea actually. Yet, let me offer my fellow citizen apologies to the British people for the misconduct by the EU27 leadership. The EU27 has not been clear enough. It has allowed itself to get infected by the irresponsibility by the UK leadership.

An issue between Member States

The EU is a union of Member States and an arrangement between governments. The EU is no usual democracy with a direct relationship between EU citizens and their collective EU government. The EU27 regard Brexit as an internal affair of the UK. EU President Donald Tusk chairs meetings of government leaders, and would see himself entirely out of place when he would tour the UK and have Town Hall sessions trying to resolve misunderstandings and pleading the common cause. Brexiteers would accuse him of meddling in internal affairs, and Tusk could only confirm this. Many Britons would see him as another Pole who should depart as soon as possible, even when he would be excellent at taking care at hospital beds or fixing the plumbing.

Clear and convincing evidence that the UK is under the spell of populism

The 2016 Referendum is clear and convincing evidence, acceptable in a decent criminal court, that the UK is under the spell of populism. In proper democracy it is Parliament that decides such issues. Who studies the mathematics of democracy can better appreciate the history that it are mostly demagogues and incompetents who resort to referenda to create the illusion as if the “will of the people” has been called upon. The 2016 Referendum was an exercise in populist lunacy and the UK government has been irresponsible concerning it. Prime Minister Theresa May clearly doesn’t have the background to understand this. In this particular respect she is no better than Silvio Berlusconi though with a feeling for understatement and a stiff upper lip, and she rather follows populism in the UK instead of steering her country out of it.

Stab-in-the-Back Myth

In this political setting, anything that the EU27 says can and basically will be used against it. The EU27 has been cautious about the risk of a Stab-in-the-Back Myth that the EU27 would be at fault for the mess that the UK is in and could be in for coming decades. When the EU27 would state with more emphasis that it would rather have the UK remain, like Garton Ash suggests, then this would likely be misrepresented as a ploy to lure the virgin UK into a place of darkness and unspeakable horror.

Take the bull by the horns

In real politik the EU27 accepted that a Member State succombed to populism. They should have been wiser. Alongside the unavoidable negotiations, the EU27 should also have discussed How to Deal with Populism in a Member State. EU scientists with basic impartiality in Town Hall meetings could have invited Britons to see this true diagnosis and monster eye to eye. It is still not too late. I myself have looked into the deeper causes of Brexit. My finding is that Britons think that they have democracy while the UK has only proto-democracy. The UK has district representation instead of equal proportionality. The UK system has been causing problems in the UK for a good part of last century, and Brexit is only a culmination.

A second referendum is populism all-over again

Garton Ash’s second referendum is populist irresponsibility all-over again. He neglects the evidence of the 2016 disaster and believes in a heaven of well designed referenda that disclose the “will of the people” like an Oracle of Delphi. His world view is locked in proto-democracy, and he doesn’t even notice the prison walls.

The advice is a moratorium

My suggestion is a Moratorium on Brexit of two years, so that the UK can discuss and improve its democracy. See the former weblog entry.

 

Wikimedia commons May and Berlusconi

Many people think that political science on electoral systems and referenda must be a science since otherwise it would not be called a science. Unfortunately, the label “political science” got coined around 1903 with the creation of the American Political Science Association (APSA), and this label rather reflects an aspiration and no achievement yet. In the UK there is the Political Studies Association (PSA), founded in 1950, baptised more modestly since there still is much scholarship in the humanities. It turns out that many statements by “political science / studies on electoral systems and referenda” aren’t scientific, and for their relevance for empirical reality they can only be compared to astrology, alchemy or homeopathy. A scientist looking at a UK General Election can only think “Garbage in, garbage out” (GIGO).

The UK has been fundamentally disinformed about its electoral system with district representation and the use of referenda like the Brexit Referendum of 2016. The UK is locked in tradition and fuzzy thinking in the humanities. The situation may be explained by the historical path that the UK has taken, but this history hasn’t included a proper application of science to the notion of democracy.

Compare the current chaos w.r.t. Brexit to the chaos with the financial crisis of 2008. On the latter, the UK Queen asked famously:

“Why did nobody notice it?”

There is a longer list of economists who issued warnings in time, with Hyman Minsky at the top and me somewhere too. The next question rather is why such warnings weren’t taken seriously in the policy making process. My diagnosis since 1990 is that there is a failure of the separation of powers, the Trias Politica, with still too much room for politicians to manipulate the information. The remedy is to create an Economic Supreme Court (ESC) that will guard the quality of information for policy. The House of Commons would still determine policy but it would get less room to disinform the public. The current UK Office for Budget Responsibility (OBR) is a far cry from what is actually needed.

With this analogy established, consider Brexit again. Might the Queen not repeat the question ? Now however there doesn’t seem to be a list of early warnings that were overlooked. Now we have a “political science” that has gotten lost in abstraction. Here, the remedy is to ask proper scientists from physics to biology to psychometrics to econometrics to look at democracy and to help “political science / studies on electoral systems” become a proper science too. My suggestion is to team up empirical scientists from the Royal Society with members of the PSA and the British Academy, and to encourage a buddy-system to start delving into this. The place to start is my paper “One woman, one vote. Though not in the USA, UK and France” at MPRA 2018, and a presentation 1270381 at Zenodo.org on the distance between votes and seats.

Many people think that the Brexit Referendum of 2016 allowed voters to express their decision, with 52% Leave and 48% Remain. However, not all voters expressed their decision but many were only guessing. A YouGov poll at the time of the GIGO 2017 showed that 17% of voters still listed Remain between different options of Leave. Voters were forced to make a strategic choice about what they feared most what might happen. See my deconstruction of this mess in the October 2017 Newsletter of the Royal Economic Society (RES).

Now there are calls for a second referendum. This call wants to resolve the current chaos by creating more chaos, and potentially a “stab in the back” myth that the 2016 supposed decision isn’t listened to. The lesson from the current chaos should rather be that referenda are generally dumb and dangerous, even in the form of the neverendum. The real problem lies in the UK system of district representation that structurally fails to reflect the views and interests of voters. The deeper problem is that the House of Commons and the electorate are disinformed by an academic field that still is comparable to astrology, alchemy or homeopathy. There is a grand scale of disinformation by famous UK scholars like Iain McLean, John Curtice, younger Alan Renwick, and (other) members of PSA.

My suggestion is that the UK switches to equal proportional representation (EPR), say adopt the Dutch system of open lists (in which you may always vote for a regional candidate though people don’t tend to do so), has proper elections, and then let the new House of Commons discuss the relation with the EU again. It is not unlikely that the EU would allow the UK the time for such a fundamental reconsideration on both its democracy and Brexit. UK political parties may need to split up to offer voters the relevant spectrum of views, though one must allow for election alliances (especially the former Dutch method of list combinations). To some readers this suggestion may remind of earlier discussions about district or proportional representation (DR vs EPR). However, there now is the key new insight about the disinformation by the “political science / studies on electoral systems”, that causes the need to re-evaluate what has been claimed in the past by the academic ivory towers, and also by the disinforming UK Electoral Reform Society (ERS). It remains to be seen whether the UK would want to switch from DR to EPR, but the first step would be to provide the public with proper information.

PS. An eye-opener can be that “political science on electoral systems” relies upon common language instead of developed definitions. Physics also borrowed common words like “force” and “mass”, yet it provided precise definitions, and gravity in Holland has the same meaning as gravity in the UK. The “political science on electoral systems” uses the same word “election” but an “election” in Holland with EPR is entirely different from an “election” in the UK with DR. In reality there is a difference between a contest (DR) or a bundling of votes to support a representative (EPR). We find that the UK is locked into confusion by its vocabulary. An analogy is the following. Consider the medieval trial by combat or the “judgement of God”, that persisted into the phenomenon of dueling to settle conflicts. A duel was once seriously seen as befitting of the words “judgement” and “trial”. Eventually civilisation gave the application of law with procedures in court. Using the same words “judgement” and “trial” for both a duel and a court decision confuses what is really involved, though the outward appearance may look the same, that only one party passes the gate. The UK suffers the same kind of confusion about the “General Election for the House of Commons” when this actually is no proper election of interest representatives but concerns contests for getting district winners. The system of DR is proto-democratic and no proper democracy that uses EPR.

Picture: Wikimedia Queen in the UK, Duel in France, Judges in The Hague.

Let us look beyond Brexit and determine the implications w.r.t. democracy itself. We can conclude that the UK has an intellectual community that is quite blind on the very notion of democracy. When the educated run astray then there is only an anchor in the democratic notions of the whole population, and this opens the doors to what is called “populism”.

I started looking into Brexit after the surprise referendum outcome in 2016. This memo sums up my findings over the last two years. The following identifies where the educated community in the UK is in need of re-educating themselves.

Earlier in 1990-1994 I already concluded that Montesquieu’s model of the separation of powers of the Trias Politica fails in a key aspect since its conception in 1748. Democracies need the fourth power of an Economic Supreme Court, see (2014). It is necessary to mention this earlier conclusion that predates Brexit, but let us now continue with findings following Brexit.

To start with: What does the UK electorate really want w.r.t. Brexit or Bremain ? Both the Referendum of 2016 and the General Election of 2017 do not provide adequate information. One would think that it is rather damning for a claimed democracy when its procedures do not result into adequate clarity on such a fundamental issue.

The 2016 Referendum Question concerned the legal issue of Leave or Remain but was disinformative about the ways of Leaving or Remaining. The political parties that are elected into the House of Commons are split on both direction and ways as well. The overall situation can only be described as chaotic. One might try to characterise this more positively as that a population with divided views generated a House of Commons with divided views, which would be democracy itself, but this neglects that there is no information about what those divided views actually are. The true process is “garbage in, garbage out” and this doesn’t fit the definition of democracy.

The very Brexit or Bremain Referendum Question fails the criteria for a decent statistical enquiry. I am surprised that the Royal Statistical Society (RSS) did not protest. The question of Leave or Remain is a binary legal issue but the true issue are the policy options. It took some time to analyse this, but with the help of Anthony Wells of YouGov.com I managed to dissect this, see (2017abc). Some 17 per cent of voters ranked Remain between different versions of Leave, which implies a grand game of guessing what to vote for, and which means that the Referendum failed on its purpose of expression of preferences. The UK Electoral Commission missed this but it does not care about this and is happy to take the legal position. They claim to provide proper information to the general public, but what they regard as “information” is regarded by statistical science as disinformation (but the RSS is silent on this). One is reminded of Byzantium instead of claimed modernity.

The main question is why the UK had the referendum in the first place. In Holland since 1917 there is system of equal proportional representation (EPR) for the House of Commons so that referenda are not required. The UK has a system of district representation (DR) that lacks such proportionality, and that invites the confusion that referenda might be used to find out what the electorate really thinks. The latter is a confusion indeed, since it neglects the important role of bargaining, see (2017c).

This diagnosis set me on the course of investigating why the USA, UK and France have DR and not EPR. My original thought was that a party that won an election would have no reason to change a system that caused its election. This would explain why the USA, UK and France were stuck with DR and did not switch to EPR. Last year I discovered that the true cause is different. My finding for the UK is that there is an amazing blindness in the UK intellectual community. The report in (2018a) causes a chill down the spine. It appears that “political science on electoral systems” is no science yet, but still solidly within the Humanities, and alike astrology, alchemy and homeopathy. The eye-opener is that these academics use the same word “election” for both DR and EPR while they actually have entirely different meanings. In reality only EPR has proper elections fitting of proper democracy. The DR system is a proto-democracy that relies on contests. Political “science” is blind to what this means not only for proper scientific analysis but also for communication with the general public. Voters are disinformed on a grand scale, both in the textbooks in government classes and in public discussion e.g. at “election” nights.

Compare physics that also borrowed words from colloquial English, like “force” and “mass”. Yet in physics these words have recieved precise meaning. In physics, gravity in Holland has the same meaning as gravity in the UK. Political “science” uses colloquial terms like “election” and “democracy” but those meanings are not fixed. An “election” in Holland with EPR is entirely different from an “election” in the UK with DR. Political “science” thus uses terms that confuse both the academics and the public. When historians describe how the West developed into democracy, they occlude the fact that the USA, UK and France are still in a proto-democratic phase.

A first complication is: There appears to be a special role for the UK Electoral Reform Society (ERS) founded in 1884 and originally known as the Proportional Representation Society. Here we find an independent and disinterested group that criticises DR and that claims to further the UK on the historical path towards EPR. However, it appears that ERS wants a transferable vote, while their claim that transferability generates proportionality is simply false. Such distortion contributed to the debacle of the 2011 Referendum on the “alternative vote”, which is a counterproductive construct to start with. When one presents the ERS with this criticism then the reply appears to be disingenuous. Instead of a clear adoption of EPR, either in the Dutch version or like the UK elections for the EU Parliament, with their wealth of experience by actual application, one can only conclude that the ERS is addicted to this notion of a transferable vote, and they want this model at any cost. Psychology might explain how such zealotism may arise but it remains far removed from proper information for the general public.

A second complication is: There appears to exist a confusion w.r.t. the interpretation of Arrow’s Impossibility Theorem on democracy. In this, there is a major role for mathematicians who mainly look at models and who neglect empirical science. This leads too far for this memo, and an overview is given in (2018e).

A third complication is: There is the interference by a grand coalition of statistics and political science (with some ambiguity whether quotation marks should be used) in creating a black hole on democracy and its measurement, see (2018bcd). Political science never managed to find a good measure for the difference between vote shares and seat shares. My proposal is to use the “sine-diagonal inequality / disproportionality” (SDID) measure, that does for democracy what the Richter scale does for earthquakes. Political science has shown less understanding of statistics, or perhaps failed in finding such a measure because statistical science did not develop this theory or did not understand what the political scientists were looking for. This hole has been plugged now, see (2018bcd). Nevertheless, this diagnosis calls for a reorganisation of university courses in statistics and political science.

The enclosed graph highlights the “perfect storm” of blindness of the intellectual community that lurks behind Brexit. The figure is documented in (2018d). The main idea is that statistics and other sciences like physics, biology, psychometrics and econometrics could help “political science on electoral systems” to become a proper science. Then science can provide adequate information to the general public.

A conclusion is: The UK electoral system has “winner take all” district representation (DR) that does not provide for equal proportional representation (EPR) of what voters want. Again the word “representation” means something else for proto-democratic DR versus democratic EPR. My suggestion is that the UK switches to EPR, say adopt the Dutch system of open lists, has new elections, and let the new House discuss Brexit or Bregret again. Bregret is defined by that the House adopted Brexit before and thus might reconsider. It is not unlikely that the EU would allow the UK the time for such a fundamental reconsideration on both electoral system and Brexit.

It remains to be seen whether the UK electorate would want to stick to the current system of DR or rather switch to EPR. The first step is to provide the UK electorate with adequate information. For this, the UK intellectual community must get its act together on what this information would be. A suggestion is to check the analysis that I have provided here.

 

References

Colignatus (2014), “An economic supreme court”, RES Newsletter issue 167, October, pp. 20-21
Colignatus (2017a), “Voting theory and the Brexit referendum question”, RES Newsletter, Issue 177, April, pp. 14-16
Colignatus (2017b), “Great Britain’s June 2017 preferences on Brexit options”, RES Newsletter, Issue 177, October, http://www.res.org.uk/view/art2Oct17Features.html
Colignatus (2017c), “Dealing with Denial: Cause and Cure of Brexit”, https://boycottholland.wordpress.com/2017/12/01/dealing-with-denial-cause-and-cure-of-brexit/
Colignatus (2018a), “One woman, one vote. Though not in the USA, UK and France”, https://mpra.ub.uni-muenchen.de/84482/
Colignatus (2018b), “Comparing votes and seats with cosine, sine and sign, with attention for the slope and enhanced sensitivity to inequality / disproportionality”, https://mpra.ub.uni-muenchen.de/84469/
Colignatus, (2018c), “An overview of the elementary statistics of correlation, R-Squared, cosine, sine, Xur, Yur, and regression through the origin, with application to votes and seats for parliament ”, https://doi.org/10.5281/zenodo.1227328
Colignatus, (2018d), “An overview of the elementary statistics of correlation, R-Squared, cosine, sine, Xur, Yur, and regression through the origin, with application to votes and seats for parliament (sheets)”, Presentation at the annual meeting of Dutch and Flemish political science, Leiden June 7-8, https://zenodo.org/record/1270381
Colignatus, (2018e), “The solution to Arrow’s difficulty in social choice (sheets)”, Second presentation at the annual meeting of Dutch and Flemish political science, Leiden June 7-8, https://zenodo.org/record/1269392

The following applies to elections for Parliament, say for the US House of Representatives or the UK House of Commons, and it may also apply for the election of a city council. When the principle is one man, one vote then we would want that the shares of “seats won” would be equal to the shares of “votes received”. When there are differences then we would call this inequality or disproportionality.

Such imbalance is not uncommon. At the US election of November 8 2016, the Republicans got 49.1% of the votes and 55.4% of the seats, while the Democrats got 48% of the votes and 44.6% of the seats. At the UK general election of June 8 2017, the Conservatives got 42.2% of the votes and 48.8% of the seats while Labour got 39.9% of the votes and 40.3% of the seats (the wikipedia data of October 16 2017 are inaccurate).

This article clarifies a new and better way to measure this inequality or disproportionality of votes and seats. The new measure is called Sine-Diagonal Inequality / Disproportionality (SDID) (weblink to main article). The new measure falls under descriptive statistics. Potentially it might be used in any area where one matches shares or proportions, like the proportions of minerals in different samples. SDID is related to statistical concepts like R-squared and the regression slope. This article looks at some history, as Karl Pearson (1857-1936) created the R-Squared and Ronald A. Fisher (1890-1962) in 1915 determined its sample distribution. The new measure would also be relevant for Big Data. William Gosset (1876-1937) a.k.a. “Student” was famously unimpressed by Fisher’s notion of “statistical significance” and now is vindicated by descriptive statistics and Big Data.

The statistical triad

Statistics has the triad of Design, Description and Decision.

  • Design is especially relevant for the experimental sciences, in which plants, lab rats or psychology students are subjected to alternate treatments. Design is informative but less applicable for observational sciences, like macro-economics and national elections when the researcher cannot experiment with nations.
  • Descriptive statistics has measures for the center of location – like mean or median – and measures of dispersion – like range or standard deviation. Important are also the graphical methods like the histogram or the frequency polygon.
  • Statistical decision making involves the formulation of hypotheses and the use of loss functione to evaluate that hypotheses. A hypothesis on the distribution of the population provides an indication for choosing the sample size. A typical example is the definition of decision error (of the first kind) that a hypothesis is true but still rejected. One might accept a decision error in say 5% of the cases, called the level of statistical significance.

Historically, statisticians have been working on all these areas of design, description and decision, but the most difficult was the formulation of decision methods, since this involved both the calculus of reasoning and the more complex mathematics on normal, t, chi-square, and other frequency distributions. In practical work, the divide between the experimental and the non-experimental (observational) sciences appeared insurmountable. The experimental sciences have the advantages of design and decisions based upon samples, and the observational sciences basically rely on descriptive statistics. When the observational sciences do regressions, there is an ephemeral application of statistical significance that invokes the Law of Large Numbers, that all error approximates the normal distribution.

This traditional setup of statistics is being challenged in the last decades by Big Data – see also this discussion by Rand Wilcox in Significance May 2017. When all data are available, and when you actually have the population data, then the idea of using a sample evaporates, and you don’t need to develop hypotheses on the distributions anymore. In that case descriptive statistics becomes the most important aspect of statistics. For statistics as a whole, the emphasis shifts from statistical decision making to decisions on content. While descriptive statistics had been applied mostly to samples, Big Data now causes the additional step how these descriptions relate to decisions on content. In fact, such questions already existed for the observational sciences like for macro-economics and national elections, in which the researcher only had descriptive statistics, and lacked the opportunity to experiment and base decisions upon samples. The disadvantaged areas now provide insights for the earlier advantaged areas of research.

The key insight is to transform the loss function into a descriptive statistic itself. An example is the Richter scale for the magnitude of earthquakes. It is both a descriptive statistic and a factor in the loss function. A nation or regional community has on the one hand the cost of building and construction and on the other hand the risk of losing the entire investments and human lives. In the evaluation of cost and benefit, the descriptive statistic helps to clarify the content of the issue itself. The key issue is no longer a decision within statistical hypothesis testing, but the adequate description of the data so that we arrive at a better cost-benefit analysis.

Existing measures on votes versus seats

Let us return to the election for the House of Representatives (USA) or the House of Commons (UK). The criterion of One man, one vote translates into the criterion that the shares of seats equal the shares of votes. We are comparing two vectors here.

The reason why the shares of seats and votes do not match is because the USA and UK use a particular setup. The setup is called an “electoral system”, but since it does not satisfy the criterion of One man, one vote, it does not really deserve that name. The USA and UK use both (single member) districts and the criterion of Plurality per district, meaning that the district seat is given to the candidate with the most votes – also called “first past the post” (FPTP). This system made some sense in 1800 when the concern was district representation. However, when candidates stand for parties then the argument for district representation loses relevance. The current setup does not qualify for the word “election” though it curiously continues to be called so. It is true that voters mark ballots but that is not enough for a real election. When you pay for something in a shop then this is an essential part of the process, but you also expect to receive what you ordered. In the “electoral systems” in the USA and UK, this economic logic does not apply. Only votes for the winner elect someone but the other votes are obliterated. For such reasons Holland switched to equal / proportional representation in 1917.

For descriptive statistics, the question is how to measure the deviation of the shares of votes and seats. For statistical decision making we might want to test whether the US and UK election outcomes are statistically significantly different from inequality / proportionality. This approach requires not only a proper descriptive measure anyway, but also some assumptions on the distribution of votes which might be rather dubious to start with. For this reason the emphasis falls on descriptive statistics, and the use of a proper measure for inequality / disproportionality (ID).

A measure proposed by, and called after, Loosemore & Hanby in 1971 (LHID) uses the sum of the absolute deviations of the shares (in percentages), divided by 2 to correct for double counting. The LHID for the UK election of 2017 is 10.5 on a scale of 100, which means that 10.5% of the 650 seats (68 seats) in the UK House of Commons are relocated from what would be an equal allocation. When the UK government claims to have a “mandate from the people” then this is only because the UK “election system” is so rigged that many votes have been obliterated. The LHID gives the percentage of relocated seats but is insensitive to how these actually are relocated, say to a larger or smaller party.

The Euclid / Gallagher measure proposed in 1991 (EGID) uses the Euclidean distance, again corrected for double counting. For an election with only two parties EGID = LHID. The EGID has become something like the standard in political science. For the UK 2017 the EGID is 6.8 on a scale of 100, which cannot be interpreted as a percentage of seats like LHID, but which indicates that the 10.5% of relocated seats are not concentrated in the Conservative party only.

Alan Renwick in 2015 tends to see more value in LHID than EGID: “As the fragmentation of the UK party system has increased over recent years, therefore, the standard measure of disproportionality [thus EGID] has, it would appear, increasingly understated the true level of disproportionality.”

The new SDID measure

The new Sine-Diagonal Inequality / Disproportionality (SDID) measure – presented in this paper – looks at the angle between the vectors of the shares of votes and seats.

  • When the vectors overlap, the angle is zero, and then there is perfect equality / proportionality.
  • When the vectors are perpendicular then there is full inequality / disproportionality.
  • While this angle variates from 0 to 90 degrees, it is more useful to transform it into sine and cosine that are in the [0, 1] range.
  • The SDID takes the sine for inequality / disproportionality and the cosine of the angle for equality / proportionality.
  • With Sin[0] = 0 and Cos[0] = 1, we thus get a scale that is 0 for full inequaliy / disproportionality and 1 for full equality / proportionality.

It appears that the sine is more sensitive than either absolute value (LHID) and Euclidean distance (EGID). It is closer to the absolute value for small angles, and closer to the Euclidean distrance for larger angles. See said paper, Figure 1 on page 10. SDID is something like a compromise between LHID and EGID but also better than both.

The role of the diagonal

When we regress the shares of the seats on the shares of the votes without using a constant – i.e. using Regression Through the Origin (RTO) – then this gives a single regression coefficient. When there is equality / proportionality then this regression coefficient is 1. This has the easy interpretation that this is the diagonal in the votes & seats space. This explains the name of SDID: when the regression coefficient generates the diagonal, then the sine is zero, and there is no inequality / disproportionality.

Said paper – see page 38 – recovers a key relationship between on the one hand the sine and on the other hand the Euclidean distance and this regression coefficient. On the diagonal, the sine and Euclidean distance are both zero. Off-diagonal, the sine differs from the Euclidean distance in nonlinear manner by means of a factor given by the regression coefficient. This relationship determines the effect that we indicated above, how SDID compromises between and improves upon LHID and EGID.

Double interpretation as slope and similarity measure

There appears to be a relationship between said regression coefficient and the cosine itself. This allows for a double interpretation as both slope and similarity measure. This weblog text is intended to avoid formulas as much as possible and thus I refer to said paper for the details. Suffice to say here is that, at first, it may seem to be a drawback that such a double interpretation is possible, yet, on closer inspection the relationship makes sense and it is an advantage to be able to switch perspective.

Weber – Fechner sensitivity, factor 10, sign

In human psychology there appears to be a distinction between actual differences and perceived differences. This is called the Weber – Fechner law. When a frog is put into a pan with cool water and slowly boiled to death, it will not jump out. When a frog is put into a pan with hot water it will jump out immediately. People may notice differences between low vote shares and high seat shares, but they may be less sensitive to small differences, while these differences actually can still be quite relevant. For this reason, the SDID uses a sensitivity transform. It uses the square root of the sine.

(PM. A hypothesis is that the USA and UK call their national “balloting events” still “elections”, is that the old system of districts has changed so gradually into the method of obliterating votes that many people did not notice. It is more likely though that that some parties recognised the effect, but have an advantage under the present system, and then do not want to change to equal / proportional representation.)

Subsequently, the sine and its square root have values in the range [0, 1]. In itself this is an advantage, but it comes with leading zeros. We might multiply with 100 but this might cause the confusion as if it would be percentages. The second digit might give a false sense of accuracy. It is more useful to multiply this by 10. This gives values like on a report card. We can compare here to Bart Simpson, who appreciates low values on his report card.

Finally, when we compare, say, votes {49, 51} and seats {51, 49}, then we see a dramatic change of majority, even though there is only a slight inequality / disproportionality. It is useful to have an indicator for this too. It appears that this can be done by using a negative sign when such majority reversal occurs. This method of indicating majority reversals is not so sophisticated yet, and at this stage consists of using the sign of the covariance of the vectors of votes and seats.

In sum: the full formula

This present text avoids formulas but it is useful to give the formula for the new measure of SDID, so that the reader may link up more easily with the paper in which the new measure is actually developed. For the vectors of votes and seats we use the symbols v and s, and the angle between the two vectors give cosine and then sine:

SDID[v, s] = sign 10 √ Sin[v, s]

For the UK 2017, the SDID value is 3.7. For comparison the values of Holland with equal / proportional representation are: LHID 3, EGID 1.7, SDID 2.5. It appears that Holland is not yet as equal / proportional as can be. Holland uses the Jefferson / D’Hondt method, that favours larger parties in the allocation of remainder seats. At elections there are also the wasted vote, when people vote for fringe parties that do not succeed in getting seats. In a truly equal or proportional system, the wasted vote can be respected by leaving seats empty or by having a qualified majority rule.

Cosine and R-squared

Remarkably, Karl Pearson (1857-1936) also used the cosine when he created R-squared, also known as the “coefficient of determination“. Namely:

  • R-squared is the cosine-squared applied to centered data. Such centered data arise when one subtracts the mean value from the original data. For such data it is advisable to use a regression with a constant, which constant captures the mean effect.
  • Above we have been using the original (non-centered) data. Alternatively put, when we do above Regression Through the Origin (RTO) and then look for the proper coefficient of determination, then we get the cosine-squared.

The SDID measure thus provides a “missing link” in statistics between centered and non-centered data, and also provides a new perspective on R-squared itself.

Apparently till now statistics found little use for original (non-centered) data and RTO. A possible explanation is that statistics fairly soon neglected descriptive statistics as less challenging, and focused on statistical decision making. Textbooks prefer the inclusion of a constant in the regression, so that one can test whether it differs from zero with statistical significance. The constant is essentially used as an indicator for possible errors in modeling. The use of RTO or the imposition of a zero constant would block that kind of application. However, this (traditional, academic) focus on statistical decision making apparently caused the neglect of a relevant part of the analysis, that now comes to the surface.

R-squared has relatively little use

R-squared is often mentioned in statistical reports about regressions, but actually it is not much used for other purposes than reporting only. Cosma Shalizi (2015:19) states:

“At this point, you might be wondering just what R-squared is good for — what job it does that isn’t better done by other tools. The only honest answer I can give you is that I have never found a situation where it helped at all. If I could design the regression curriculum from scratch, I would never mention it. Unfortunately, it lives on as a historical relic, so you need to know what it is, and what misunderstandings about it people suffer from.”

At the U. of Virginia Library, Clay Ford summarizes Shalizi’s points on the uselessness of R-squared, with a reference to his lecture notes.

Since the cosine is symmetric, the R-squared is the same for regressing y given x, or x given y. Shalizi (2015, p18) infers from the symmetry: “This in itself should be enough to show that a high R² says nothing about explaining one variable by another.” This is too quick. When theory shows that x is a causal factor for y then it makes little sense to argue that y explains x conversely. Thus, for research the percentage of explained variation can be informative. Obviously it matters how one actually uses this information.

When it is reported that a regression has an R-squared of 70% then this means that 70% of the variation of the explained variable is explained by the model, i.e. by variation in the explanatory variables and the estimated coefficients. In itself such a report does not say much, for it is not clear whether 70% is a little or a lot for the particular explanation. For evaluation we obviously also look at the regression coefficients.

One can always increase R-squared by including other and even nonsensical variables. For a proper use of R-squared, we would use the adjusted R-squared. R-adj finds its use in model specification searches – see Dave Giles 2013. For an increase of R-adj coefficients must have an absolute t-value larger than 1. A proper report would show how R-adj increases by the inclusion of particular variables, e.g. also compared to studies by others on the same topic.  Comparison on other topics obviously would be rather meaningless. Shalizi also rejects R-adj and suggests to work directly with the mean squared error (MSE, also corrected for the degrees of freedom). Since R-squared is the cosine, then the MSE relates to the sine, and these are basically different sides of the same coin, so that this discussion is much a-do about little. For standardised variables (difference from mean, divided by standard deviation), the R-squared is also the coefficient of regression, and then it is relevant for the effect size.

R-squared is a sample statistic. Thus it depends upon the particular sample. A hypothesis is that the population has a ρ-squared. For this reason it is important to distinguish between a regression on fixed data and a regression in which the explanatory variables also have a (normal) distribution (errors in variables). In his 1915 article on the sample distribution of R-squared. R.A Fisher (digital library) assumed the latter. With fixed data, say X, the outcome is conditional on X, so that it is better to write ρ[X], lest one forgets about the situation. See my earlier paper on the sample distribution of R-adj. Dave Giles has a fine discussion about R-squared and adjusted R-squared. A search gives more pages. He confirms the “uselessnes” of R-squared: “My students are often horrified when I tell them, truthfully, that one of the last pieces of information that I look at when evaluating the results of an OLS regression, is the coefficient of determination (R2), or its “adjusted” counterpart. Fortunately, it doesn’t take long to change their perspective!” Such a statement should not be read as the uselessness of cosine or sine in general.

A part of history of statistics that is unknown to me

I am not familiar with the history of statistics, and it is unknown to me what else Pearson, Fisher, Gosset and other founding and early authors wrote about the application of the cosine or sine. The choice to apply the cosine to centered data to create R-squared is deliberate, and Pearson would have been aware that it might also be applied to original (non-centered) data. It is also likely that he would not have the full perspective above, because then it would have been in the statistical textbooks already. It would be interesting to know what the considerations at time were. Quite likely the theoretical focus was on statistical decision making rather than on description, yet this for me unknown history would put matters more into perspective.

Statistical significance

Part of the history is that R.A. Fisher with his attention for mathematics emphasized precision while W.S. Gosset with his attention to practical application emphasized the effect size of the coefficients found by regression. Somehow, statistical significance in terms of precision became more important than content significance, and empirical research has rather followed Fisher than the practical relevance of Gosset. This history and its meaning is discussed by Stephen Ziliak & Deirdre McCloskey 2007, see also this discussion by Andrew Gelman. As said, for standardised variables, the regression coefficient is the R-squared, and this is best understood with attention for the effect size. For some applications a low R-squared would still be relevant for the particular field.

Conclusion

The new measure SDID provides a better description of the inequality or disproportionality of votes and seats compared to existing measures. The new measure has been tailored to votes and seats, by means of greater sensitivity to small inequalities, and because a small change in inequality may have a crucial impact on the (political) majority. For different fields, one could taylor measures in similar manner.

That the cosine could be used as a measure of similarity has been well-known in the statistics literature since the start, when Pearson used the cosine for centered data to create R-square. For the use of the sine I have not found direct applications, but its use is straightforward when we look at the opposite of similarity.

The proposed measure provides an enlightening bridge between descriptive statistics and statistical decision making. This comes with a better understanding of what kind of information the cosine or R-squared provides, in relation to regressions with and without a constant. Statistics textbooks would do well by providing their students with this new topic for both theory and practical application.

There is a weird brew of populism and District Representation (DR). You might think that countries with Proportional Representation (PR) would be most sensitive to populism, but it is rather the reverse. Countries with DR appear to be much more affected, like the France, UK and USA that use First Past The Post (FPTP).

Countries with DR run the risk that the seats in the House of Commons do not reflect the popular vote, and then they might try to repair this with a referendum, that is proportional. In countries with PR there would be no need for referenda.

The UK had the Brexit referendum of June 23 2016, that generated a relatively high turnout of 72.2%, with 51.9% Leave and 48.1% Remain. The Leave vote concerned only 72.2% * 51.9% = 37.5% of the electorate, and apparently the Leavers were quite motivated to turn out.

Many wonder how the UK general election of June 8 2017 squares with this referendum. In the previous weblog text, I already discussed caution. Some key aspects for digging deeper are:

  • The election was on many more issues than only Brexit, and had a turnout of 68.8%. A poll of YouGov showed that 17% who voted at the referendum didn’t vote in 2017.
  • Turnout is not proportional in the Remain / Leave segments.
  • Though the UK is set to Leave, it matters what you call “Leave”. The UK has a discussion about Hard and Soft Brexit, see these options. The political parties tend to be ambiguous about what they want, and voters thus have to guess.

PM. The events after the June 8 elections show the complexity of the situation. Labour leader Jeremy Corbyn apparently favours a hard Brexit like Conservative PM Theresa May. The evening of June 29 showed a House rejection by 227 abstaining, 322 against and 101 for a Queen Speech motion to target for remaining in the single market and customs union (regarded as a soft Brexit). Yes voters were Lab 49, LD 12, SNP 34, PC 4, Green 1, Hermon 1. It might still be that some prefer Remain but only vote for a soft Brexit to avoid a hard one. Labour MPs who abstained might have done so only tactically. The whip rule was not to vote for this particular amendment but to vote for the Labour amendment, to deliver a Brexit that prioritises jobs and delivers the “exact same benefits” of the European single market and customs union. The latter Labour motion is quite an incongruity. Yet Corbyn demoted some frontbenchers for not sticking to the party whip.

Limitations to current representation

For both PR and DR alike, there is the problem that the House doesn’t represent (i) who didn’t vote and (ii) whose votes got wasted. There is also the distinction between the registered electorate and the unregistered.

See the case of Holland 2017 with PR, here.

The wasted votes in the UK amount to 3.5% of the votes. A solution might be to leave 3.5% of the 650 seats empty. Alternatively, the standard majority of the House of 326 seats is replaced by a qualified majority of 337 seats.

The 14.5 million electors who didn’t turn out are more than the 13.6 million who voted for the Conservatives, who got  317 seats. An alternative might be to leave 202 seats empty or use a qualified majority of 489.

The present situation thus means that the Conservatives with their 317 seats seem to be overpresented with their view on Brexit. We don’t really know, since the Unregistered and Don’t Vote did not come to vote to show their opinion.

YouGov data on Remain or Leave

YouGov provides us with (at least) two polls for 2015 and 2017 that tell us how parties are divided on Remain or Leave. In this, the 18 seats for Northern Ireland tend to be excluded, so that the data concern Great Britain, with England, Wales and Scotland.

The first poll is from 2015, and let me quote their graph. Observe that the Undecideds are not in the graphs. Apparently 7% of the Ukippers did not want to Leave immediately.

The second poll is after the 2017 election, and asks how those voted in 2017 also voted in 2015 and the referendum. Let me again quote from their graph, and see their website for the data sheet. Observe that the Undecideds are now excluded, since the Undecideds obviously did not vote either Yes or No.

Transforming these data in party flows

The challenge is to transform these data into party flows. Considerations are:

  • The data on 2015 are rather rough while the data on 2017 benefit from the 2016 referendum.
  • The poll of 2015 however is still more useful since many voters in 2015 may not have participated in the referendum. Thus, using the 2015 poll, the Undecideds of 2015 can be allocated to Remain or Leave, based upon party flavour.
  • From the voters of the referendum in 2016, we can subtract the deceased, then allocate the transition flows as observed in the poll of 2017, with e.g. the key information that 15% of Remain and 26% of Leave in 2016, thus on average 20.7%, did not vote in 2017. Thus we should not be surprised if the 2017 outcome might be relatively more in favour of Remain.
  • For the transition flows, we assume that the dispositions to Remain or Leave do not change. Check this YouGov poll in March 2017. For example, when a Conservative Leaver switches to Labour, then this indicates a shift from Hard to Soft, and not a shift from Soft to Remain.
  • The above gives us the divisions in the 2016 electorate that also voted in 2017.
  • We allocate the new voters in same proportions: not only the attainers (coming of age, turnout of 57%) but also those who didn’t vote at the referendum, and the new registrations for the electorate (who we might assume that they only register to actually go and vote). These data are rough, namely measured over the full year, so that we must assume e.g. that the deaths in the last half of 2016 are about the same as those in the first half of 2017.

The voter dynamics are a bit remarkable. Of the vote of about 32 million there is a stable core of only 26 million. The 26% leavers who do not vote at the general election in 2017 amount to 4.4 million voters. The surviving non-voters at the referendum amount to 12.3 million, of which 5 million or 41.4%, decide to vote at the general election in 2017,  while the other 7.2 miljoen do not show up at both occasions.

Results of these considerations

Northern Ireland and other parties have been included again, so we leave GB and return to the UK.

  • For the minor parties we may assume (see also the BBC on MPs) that Remain are Plaid Cymru, Sinn Fein, Independent Unionist (Hermon), and Leave is DUP. The popular vote also has parties not represented. UKIP will be Leave, and the Speaker and the remaining wasted vote will be Blank.
  • Percentages of the popular vote will include the wasted vote of 3.5% (including UKIP) in the denominator.

Remain is horizontal, Leave is vertical. The diagonal or 45º line gives the split. Below the diagonal a party has more Remain votes, above the diagonal it has more Leave votes. 2015 has Squares and 2017 has Triangles.

The axes are in millions of voters. For example, UKIP (on the bottom left) in 2015 had almost 4 million votes, of which apparently 7% Remain. UKIP in 2017 lost almost all of its votes, mostly to the Leave part of the Conservatives. For example, LD (LibDem) is stationary.

The votes for the House of Commons are a sum and would not fit in the graph, and thus 11 million votes have been subtracted on both axes.

  • The division in the House in 2015 was {Remain, Leave} = {17.3, 12.8} but depicts {6.3, 1.8}.
  • In 2017 this became {16.5, 15.2} which depicts {5.5, 4.2}.

A major explanation for this huge shift in public opinion is that many Remainers apparently want to respect the Brexit referendum outcome. The vote on June 8 also was after invoking article 50. Voters regard Brexit as a given, and voted for parties to make the best of it. See this YouGov poll on the Re-Leavers.

The following is a chart for the division in 2017, again on votes and not seats. Remain still seems to have the larger share of 51.0% compared to Leave at 47.2%. Observe that the latter includes UKIP though it didn’t get a seat. The remaining 1.8% Blank are for the Speaker and the remainging wasted vote. These parties may well have an opinion, or their own subdivisions, but those do not show here because they don’t show in above polls.

Northern Ireland

Prime Minister May made a deal with DUP, including that DUP must respect the Brexit deal that May will achieve with the EU. The 317 Conservative seats and the 10 seats for DUP generate a majority of 327, just 1 above the standardly required 326.

Let us look closer at this. The following data have been retrieved from the BBC.

In 2015 DUP had 8 seats. DUP in 2017 managed to get 2 more seats at the cost of others, with a huge wasted vote of 32.6%. A seat in the UK House of Commons required only 30,410 votes while the UK average is 47,901. At that rate NI should have 41 seats if the total electorate should be represented. Then a majority of 50% would require 21 seats, more than there actually are.

The Lorenz curve for Northern Ireland looks quite like the unequal Lorenz curve of the UK in 2015, when UKIP got only 1 seat, see the graphs in an earlier weblog text. There is a PR Gini of 36.7%, while Holland has a PR Gini of 3.6. The excel sheet for Northern Ireland is: 2017-Northern-Ireland-Lorenz-Gini

PM 1. Sinn Fein apparently never visits the sessions of the UK Parliament. This doesn’t seem to be relevant for this discussion that concerns the popular vote.

PM 2. In the EU Parliament smaller countries like Holland have a disproportionate number of seats compared to Germany. The situation is similar for NI in the UK. This would tend not to be relevant for the present discussion, except that the low value in NI in 2017 derives from the huge wasted vote.

Splitting up parties ?

Why doesn’t the UK split up the parties along the Remain / Leave divide ? Thus we would get ConR, ConL (Hard), LabR, LabL (Soft), and so on. With proportional representation (PR), then we would not have to rely on polling, but would see the proper allocations directly in the House of Commons.

There might be other (attractive or unattractive) features. When Mrs. May would have been part of the ConR party in 2015, then this would have made it more difficult for her to start leading the ConL party after the Brexit referendum outcome. Or when Corbyn would have been part of the LabL party in 2015 then he could not have easily gotten a hold on the LabR as happens now.

There was an entertaining poll on this very idea itself by YouGov in 2015, here. That poll isn’t quite convincing given the wrong forecast for the Brexit referendum outcome, which suggests some misrepresentation.

However, the system of DR tends to make such break-ups unattractive for the parties involved. Smaller parties are destined to lose in the FPTP system. Thus another argument for PR would be that it provides voters with more clarity on party positions. The final result may well be a compromise, but this can be bargained by the professionals in Parliament, and better is not tried by the voters in the isolation of the ballot box.

Also, I have argued before that the Brexit referendum question was flawed in design. We don’t know what the voters really want. We might need to further split up the parties, e.g. in “Labour Leave, as UK” and “Labour Leave, but Scotland Independent so that Scotland can Remain” and so on. In countries with PR like Holland, one tends to think that parties divide up along issues that people tend to think of as fundamental, in which ideology tends to be of key importance.

The issue of Brexit might not be as fundamental as many people in the UK seem to think. The issue of immigration got translated into the question on Brexit, and this might have to do with the DR structure, see also France. This might be a topic to look closer into.

Conclusions

Conclusions are:

  • Above calculations obviously are fairly rough, and based upon perhaps arbitrary assumptions (but that is what arbitrage is). They basically set the stage for a better opinion poll that replaces these uncertainties by normal poll variety.
  • Above estimate suggests that the popular vote would be still very close to a majority on Remain.
  • The above doesn’t look at the views of the 1.8% of the vote that hasn’t been in the YouGov polls that were used here or that could not easily been determined by the other reports.
  • The share for Leave is a mixed bag, with Hard and Soft.
  • The Conservatives have a disproportionate share of the seats, which causes that their view on Brexit finds disproportion too (and their view might be the view of their leadership).
  • Northern Ireland has a huge disproportion in 2017, similar to the UK House in 2015. The Conservative + DUP majority in 2017 thus is of dubious value.
  • When the UK electorate better understands that the Brexit referendum question was flawed in design (see here), then many voters will lose the tendency to vote for Leave only out of respect for the Brexit referendum result, and then vote for their own opinion.

The main point is: We see the weird brew of populism and DR.

  • In 2015, UKIP with 12.5% of the vote got only 1 seat, and the unrest in the Conservative party caused David Cameron to call the referendum: which is populism, since a democratic response would have been to call for PR.
  • Now in 2017 a disproportionality in Northern Ireland seems to facilitate the Hard Brexit that Theresa May now seems to want.

Annette Bongardt and Francisco Torres (ABFT) argued about the UK Parliament: “Parliament has a strong and clear mandate for Brexit, Remainers and EU politicians shouldn’t question it“. Their reasoning can be rejected on key steps.

(1) Parliament already has a mandate

Parliament has a mandate, potentially provided by the Magna Carta of 800 years ago, though historians and legal experts will discuss aspects.

  • There is no reason to argue that this mandate would vary with a particular issue.
  • When someone questions Brexit then this doesn’t put Parliament’s mandate into doubt.
(2) Don’t confuse a general vote and a single issue

It might be possible for political scientists to look at a particular issue and argue that the mood in Parliament concurs with the public mood. This would require a poll targeted on that issue, both for Parliament and the public, so that we can do a statistical test on the difference of the averages. ABFT provide no such a poll. They refer to the general election, but the election concerned more issues. It is too simple to argue that the positions of the parties and candidates were clear on Brexit and that the popular votes concurred with such views.

(3) The Brexit referendum result doesn’t provide evidence

ABFT refer to the Brexit referendum of 2016 as one way how the electorate has expressed its view. However, scientists should clarify that the Brexit referendum question was flawed in its design. I explained this in an earlier LSE Brexit blog text of May 17, see here. My text relies upon a sound theoretical foundation. Representative democracy should not be confused with populist referenda, since voters in the ballot box cannot bargain.

There is no need to repeat my text here. The discussion on the weblog however was helpful in highlighting the distinction between the legal situation and the moral issue. Whether one legally invokes article 50 is a binary Yes / No issue. The Brexit referendum question was not about this legality but about policy preferences.

The referendum question wasn’t:

  • “Britain has to invoke article 50 in 2017 whatever happens”
  • versus “It is not so that Britain must invoke article 50 in 2017 whatever happens”.

For policy, there are various options, and electors have (conditional) expectations. With this ambiguity, the referendum question generated a situation of “Garbage in, garbage out“. We really don’t know what the electorate wants.

For example, some Scots who voted for both independence and Remain might now decide to stay in the UK with Brexit, which means both dependence and Leave and thus is quite opposite to their original views. Apparently they fear many years in the wilderness when out of both EU and UK. Clearly these voters have had conditional expectations and they have not been invoking legal rules. The Brexit referendum question clearly doesn’t provide the clarity that many attach to it.

(4) The role of scientists

Article 50 has been invoked and Brexit will happen, potentially abruptly on March 29 2019 when there is no agreement. One might argue that it is silly to continue to mention the problem of the Brexit referendum question.

However, my impression is that the 27 EU members may well be sensitive to the scientific observation that the Brexit referendum question was flawed in design. An international agreement on this observation, potentially also at the ECJ, might create an option for the UK to propose to annul the invoking of article 50.

If the UK should wish to annul Brexit before March 29 2019 then this can only be done with agreement of the 27 EU members. These members will not be swayed easily when the UK would use economic and financial arguments to explain its regret. But the issue of the referendum question is clear and impartial. The diagnosis may well be that the UK has fallen victim to a populist mood, and up to now lacks insufficient checks and balances to correct this. It fits the role of scientists to clarify this, which in itself is a check and balance.

ABFT propose that scientists defend the Brexit referendum question as sound, or at least want them to be silent, given that article 50 has been invoked and Parliament apparently has no intention of trying to annul it. I would hope that they are open to the idea that scientific criticism still would be possible.

They present events as a rational story from referendum to Parliamentarian mandate, while the events might well be diagnosed as an accidental course of history, in which the UK happened to take a one-way street because a street sign was flawed.

A YouGov poll also showed that people show loyalty to a seeming majority:

“There is a third group who change the dynamics of EU-related arguments – the “Re-Leavers.” These are people who voted to Remain in the EU and many still think that leaving was the wrong decision, but crucially now believe the government has a duty to carry out the will of the British people.”

“When taking this into account, we can split the country into three groups instead of two: The Hard Leavers who want out of the EU (45%); the Hard Remainers who still want to try to stop Brexit (22%); and the Re-Leavers (23%). The other 9% don’t know.” (YouGov May 12 2017)

Also the UK audience would be served with a better understanding that the Brexit referendum question was flawed.

(5) Democracy versus populism

My comments w.r.t. Brexit are scientifically warranted, yet ABFT in their final paragraph suggest that this criticism is “subverting the popular mandate”, “undermining the position of the EU chief negotiator” and “a subversion of the democratic process that led to the country’s decision to exit the EU”. Referring to the Brexit referendum result they ask: “Were there no lessons learnt from the rise of populism?”

ABFT are confused on the distinction between representative democracy (Parliament) and populism (referenda, neverendum). David Cameron’s decision to have a referendum was populism itself, while a democrat would have adopted proportional representation (PR), see below. See this interview by Protesilaos Stavrou on the distinction. Potentially one might use a referendum to ratify a constitutional change, but then one would tend to require that at least 1 / 2 of the population would decide, say a 3 / 4 majority of a turnout of 2 / 3. In Holland, a constitutional change, adopted (in proposal) by one parliament, requires ratification by another parliament after new elections. The Brexit referendum did not meet such standards (a turnout of 72% and a majority of 52%), apart from the design flaw on the question. It is a bit too simple to hold that there are now two UK Parliaments who are on a course towards Brexit, since article 50 was invoked by only one Parliament (referring to that flawed referendum).

ABFT are also confused on subversion. When there are serious points on content then those have to be dealt with, and it doesn’t help to neglect or denounce valid criticism.

(6) Proportional Representation (PR) versus District Representation (DR)

At first it seems as if proportional representation (PR), differing from current district representation (DR), doesn’t matter, and would be another topic than Brexit. It is a dead topic too, as John Cleese already showed in 1987, here. The ABFT article however clarifies that they entertain some assumptions that better be discussed too.

  1. The use of DR rather than PR is part of the lack of checks and balances that explain the populist drift in the UK. While DR strengthens existing powers, PR allows easy entry of challengers, which is the competition that economists like to see. Brexit would quite likely never have happened if the UK had had PR. In 2015 UKIP got 12.5% of the votes and only 1 seat. With a similar share of seats, UKIP would have become just one of the parties instead of the nightmare of the mainstream parties. In Holland Geert Wilders with a similar percentage has a marginal existence. If needed, mainstream politicians can agree on a Grand Coalition, like in Germany.
  2. ABFT suggest that support for Conservatives or Labour might mean support for either Hard or Soft Brexit but then they neglect the logic of DR, that voters must vote strategically.
  3. It is better to discuss annulment of Brexit within an environment with PR than one with DR. Britain might have a year to redesign its electoral system and have proper elections.

PR is the key design criterion for democracy, and districts are mainly a historical hangup. Consider n voters and s = 650 seats, so that the quota is q = n / s. This allows s / 2 = 325 districs of size 2q, since s / 2 * 2q = n again. With 45 million voters there might be an average distict size of about 140,000, correcting for turnout. Let a district candidate be elected when he or she has more than the quota q. Normally this amounts to q / (2q) = 50% of the district. One might allow a lower turnout in districts, and let a candidate be elected with at least 50% of the local vote. The unfilled seats can be filled by the nationwide PR criterion. Thus, a fundamental choice for PR still allows a feature of districts if so desired.

In France, the UK, USA and India DR is the key design feature whatever happens to PR. They haven’t overcome the historical hangup yet.

The distance of DR to PR can be expressed in the PR Gini coefficient, see the excel sheet and graphs. David Cameron in 2015 had a coefficient of 29.7%. In 2017 Theresa May has a PR Gini coefficient of 15.6% while Holland has 3.6%. The UK thus is strikingly disproportional.

The major non-PR impact in Holland is from the 2% wasted votes for small parties that get zero seats. In 2017 the UK had 3.5% wasted votes for parties that got no seats. One might argue that the wasted votes should be omitted from the Gini, yet, they rather stand out as a sore spot in current representation. A proportional representation of the wasted vote w in total n is possible by leaving seats empty or by filling the seats and taking a qualified majority f = 1/2 / (1 – w / n). In 2017 f = 50% / 96.5% = 51.8%. A representative majority in a full House of 650 seats then requires 337 seats, and not 326. See here.

There is a curious miscomprehension in the UK about what democracy actually is.

(a) This miscomprehension also exists in the Electoral Reform Society (ERS). There is a ranked system called “Single Transferable Vote” (STV) that has some PR properties when applied to the whole country. ERS however applies it to districts, and DR destroys nationwide PR again. Incongruously, the ERS keeps saying that their STV would be PR while it isn’t. See my criticism and counterexample here. The continued support of ERS for districts is part of the confusion that blocks the change to PR. (And with 4 candidates per district, their districts might need to have some 500,000 voters, curiously undermining the reason of “closeness” to have a district.)

(b) The 2011 referendum on PR was actually a referendum on the method of “Alternative Vote” (AV), which is a suboptimal suggestion too.

(c) It is apparently a misconception and dogma amongst UK voting theorists too that the (more complex) methods of ranked voting like STV or AV must be used at the level of voters. There is no need for this. It would suffice if the UK would adopt the Dutch system of Open Party Lists. The (more complex) methods of ranked voting can be applied by the professionals in Parliament, if needed, and those methods would still be proportional if the party weights were proportional.

(d) There is now an initiative “Make Votes Matter” (MVM) that strictly targets PR but that suffers from such conceptual problems too.

  • ERS signed their declaration though ERS, as said, also proposes a system of STV with districts that is not PR.
  • MVM might generate a discussion on ranked systems while such complexity might block PR again. It is better to clearly state a preference for “PR in Open Party Lists”, for otherwise we might end up with another situation that it is unclear what people signed up or voted for.
(6) Conclusion

Parliament’s mandate comes rather from Magna Carta, not Brexit, and scientists have every reason to question both Brexit and the lack of proportional representation (PR).

Addendum

I now notice the contribution by Jonathan Portes on the LSE Brexit blog about the influence of the Condorcet paradox (June 15 2016, that appeared on the NIESR blog on June 6 2016). I referred to voting theory too, though after the referendum of June 23, in this comment of June 29 2016, that was later summarized on the LSE Brexit blog in May 2017.

  • Portes suggests that there is a Condorcet paradox, while my argument only mentions that there might be one, and that we basically don’t know, even after the Brexit referendum “outcome”. The argument by Portes is less strong since he provides a speculation, and others might argue that it is only a speculation.
  • My main reason to refer to the Condorcet paradox was to explain that many voting theorists themselves do not properly understand voting theory. See the argument about the distinction between voting and deciding. Indeed, Portes repeats the confusion: “We may not be inconsistent individually but we can be so collectively.” Potentially a collective might be inconsistent, of course, as an individual might be. Yet, the point concerns the distinction between intransitive vote counts and the transitive decisions (e.g. indifference) based upon such vote counts.

For the Brexit referendum question, the problem might likely be a bit different. With R for Remain, S for Soft (EEA) and H for Hard (WTO), there are 6 possible strict preferences, from R > S > H (Theresa May before the referendum) to H > S > R (Theresa May after the referendum). If S and H are collected in L then there arises the claimed binary choice between R and L. Voters who are in the categories S > R > H or H > R > would face a hard question, and might decide not to turn out, or develop assumptions about what the actually might mean given what what they think about future developments. Similarly for the versions of R. 

Overall, the argument suffices that Proportional Representation is the proper method for modern democracy, and that referenda are an instrument of populism, notably within systems with District Representation. See the next weblog entry.

If you don’t have proportional representation (PR) then some voters get representatives they did not vote for. Thus it isn’t very democratic not to have PR.

The last weblog criticised the UK Electoral Reform Society (ERS) for erroneously claiming that Single Transferable Vote (STV) was PR.

ERS namely adopts districts, which causes STV to lose the limited PR properties that it has.

A persons affiliated with ERS answered to this criticism:

“We are well aware of the tension between the desire for (overall) proportionality and the desire for guaranteed local representation.  This tension is apparent among British electors when opinion polls have asked relevant questions about the outcomes of voting systems.  British electors want both overall proportionality (of parties) AND the local representation provided by exclusively single-member districts.  That is just not possible, so we aim for a compromise between local representation and overall proportionality through appropriately-sized multi-member districts. (…).” (Personal communication)

This is an unsatisfactory answer since there simply is no such “compromise”. When one must choose between a square and a circle then the answer is not some other graphic with some measure of deviation. If there is no PR then there is no PR, and then ERS should not claim that they have PR. To express their “compromise”, ERS speaks about “STV-PR” but this is like speaking about square-circles, and comes with the grating sound from nails across a blackboard.

If n is the number of voters, s the number of seats, then q = n / s is the threshold or quota, of voters per member. A candidate can be elected when he or she meets the quota. When the district size is 2q, then the district representative must get 50%+1 of the vote to attain the quota. At best s / 2 seats can be filled in this manner, since s / 2 * 2q = n again. All unfilled seats can be allocated using overall PR. This shows that districts are not a key design feature, while PR is. (These formulas can be adjusted for turnout, when district size is defined in terms of the electorate and not actual voters. See here.)

By focusing on districts, ERS loses track of the key design feature, and it lets its logic be occluded by a less relevant issue.

Wikipedia follows ERS

Apparently the editors at wikipedia follow ERS rather uncritically. The wikipedia statement in red is what ERS claims falsely and what is adopted by wikipedia too. The statement in green is true. Since the statement in green is true, the statement in red can only be true by chance.

Proportional representation (PR) characterizes electoral systems by which divisions in an electorate are reflected proportionately in the elected body. If n% of the electorate support a particular political party, then roughly n% of seats will be won by that party. The essence of such systems is that all votes contribute to the result: not just a plurality, or a bare majority, of them. Proportional representation requires the use of multiple-member voting districts (also called super-districts); it is not possible using single-member districts alone.[1][2][3] In fact, the most proportional representation is achieved when just one super-district is used.

The two most widely used families of PR electoral systems are party list PR and single transferable vote (STV).[4][5] Mixed member proportional representation (MMP), also known as the Additional Member System, is a hybrid Mixed Electoral System that uses party list PR as its proportional component. MMP has the potential to be proportional or semi-proportional depending on a number of factors such as the ratio of first past the post (FPTP) seats to PR seats, the existence or nonexistence of compensatory seats to make up for overhang seats, and election thresholds.[6][7][8][9]   (Source: Wikipedia on PR)

ERS thus is confusing the world including wikipedia. My advice for the editors of wikipedia (and the ERS) is:

  • Maintain conceptual integrity.
  • Restrict PR to the notion that p% of the votes translates into p% of the seats.
  • For PR the first preferences are relevant and not what is done with the subsequent preferences. Thus do not label STV as a PR-system but as “potentially PR”, or as STV-PPR.
  • For PR it suffices when the electorate selects parties. A single candidate is a party with a single candidate.
  • The professionals in parliament can use more complex systems like STV. The use of STV (there) must be compared to other systems, like Borda Fixed Point.
  • Get rid of the hangup on district representation.

Unfortunately, the person affiliated with ERS writes to me, with an unrelenting hangup about districts, and neglecting that PR should hold nation-wide:

“Neither the ERS nor I would be prepared to label STV-PT as “potentially PR” or anything similar.  I have seen some academics describe STV-PR as “a semi-proportional” system.  That is just nonsense.  For the same district magnitude, STV-PR and party-list PR both deliver the same degree of proportionality.  The fact that some electorates are prepared to accept electoral districts that cover the whole country for party-PR but don’t like the idea of “large” electoral districts for STV-PR is completely irrelevant.  It is the district magnitude that is the determining factor, not the voting system.”  (Personal communication)

Scotland is an example

Scotland has four electoral systems, and I copy from Wikipedia:

Does this mean that Scotland comprehends democracy or that they don’t ?

The Party List System as used for the EU Parliament generates proportional representation (PR), and this would be the criterion for representative democracy.

(Obviously, for the election of a local council, the norm for PR are the local votes, and not nationwide PR. Once the issue here is reduced to apportionment, then STV is one of the options and a choice depends upon one’s criteria.)

Let us look at the Scottish implementation Additional Member System (AMS) a.k.a. Supplementary Member System a.k.a. Mixed Member System (MMS). I would prefer the latter term, since there is nothing “additional” about an elected MP. Sometimes the term “Mixed Member Proportional” (MMP) is used but this is only warranted when there really is overall PR.

The current Scottish system

Scotland has 73 constituencies, in which the candidate is selected by FPTP. There are 8 regions with 7 seats per region, to a total of 56 regional seats. These “additional seats” are used to make the outcome more proportional. Brief explanations of the current Scottish system are by the Parliament itself and The Scotsman. The Scottish Parliament elections of May 5 2016 have these full data. The turnout was 55.6%.

Scotland like the UK has a hangup on the distinction between the local candidate and the party. It is claimed: “In the second vote the voter votes for a party rather than a candidate.” Indeed, when the first vote has a FPTP selection, then voters may be forced to vote strategically for a candidate of reduced preference, in trying to prevent that a worst candidate is selected. Thus the explanation about local representation may be a misrepresentation about what might really motivate voters.

When we compare the votes for the constituencies (districts) and the regions, then we don’t see much of a difference, except for the Greens and Others. (This are totals though, and there might be differences over districts.)

District

Region

Party

Votes

Votes

Con

501,844

524,222

Green

13,172

150,426

Lab

514,261

435,919

LD

178,238

119,284

SNP

1,059,898

953,587

Others

11,741

102,314

Total

2,279,154

2,285,752

We take the summed region vote as determining what the proportions for the parties should be. The additional 56 seats and their restriction to regions are not enough for correction of the error in the local vote. The SNP got 7% more seats than warranted under PR.

District

Region

 All
Party

Seats

Seats

Seats

%Seats

%Votes

%S-%V

Con

7

24

31

24.0

22.9

1.1

Green

0

6

6

4.7

6.6

-1.9

Lab

3

21

24

18.6

19.1

-0.5

LD

4

1

5

3.9

5.2

-1.3

SNP

59

4

63

48.8

41.7

7.1

Others

0

0

0

0.0

4.5

-4.5

Total

73

56

129

100.0

100.0

An alternative for Scotland

Let us consider a rough alternative for Scotland:

  • A local winner must get at least 50% of the vote of a district (constituency).
  • All 129 seats are allocated in proportion to the summed region vote.

The data file allows us to determine which candidates are elected now. This generates a quite different result. In the local vote, only 29 candidates manage to get at least 50% of their district (constituency). 95 candidates are selected via the Party List, which puts the ERS argument for locality into perspective. In this rough alternative, there are 5 seats that cannot be allocated due to rounding errors. But having 4% empty seats is not unfair given that 4.5% of the votes are wasted on the small parties.

District

Region

 All
Party

Seats

Seats

Seats

%Seats

%Votes

%S-%V

Con

1

29

30

23.3

22.9

0.3

Green

0

8

8

6.2

6.6

-0.4

Lab

0

25

25

19.4

19.1

0.3

LD

2

5

7

5.4

5.2

0.2

SNP

26

28

54

41.9

41.7

0.1

Others  0  0  0

0.0

4.5

-4.5

Total

29

95

124

96.1

100.0

A general observation

The quota is q = 2,285,752 / 129 = 17720. Above criterion of 50% of the local vote might be too lax. With 73 districts, the number or electors per district might be too small. If the number of districts is 129 / 2 ≈ 65, then the average district has size 2q, and the criterion of at least 50% of the votes would fit the overall condition of winning a seat via satisfying q.

A google showed this page by Andrew Ducker who also wondered about PR in Scotland. He mentions: (1) The region votes must be summed for nationwide PR indeed. (2) A 50%:50% distinction between local and national seats would be helpful indeed. In reply to this: why still allow FPTP when it may cause that a minority winner would become the “representative” ? It is better to require at least q and/or at least 50% of the district.

The UK Electoral Reform Society (ERS)

The UK ERS falsely claims that STV applied to districts would be PR while it is not. The ERS also criticises the Scottish system, but perhaps for the wrong reasons.

In 2011, the current Scottish system was already in place, and the ERS advised a change. See the Guardian or the BCC:

One of the authors of the report, Prof John Curtice of Strathclyde University, said: “The widespread expectation that the Scottish Parliament would be a multi-party parliament, in which no party would ever have an overall majority, has been dashed. “In truth, although the electoral system bequeathed to the Scottish Parliament by Labour was far more proportional than first-past-the-post, it was never one that was best fitted to the realisation of that original expectation. “It still favours larger parties over smaller ones, who, indeed, are actually being discouraged from standing in the constituency contests.” (BBC 2011-11-15)

A similar critique is given w.r.t. the 2016 outcome. Some changes like an “open party” list (i.e. the ability to vote for individual party candidates on the list) and the allocation of Sainte-Laguë may indeed be mentioned.

But this is small beer compared to the major critique on the Scottish system, that it still allows for the hangup on district representation.

While the ERS should warn voters and legislators about this hangup, the ERS suffers from this hangup itself too, and propounds STV for districts, which destroys PR.

The person affiliated with ERS writes to me:

I am not in favour of electing MPs (or other representatives) in two different ways. In Scotland we have experience of the Scottish Parliament where MSPs are elected by the Additional Member System (AMS = a regionalised version of MMP). Some of the worst problems of electing MSPs in two different ways (Constituency and Region) have abated over the years, but the tension remains and surfaces from time to time. It would have been much better if all the MSPs had been elected by STV-PR, but AMS was a political compromise as one the major parties (Labour) would just not accept STV-PR at any price. (Personal communication)

Again, this person at ERS suggests that STV would be PR, even calling it STV-PR, while the very application of STV to districts destroys the PR.

Missing Scottish voters

ERS Scotland director Willie Sullivan wrote a book about the structurally low turnout for Scottish elections: “The Missing Scotland: Why over a million Scots choose not to vote and what it means for our democracy” (publisher).

In an article, Sullivan summarises:

“If the working people wanted democracy, why do so many now not vote? Surely these are the people that should be most eager to flex their democratic muscle? In research for my book, Missing Scotland, I tried to find out why more than a million Scots choose not to vote. What I found is worrying. Most important of all, people don’t think voting will make anything better. They have tried voting, and they have tried not voting, and there is no difference. They think politicians are all the same, don’t understand their lives and they make promises they never keep. This is not a question of not caring. The people I spoke to care a lot about their families and communities. They are worried about losing their homes or their jobs. They even like the idea of democracy, they just don’t think we have it. Not voting is often a deliberate act.”

I haven’t read this book, but only find it relevant enough to mention its existence. My guess is that Sullivan hasn’t mentioned two elements:

  1. When the Scottish electoral system was changed, they didn’t adopt the PR system like in Holland, but kept their hangup on districts, and ERS itself was an agent in this. Potentially Sullivan might feel ashamed that he doesn’t quite comprehend what democracy is.
  2. Scotland isn’t aware of the failure of the Trias Politica model and the need for an Economic Supreme Court.

Conclusion

My finding is that major political distortions in the UK, France, USA and India arise because of lack of PR.  A lobby for STV for districts doesn’t resolve this, and it is falsely claimed to be PR. Thus I would tend to advice electoral reform in this order of priority:

  • first PR, like the system in Holland or the EU Parliament (Open Party List)
  • if this is up and running, secondly allow for an element of locality for half of the seats (s / 2, district size 2q, and the district representative is elected with at least 50% of the district vote, potentially corrected for turnout)
  • if this is up and running, improve the system by allowing voters freedom on how they vote
  • compare STV and Borda Fixed Point and other methods for the selection of the local representative.

The UK Electoral Reform Society hinders clarity on electoral reform since they show a hangup on districts. They better focus on establishing Proportional Representation (PR), while regarding the issue of districts as of secondary importance.

Given overall PR, one might even let voters determine on the ballot how to deal with the district representation, for the s / 2 seats available for district representation.

  1. Some voters might vote for a party, and be done with that. Seats are allocated to the party in proportion to the total number of votes. (Closed Party List) Some voters might wish to select a party but also a particular person in that party, so that the party order takes over if the person would not be elected. (Open Party List) These approaches can be combined (as in Holland) when the Closed List voters vote for the party leader.
  2. Some voters might indicate where their vote would go, if their party of choice isn’t elected. (Remember that a single candidate is a party with a single candidate.)
  3. Other voters might wish to vote for particular candidates across parties, and then might want to indicate how votes would have to be transferred if the candidate doesn’t get elected. (Otherwise it is apportioned automatically.) There is still the comparison between STV and e.g. (repeated) application of the Borda Fixed Point method. STV runs the risk of eliminating a compromis candidate, who receives few votes in the initial stage, but who can collect support because of secondary preferences. This might not be relevant for the party proportion but be quite relevant for voters and the candidates themselves. This would not be an issue of PR but of Quality Representation (QR).

PS. Dan Hodges (Telegraph June 1 2015) has a very entertaining article “No, Britain does not want proportional representation“. The weak spot in his argument is that the 2011 referendum on AV was misrepresented as a referendum on PR while it actually was a referendum on AV. The strong point is that ERS cannot be convincing if its arguments are confused. There still is a case for sound arguments and good education.

PPS. The subtle relation between proportional representation (PR) and district representation (DR) shows also in the existence of a Senate or House of Lords, in which districts / States might be represented by 2 senators per State like in the USA. For a Senate the DR might be acceptable since the Senate has the role of guardian for the nation itself. The House would be sensitive to the preferences of the electorate, and in that case PR would be logical.