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This weblog entry copies the earlier entry that used an estimate.
Now we use the actual YouGov data, below.
Again we can thank YouGov and Anthony Wells for making these data available.
The conclusions do not change, since the estimate apparently was fairly good.
It concerns a very relevant poll, and it is useful to have the uncertainty of the estimate removed.

The earlier discussion on Proportional Representation versus District Representation has resulted in these two papers:

Brexit stands out as a disaster of the UK First Past The Post (FPTP) system and the illusion that one can use referenda to repair disproportionalities caused by FPTP. This information about the real cause of Brexit is missing in the otherwise high quality overview at the BBC.

The former weblog text gave an overview of the YouGov polling data of June 12-13 2017 on the Great Britain (UK minus Northern Ireland) preference orderings on Brexit. The uncertainty of the estimate is removed now, and we are left with the uncertainty because of having polling data. The next step is to use these orderings for the various voting philosophies. I will be using the website of Rob LeGrand since this makes for easy communication. See his description of the voting philosophies. Robert Loring has a website that referred to LeGrand, and Loring is critical about FPTP too. However, I will use the general framework of my book “Voting theory for democracy” (VTFD), because there are some general principles that many people tend to overlook.

Input format

See the former entry for the problem and the excel sheet with the polling data of the preferences and their weights. LeGrand’s website requires us to present the data in a particular format. It seems best to transform the percentages into per-millions, since that website seems to require integers and we want some accuracy even though polling data come with uncertainty. There are no preferences with zero weights. Thus we get 24 nonzero weighted options. We enter those and then click on the various schemes. See the YouGov factsheet for the definition of the Brexit options, but for short we have R = Remain, S = Soft / Single Market, T = Tariffs / Hard, N = No Deal / WTO. Observe that the Remain options are missing, though these are important too.

248485:R>S>T>N
38182:R>S>N>T
24242:R>T>S>N
19394:R>T>N>S
12727:R>N>S>T
10909:R>N>T>S
50303:S>R>T>N
9091:S>R>N>T
22424:S>T>R>N
66667:S>T>N>R
9091:S>N>R>T
36364:S>N>T>R
6667:T>R>S>N
3636:T>R>N>S
12121:T>S>R>N
46667:T>S>N>R
15758:T>N>R>S
135152:T>N>S>R
9697:N>R>S>T
9091:N>R>T>S
8485:N>S>R>T
37576:N>S>T>R
16970:N>T>R>S
150303:N>T>S>R

Philosophy 1. Pareto optimality

The basic situation in voting has a Status Quo. The issue on the table is that we consider alternatives to the Status Quo. Only those options are relevant that are Pareto Improving, i.e. that some advance while none lose. Commonly there are more Pareto options, whence there is a deadlock that Pareto itself cannot resolve, and then majority voting might be used to break the deadlock. Many people tend to forget that majority voting is mainly a deadlock breaking rule. For it would not be acceptable when a majority would plunder a minority. The Pareto condition thus gives the minority veto rights against being plundered.

(When voting for a new Parliament then it is generally considered no option to leave the seats empty, whence there would be no status quo. A situation without a status quo tends to be rather exceptional.)

In this case the status quo is that the UK is a member of the EU. The voters for R block a change. The options S, T and N do not compensate the R. Thus the outcome remains R.

This is the fundamental result. The philosophies in the following neglect the status quo and thus should not really be considered.

PM 1. Potentially though, the S, T and N options must be read such that the R will be compensated for their loss.

PM 2. Potentially though, Leavers might reason that the status quo concerns national sovereignty, that the EU breaches upon. The BBC documentary “Europe: ‘Them’ or ‘Us’” remarkably explains that it was Margaret Thatcher who helped abolish the UK veto rights and who accepted EU majority rule, and who ran this through UK Parliament without proper discussion. There seems to be good reason to return to unanimity rule in the EU, yet it is not necessarily a proper method to neglect the rights of R. (And it was Thatcher who encouraged the neoliberal economic policies that many UK voters complain about as if these would come from the EU.)

Philosophy 2. Plurality

On LeGrand’s site we get Plurality as the first step in the Hare method. gets 35% while the other options are divided with each less than 35%. Thus the outcome is R.

(The Brexit referendum question in 2016 was flawed in design e.g. since it hid the underlying disagreements, and collected all dissent into a single Leave, also sandwiching R between various options for Leave.)

Philosophy 3. Hare, or Instant Run-off, a form of Single Transferable Vote (STV)

When we continue with Hare, then R remains strong and it collects votes when S and N drop off (as it is curiously sandwiched between options for Leave). Eventually R gets 45.0% and T gets 55.0%. Observe that this poll was on June 12-13 2017, and that some 25% of the voters “respect” the 2016 referendum outcome that however was flawed in design. I haven’t found information about preference orderings at the time of the referendum.

Philosophy 4. Borda

Borda generates the collective ranking S > T > R > N. This is Case 9 in the original list, and fortunately this is single-peaked.

Philosophy 5. Condorcet (Copeland)

Using Copeland, we find that S is also the Condorcet winner, i.e. wins from each other option in pairwise contests. This means that S is also the Borda Fixed Point winner.

Conclusions

The major point of this discussion is that the status quo consists of the UK membership of the EU. Part of the status quo is that the UK may leave by invoking article 50. However, the internal process that caused the invoking of article 50 leaves much to be desired. Potentially many voters got the suggestion as if they might vote about membership afresh without the need to compensate those who benefit from Remain.

Jonathan Portes suggested in 2016 that the Brexit referendum question was flawed in design because there might be a hidden Condorcet cycle. The YouGov poll didn’t contain questions that allows to check this, also because much has happened in 2016-2017, including the misplaced “respect” by 25% of the voters for the outcome of a flawed referendum. A key point is that options for Remain are not included, even though they would be relevant. My impression is that the break-up of the UK would be a serious issue, even though, curiously, many Scots apparently rather prefer the certainty of the closeness to a larger economy of the UK rather than the uncertainties of continued membership of the EU when the UK is Leaving.

It would make sense for the EU to encourage a reconsideration within the UK about what people really want. The Large Hadron Collider is expensive, but comparatively it might be less expensive when the UK switches to PR, splits up its confused parties (see this discussion by Anthony Wells), and has a new vote for the House of Commons. The UK already has experience with PR namely for the EU Parliament, and it should not be too complex to use this approach also for the nation.

Such a change might make it also more acceptable for other EU member states if the UK would Breget. Nigel Farage much benefited from Proportional Representation (PR) in the EU Parliament, and it would be welcome if he would lobby for PR in the UK too.

Nevertheless, given the observable tendency in the UK to prefer a soft Brexit, the EU would likely be advised to agree with such an outcome, or face a future with a UK that rightly or wrongly feels quite maltreated. As confused as the British have been on Brexit, they might also be sensitive to a “stab-in-the-back myth”.

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In a July weblog entry, I reported on a rather important YouGov poll. YouGov.com and Anthony Wells were so kind to provide the underlying poll data. Earlier I estimated some rankings, but thanks to this kindness we now have certainty about the poll data, so that only the uncertainty remains due to polling itself. It also appeared that what I had categorized as a hard (H) Brexit better be rephrased as the No Deal (N) case. I will maintain the label on the Tariff (T) option, that some would call hard.

The UK general election was on June 8 and the poll was taken on June 12-13 so that the persons polled will have had vivid recollections. For this reason, these polling data can be considered quite important.

The poll generated data about confusions in the British electorate. It is useful to belabour the point, for Brexit is a key event and would have quite some impact for the coming decades. I would respect the UK decision to leave the EU but have my doubts when it is not based upon Proportional Representation (PR). A referendum gives proportions but referenda tend to be silly and dangerous, as they are an instrument of populism rather than of representative democracy. Indeed, it appears that the Brexit referendum question was flawed in design. The YouGov poll helps us to observe how confused a major section of the UK electorate is. Let us dig a bit deeper.

The following copies my weblog text of July 11, but now replacing the estimate by the real data.

Representation of preferences via a ranking matrix

Let voters consider the options R = Remain, S = European Economic Area (EEA) a.k.a. Single Market a.k.a Soft, T = Tariffs a.k.a. Hard, N = No Deal, World Trade Organisation (WTO). A consistent Remainer would tend to have the ranking R > S > T > N, and a consistent Leaver would tend to have this in reverse.

The YouGov poll presents the data in a ranking matrix, with the first preferences in the first row, then the second preferences, and so on. For the Brexit referendum outcome of 48% Remain and 52% Leave, for example, we might have the following setup. It is a guess, since the particular ways of Leaving were not included in the referendum question (and neither for Remaining). This example however is the result that you would expect if Remainers and Leavers would have the mentioned consistent orderings.

Observe that each voting weight (take e.g. 48) for a preference order list is put in precisely one place per row and per column, i.e. that it doesn’t occur more times in a single row or column. This explains why the border sums add up to 100.

The YouGov poll of June 12-13 2017

The YouGov data, that I have been referring to, contain the results of a poll of 1651 adults in Great Britain, i.e. the UK excluding Northern Ireland. From page 13-16 we can collect these data for the whole of Great Britain for 2017. YouGov states that the sample has been weighted for social-economic and political indicators. It is not clear to me how the “Don’t know”s are being handled for this particular issue. See also this discussion by Anthony Wells.

We can observe:

  • These are percentages, and both the row sums and the column sums should be 100, except for rounding errors.
  • 35% has Remain in the first position, 47% has it in the last position, so that 9 + 8 ≈ 17% (a 1% missing due to rounding) has a confused position, in which Remain is sandwiched between some options for Leaving. We would wonder how such people would vote in a referendum when they are presented with only two options R or L. One cannot say that the referendum was only about the first positions in the rankings, for voters would tend to develop an expectation about what would be the likely kind of Brexit and vote accordingly. Some of these 17% might have voted Remain because they disliked the otherwise expected version for Leave. This might indicate that the outcome for Remain was overstated. Yet we have no information on subdivisions of Remain, that might cause an opposite effect. Some might be okay with Remain as it is but vote for Leave because they fear that the UK otherwise might also join up on the Eurozone or some United States of Europe. The reason why the Brexit referendum question was flawed in design is that it left too much to guess here.
  • Remarkably, the split between R and L now in June 2017 would be 35% versus 65% instead of 48% versus 52% in 2016. In one single year Great Britain switched from fairly divided to a seemingly clear preference for Brexit (though divided upon how) ? I very much doubt this distribution, see this discussion on populism and DR. The electoral data still suggest more than 50% for Remain. In the July weblog entry it is discussed that some 26% of the electorate say that they voted for Remain but accept the loss at the referendum, so that they “play along” with the winning side, focusing on what would be the best option for Leave. This seems loyal to some notion of democracy, but it would also be a misplaced loyalty to the flawed Brexit referendum question. (One can respect such loyalty, but it still makes sense to discuss it.)

Using techniques of apportionment we estimated the number of people per cell in the poll. However, we now have the actual data (rounded to one digit from multi-digit percentages times 1651):

Possible permutations of rankings

With 4 options there are 4 possibilities for a first place, 3 remaining for the second place, 2 remaining for the third place, and then the final one follows. Thus there are 4 x 3 x 2 x 1 = 24 permutations for possible rankings. We already saw two of these: R > S > T > N and its reverse. Above ranking matrix is actually based upon these 24 possibilities.

Some of these 24 possibilities will be rather curious. It is not clear what to think about > N > S > for example (Case 5 below). This would be a Remainer who would rather prefer No Deal to the EEA or some agreement not to have a trade war on tariffs. A tentative explanation is that this voter has a somewhat binary position, as Remain versus No Deal At All, while the other options are neglected.

Policy options can also be sorted in logical order. This gives rise to the theory of Single Peakedness. For the topics of R, S, T and N there is a logical scale from left to right. An example of single-peakedness is Case 7 below, with a ranking S > R > T > N. See the graph below. The 1st rank gets utility level 4, the 2nd rank gets utility level 3, the 3rd rank gets utility level 2, and the 4th rank gets utility level 1. The utility levels are just the reversed of the ranks, but then the case must be reordered to the logical order.

Voting theory has a core that assumes that voters are both autonomous and rational, so that any preference would have some logic. The logical order R, S, T and N might seem arbitrary to some voters who may think otherwise. We do not impose that order but invite voters who think otherwise to explain why they choose a different order. Potentially each voter has his or her own criteria so that the best is on top, and all other options follow in proper order. Voters with multiple peaks in their preferences would have more to explain to us to understand them than voters with a single peak. Without a good explanation, we cannot reject the possibility that there is some confusion.

Presentation of preferences via preference orderings

The following are the YouGov data for the preferences orderings that underlie above YouGov results on percentages. See the excel sheet in the Appendix. This table shows only the percentages and not the numbers of people in the poll (that add up to above table), since the percentages are the main finding. Single dots are zero’s. The ConR / L and LabR / L subdivisions concern the voters in the poll who voted R or L in the 2016 Brexit referendum and who voted Con or Lab in 2017. They form only a part of the sample, so their sum doesn’t add up to the total on the left.

Discussion on GB

Some observations are:

  • The YouGov summary ranking matrix already showed a rather even split on S, T and N, but the data give a landscape with even more diversity in opinions.
  • Only 24.8% has the preference R > S > T > N and only 15.0% its reverse, so that 60.1% has some mixture.

Above results for GB can be split up in on the peaks and sandwich. The combinations give the following percentages:

  • The mentioned 60.1% split up again in 33.3% who are single peaked, and 26.8% who have multiple peaks.
  • The sandwich of 17.3% splits up into 8.5% with a single peak and 8.8% with multiple peaks.
  • Of the 26.8% with multiple peaks there are 10.5% who can join the Remainers with a first preference and there are 7.4% who can join the leavers with Remain in the last position (but various ways how to Leave).

The 8.8% would be a relevant section of the vote. They all voted Leave, but divided on S, T and N. Potentially the outcome of the 2016 Brexit referendum has been decided by the 8.8% GB voters who have Remain neither in the first or last position, and who do not follow the standard logical order on the options.

Discussion on ConR / L and LabR / L

The division of ConR / L and LabR / L is losing its relevance because it are dwingling groups, they are changing loyalties, and their 2016 votes are becoming history while there are new issues. Yet, the 2016 referendum question was flawed, and it is relevant to see how sizeable parts of the UK electorate deal with the logical conundrum that they took part in.

  • The 17.3% of the votes with Remain sandwiched can be found in the subdivisions in similar proportions.
  • 28.6% of ConR voters and 55.2% of LabR voters are united on the preference R > S > T > N. Presumably this was also the case in 2016, or there must be factors that increased or reduced consistency or confusion.
  • 30.8% of ConL and 22.4% of LabL are united on the preference N > T > S > R. Presumably this was also the case in 2016, or there must be factors that increased or reduced consistency or confusion.
  • One might expect that ConR / L and LabR / L voters of 2016 would have the benefit of a party preference and thus show more consistency, yet the distribution of views is quite as much, and the sandwich with multiple peaks is quite present.
  • The 2016 Conservative Remainers are loyal for 45.2% to the old point of view, but still vote for a Conservative party that is set on Leave. Part will be the misplaced loyalty for the flawed referendum. Alternatively, they voted for a minority in this party that still tries to bring balance ? (A good poll requires a focus group.) (And there is more in the world than just Brexit.)
  • The 2016 Labour Remainers are 76.1% loyal to the old point of view. Yet Labour leader Corbyn also prefers a Brexit. It might be the pecularities of the British system of District Representation (DR) that caused these voters not to switch to LibDem. (But the LibDem also have a liberal policy that many voters for Labour dislike. The system of DR doesn’t favour the entry of new political competitors.)
  • The 2016 Leavers have a high loyalty to the old view, ConL 88.2% and LabL 73.3%. Yet this doesn’t diminish the diversity of opinion about how to Leave.
Conclusions
  • The ranking matrix is a fine way to summarize results, yet the preference ordering are more accurate on the underlying and relevant orders. The ranking matrix is merely a matter of presentation by the statistical reporter. A person in a poll who can answer on a ranking matrix in fact gives the personal preference ordering. The statistician can compound these data while not losing information on the permutations. From the permutations it is always possible to create a ranking matrix, yet the reverse requires estimation techniques which generate needless uncertainty.
  • Asking for voter preference orderings in a poll is a useful exercise. It is not intended to propose this for general elections. For general elections it suffices that voters exercise a single vote for a party of choice. The condition however is Proportional Representation, otherwise there are serious distortions, see the earlier discussion on this weblog.
  • The information on the rankings and implied preference orderings suggest a rather large state of confusion in the electorate of Great Britain. The notion of single-peakedness appears to be quite useful in highlighting the issue of the preference order. Perhaps we cannot quite call this “confusion” since voters might have their own logic to order the four options. Until there is more clarity on what strikes one as illogical, the term “confusion” seems apt though.
  • It must be greatly appreciated that YouGov and Anthony Wells made these data available, since they provide a key insight in the state of opinion in Great Britain close to the general election of June 8 2017.
Appendix September 18 2017

The excel workbook with the full YouGov data and the earlier estimate is: 2017-09-18-YouGov-Rankings-full-data

The earlier discussion on Proportional Representation versus District Representation has resulted in this paper: Two conditions for the application of Lorenz curve and Gini coefficient to voting and allocated seats, MPRA 80297.

Brexit stands out as a disaster of the UK First Past The Post (FPTP) system and the illusion that one can use referenda to repair disproportionalities caused by FPTP. This information is missing in the otherwise high quality overview at the BBC.

In the earlier Puzzle on the YouGov poll I estimated Brexit preference orderings from a summary statistic published by YouGov. The next step is to use these orderings for the various voting philosophies. I will be using the website of Rob LeGrand since this makes for easy communication. See his description of the voting philosophies. Robert Loring has a website that referred to LeGrand, and Loring is critical about FPTP too. However, I will use the general framework of my book “Voting theory for democracy” (VTFD), because there are some general principles that many people tend to overlook.

Input format

See the Puzzle weblog text for the problem and the excel sheet with the estimate of the preferences and their weights. LeGrand’s website now requires us to present the data in a particular format. It seems best to transform the percentages into per-millions, since that website seems to require integers and we want some accuracy even though the estimate is tentative. We can also drop the preference rankings with zero weights. Thus we get 14 nonzero weighted options. We enter those and then click on the various schemes. See the YouGov factsheet for the definition of the Brexit options, but for short we have R = Remain, S = Soft / Single Market, T = Tariffs, H = Hard / WTO. Observe that the Remain options are missing, though these are important too.

261841:R>S>T>H
53499:R>S>H>T
38386:R>T>H>S
60161:S>R>T>H
30087:S>R>H>T
44443:S>T>R>H
34960:S>T>H>R
22354:S>H>T>R
24777:T>S>H>R
15640:T>H>R>S
181873:T>H>S>R
49951:H>S>T>R
20475:H>T>R>S
161553:H>T>S>R

Philosophy 1. Pareto optimality

The basic situation in voting has a Status Quo. The issue on the table is that we consider alternatives to the Status Quo. Only those options are relevant that are Pareto Improving, i.e. that some advance while none lose. Commonly there are more Pareto options, whence there is a deadlock that Pareto itself cannot resolve, and then majority voting might be used to break the deadlock. Many people tend to forget that majority voting is mainly a deadlock breaking rule. For it would not be acceptable when a majority would plunder a minority. The Pareto condition thus gives the minority veto rights against being plundered. (When voting for a new Parliament then it is generally considered no option to leave the seats empty, whence there would be no status quo. A situation without a status quo tends to be rather exceptional.)

In this case the status quo is that the UK is a member of the EU. The voters for R block a change. The options S, T and H do not compensate the R. Thus the outcome remains R.

This is the fundamental result. The philosophies in the following neglect the status quo and thus should not really be considered.

PM 1. Potentially though, the S, T and H options must be read such that the R will be compensated for their loss.

PM 2. Potentially though, Leavers might reason that the status quo concerns national sovereignty, that the EU breaches upon. The BBC documentary “Europe: ‘Them’ or ‘Us’” remarkably explains that it was Margaret Thatcher who helped abolish the UK veto rights and who accepted EU majority rule, and who ran this through UK Parliament without proper discussion. There seems to be good reason to return to unanimity rule in the EU, yet it is not necessarily a proper method to neglect the rights of R. (And it was Thatcher who encouraged the neoliberal economic policies that many UK voters complain about as if these would come from the EU.)

Philosophy 2. Plurality

On LeGrand’s site we get Plurality as the first step in the Hare method. gets 35% while the other options are divided with each less than 35%. Thus the outcome is R.

(The Brexit referendum question in 2016 was flawed in design e.g. since it hid the underlying disagreements, and collected all dissent into a single Leave, also sandwiching R between various options for Leave.)

Philosophy 3. Hare, or Instant Run-off, a form of Single Transferable Vote (STV)

When we continue with Hare, then R remains strong and it collects votes when S and H drop off (as it is curiously sandwiched between options for Leave). Eventually R gets 44.4% and T gets 55.6%. Observe that this poll was on June 12-13 2017, and that some 25% of the voters “respect” the 2016 referendum outcome that however was flawed in design. I haven’t found information about preference orderings at the time of the referendum.

Philosophy 4. Borda

Borda generates the collective ranking S > T > R > H. This is Case 9 in the original list (including zero weights), and fortunately this is single-peaked.

Philosophy 5. Condorcet (Copeland)

Using Copeland, we find that S is also the Condorcet winner, i.e. wins from each other option in pairwise contests. This means that S is also the Borda Fixed Point winner.

Conclusions

The major point of this discussion is that the status quo consists of the UK membership of the EU. Part of the status quo is that the UK may leave by invoking article 50. However, the internal process that caused the invoking of article 50 leaves much to be desired. Potentially many voters got the suggestion as if they might vote about membership afresh without the need to compensate those who benefit from Remain.

Jonathan Portes suggested in 2016 that the Brexit referendum question was flawed in design because there might be a hidden Condorcet cycle. The YouGov poll didn’t contain questions that allowed to check this, also because much has happened in 2016-2017, including the misplaced “respect” for the outcome of a flawed referendum. A key point is that options for Remain are not included, even though they would be relevant. My impression is that the break-up of the UK would be a serious issue, even though, curiously, many Scots apparently rather prefer the certainty of the closeness to a larger economy of the UK rather than the uncertainties of continued membership of the EU when the UK is Leaving.

It would make sense for the EU to encourage a reconsideration within the UK about what people really want. The Large Hadron Collider is expensive, but comparatively it might be less expensive when the UK switches to PR, splits up its confused parties, and has a new vote for the House of Commons. The UK already has experience with PR namely for the EU Parliament, and it should not be too complex to use this approach also for the nation. Such a change might make it also more acceptable for other EU member states if the UK would Breget. Nigel Farage much benefited from Proportional Representation (PR) in the EU Parliament, and it would be welcome if he would lobby for PR in the UK too.

Nevertheless, given the observable tendency in the UK to prefer a soft Brexit, the EU would likely be advised to agree with such an outcome, or face a future with a UK that rightly or wrongly feels quite maltreated. As confused as the British have been on Brexit, they might also be sensitive to a “stab-in-the-back myth”.

The French general elections for the Legislative were held on June 11 and 18 2017. The results provided by the French government are presented more accessible in wikipedia (a portal and no source), and have been used in this 2017-France-Lorenz-Gini excel sheet to determine the Lorenz curve and Gini coefficient.

The earlier discussion on Lorenz curve and Gini was about the Dutch and UK general elections.

Both UK and France have district representation (DR) with a First Past the Post rule. In the UK this causes strategic voting, in which a voter may not vote for the candidate of first choice, but tries to block a candidate who might win but would be worst. France has elections in two rounds so that there is less need for such a strategy. The second round is between the two top candidates in the district, and thus one might try to get at least one good candidate in that position.

Proportional representation (PR) may allow a larger (but fairer) share of the seats for the more extreme parties, like the party of Geert Wilders in Holland, yet PR also allows more stability for the center. Thus PR tends to avoid the swings between extremes that might happen in systems of district representation (DR).

Two rounds mean two sets of data

The French system seems to make it more difficult to determine the Lorenz curve and Gini coefficient. There are two rounds, and thus there is the question what data to take. However, the following choice suggests itself:

  • The data of the first round provide the first preferences, and thus provide the votes.
  • The data of both rounds provide the seats.

This choice finds support in the data. The first round has a turnout of 48.7% and 0.5 million invalid or blank votes. In the second round, more people remain at home, with a turnout of 42.6%, while those who vote produce almost 2 million invalid or blank votes, who apparently disprove of the available candidates or the system itself. Thus the higher turnout and lower blanks in the first round suggest that these indeed present the first preferences (with some limited level of strategy).

The Lorenz curve and Gini

The Lorenz curve shows a rather surprising level of inequality, with a Gini of 41.6%. Compare the value of Holland with a Gini of 3.6%. If the blue line would cover the pink diagonal then there would be full proportionality.

Data on turnout

The following table gives the data on turnout for the first round. The votes for “Elected in the House” is for parties that eventually got elected in the Legislative. The votes for “Not in the House” is for a radical leftist party that got votes in the first round but got no seat in none of the rounds.

The wasted vote consists of the invalid and blank votes and the latter “Not in the House”, to a total of almost 3%. A standard majority would be 289 seats of a House of 577 seats. If one would keep account of the wasted vote, then one might leave seats empty, or use a qualified majority of 298 seats, thus 9 more than usual.

When we divide the electorate by the number of votes per seat, then the Legislative would require 1222 rather than 577 seats. A majority would require 611 seats, which is more than the actual number of seats used. If one would want to keep account of the voters who did not turn out, then 51.3% or 296 of the 577 seats would be empty, or one would use the 611 seats as a qualified majority.

An example of the inequality

The new French President Emmanuel Macron had the highest score of 24% of the vote in the first round of the Presidential elections of 2017, with runner-up Marine Le Pen with 21.3%. Macron then won the second round with 66.1% (20.7 million) against Marine Le Pen with 33.9% (10.6 million) of the vote.

For the Legislative, Macron’s party REM got 27.6% while the Front National (FN) got 12.9% in the first round. For the Legislative Le Pen managed to get only 3 million votes, compared to the potential of 10.6 million at the presidential elections. With both rounds REM got 308 seats and FN got 8 seats.

These ratios would turn, if Le Pen would manage to motivate the voters of the presidential race to also support her for the Legislative. If the other parties would have a divided vote then Le Pen would benefit from First Past The Post.

Conclusions

For the UK in 2017 we calculated a Gini of 15.6% but this was a very tentative number since we had no estimate about the amount of strategic voting involved. For France we have an indication of the first preferences, namely from the first round.

France appears to have a surprisingly high Gini of 41.6%, which can be compared to the system of proportional representation (PR) in Holland that generates 3.6%.

This political inequality doesn’t bode well for the feelings amongst the French electorate about whether they are represented. The low turnout seems to reflect dissatisfaction rather than satisfaction. Such dissatisfaction might also translate into a protest vote over 4 years, especially when Macron doesn’t deliver.

Many observers in Europe seem to be happy with the election of Macron and his party REM, but the outcome is quite disproportional. If this disproportionality can happen for one party then it might also happen for another party – that one doesn’t like as much.

In the former weblog entry, I reported on a rather important YouGov poll. The UK general election was on June 8 and the poll was taken on June 12-13 so that we may assume that persons polled had still vivid recollections. The poll generated data about confusions in the British electorate. It is useful to belabour the point, for Brexit is a key event and would have quite some impact for the coming decennia. I would respect the UK decision to leave the EU but have my doubts when it is not based upon Proportional Representation (PR). A referendum gives proportions but referenda tend to be silly and dangerous, as they are an instrument of populism rather than of representative democracy. Indeed, it appears that the Brexit referendum question was flawed in design. The YouGov poll helps us to observe how confused a major section of the UK electorate is. Let us dig a bit deeper.

Representation of preferences via a ranking matrix

Let voters consider the options R = Remain, S = European Economic Area (EEA) a.k.a. Single Market a.k.a Soft, T = Tariffs, H = World Trade Organisation (WTO) a.k.a. Hard. A consistent Remainer would tend to have the ranking R > S > T > H, and a consistent Leaver would tend to have this in reverse.

The YouGov poll presents the data in a ranking matrix, with the first preferences in the first row, then the second preferences, and so on. For the Brexit referendum outcome of 48% Remain and 52% Leave, for example, we might have the following setup. It is a guess, since the particular ways of Leaving were not included in the referendum question. This example however is the result that you would expect if Remainers and Leavers would have the mentioned consistent orderings.

Observe that each voting weight (take e.g. 48) for a preference order list is put in precisely one place per row and per column, i.e. that it doesn’t occur more times in a single row or column. This explains why the border sums add up to 100.

The YouGov poll of June 12-13 2017

The YouGov data, that I have been referring to, contain the results of a poll of 1651 adults in Great Britain, i.e. the UK excluding Northern Ireland. From page 13-16 we can collect these data for the whole of Great Britain for 2017. YouGov states that the sample has been weighted for social-economic and political indicators. It is not clear to me how the “Don’t know”s are being handled for this particular issue. See also this discussion by Anthony Wells.

We can observe:

  • These are percentages, and both the row sums and the column sums should be 100, except for rounding errors.
  • 35% has Remain in the first position, 47% has it in the last position, so that 9 + 8 ≈ 17% (a 1% missing due to rounding) has a confused position, in which Remain is sandwiched between some options for Leaving. We would wonder how such people would vote in a referendum when they are presented with only two options R or L. One cannot say that the referendum was only about the first positions in the rankings, for voters would tend to develop an expectation about what would be the likely kind of Brexit and vote accordingly. Some of these 17% might have voted Remain because they disliked the otherwise expected version for Leave. This might indicate that the outcome for Remain was overstated. Yet we have no information on subdivisions of Remain, that might cause an opposite effect. Some might be okay with Remain as it is but vote for Leave because they fear that the UK otherwise might also join up on the Eurozone or some United States of Europe. The reason why the Brexit referendum question was flawed in design is that it left too much to guess here.
  • Remarkably, the split between R and L now in June 2017 would be 35% versus 65% instead of 48% versus 52% in 2016. In one single year Great Britain switched from fairly divided to a seemingly clear preference for Brexit (though divided upon how) ? I very much doubt this distribution, see the pre-former weblog discussion. The electoral data still suggest more than 50% for Remain. In the former weblog entry it is discussed that some 26% of the electorate say that they voted for Remain but accept the loss at the referendum, so that they “play along” with the winning side, focusing on what would be the best option for Leave. This seems loyal to some notion of democracy, but it would also be a misplaced loyalty to the flawed Brexit referendum question. (One can respect such loyalty, but it still makes sense to discuss it.)

Using techniques of apportionment we can estimate the actual number of people per cell in the poll. My estimate is (and YouGov would have the true numbers):

Possible permutations of rankings

With 4 options there are 4 possibilities for a first place, 3 remaining for the second place, 2 remaining for the third place, and then the final one follows. Thus there are 4 x 3 x 2 x 1 = 24 permutations for possible rankings. We already saw two of these: R > S > T > H and its reverse. Above ranking matrix is actually based upon these 24 possibilities.

Some of these 24 possibilities will be rather curious. It is not clear what to think about > H > S > for example (Case 5 below). This would be a Remainer who would rather prefer a Hard Brexit to the EEA or some agreement not to have a trade war on tariffs. A tentative explanation is that this voter has a somewhat binary position, as Remain versus Hard Brexit, while the other options are neglected.

Voting theory may assume voters that are both autonomous and rational, so that any preference would have some logic. This gives rise to the theory of Single Peakedness. Potentially each voter has his or her own criteria so that the best is on top, and all other follow in proper order. However, for the topics of R, S, T and H there is a logical scale from left to right. Voters with multiple peaks in their preferences have more to explain than voters with a single peak. An example of single-peakedness is Case 7 below, with a ranking S > R > T > H. See the graph below. The 1st rank gets utility level 4, the 2nd rank gets utility level 3, the 3rd rank gets utility level 2, and the 4th rank gets utility level 1. The utility levels are just the reversed of the ranks, but then the case must be reordered to the logical order.

Presentation of preferences via preference orderings

The following are estimates for the preferences orderings that would underlie above YouGov results. The estimate minimises the sum of squared error on that ranking matrix, with a weight of 10 for the error on the first preferences. See the excel sheet in the Appendix. This table shows only the percentages and not the numbers of people in the poll (that add up to above table), since the percentages are the main estimation result. Single dots are zero’s. Some have been caused by explicitly setting the possibility of such a preference ordering to zero, see the “comment” keyword for the reason. (A technical reason are also the degrees of freedom.) The ConR / L and LabR / L subdivisions concern the voters in the poll who voted R or L in the 2016 Brexit referendum and who voted Con or Lab in 2017. They form only a part of the sample, so their sum doesn’t add up to the total on the left. The percentages have a decimal to allow easier identification, not for claimed accuracy.

Discussion on GB

Some observations are:

  • The YouGov summary ranking matrix already showed a rather even split on S, T and H, but the estimate generates a landscape with even more diversity in opinions.
  • Only 26.2% has the preference R > S > T > H and only 16.2% its reverse, so that 57.7% (addition effect) have some mixture.

Above results for GB can be split up in on the peaks and sandwich. The combinations give the following percentages:

  • The mentioned 57.7% split up again in 34.6% who are single peaked, and 23.1% who have multiple peaks.
  • The sandwich of 17.1% splits up into 10.4% with a single peak and 6.7% with multiple peaks.
  • Of the 23.1% with multiple peaks there are 9.1% who can join the Remainers with a first preference and there are 7.3% who can join the leavers with Remain in the last position (but unclear how to Leave).

The 6.7% would be a relevant section of the vote. They all voted Leave, but divided on S, T and H. Potentially the outcome of the 2016 Brexit referendum has been decided by the 6.7% GB voters who have Remain neither in the first or last position, and who do not follow the standard logical order on the options.

Discussion on ConR / L and LabR / L

The division of ConR / L and LabR / L is losing its relevance because it are dwingling groups, they are changing loyalties, and their 2016 votes are becoming history while there are new issues. Yet, the 2016 referendum question was flawed, and it is relevant to see how sizeable parts of the UK electorate deal with the logical conundrum that they took part in.

  • The 17% of confused votes on the first preference can be found in the subdivisions in similar proportions.
  • 33.5% of ConR voters and 61.1% of LabR voters are united on the preference R > S > T > H. Presumably this was also the case in 2016, or there must be factors that increased or reduced consistency or confusion.
  • 28.9% of ConL and 19.4% of LabL are united on the preference H > T > S > R. Presumably this was also the case in 2016, or there must be factors that increased or reduced consistency or confusion.
  • One might expect that ConR / L and LabR / L voters of 2016 would have the benefit of a party preference and thus show more consistency, yet the distribution of views is quite as much, and the sandwich with multiple peaks is quite present.
  • The 2016 Conservative Remainers are loyal for 45.5% to the old point of view, but still vote for a Conservative party that is set on Leave. Part will be the misplaced loyalty for the flawed referendum. Alternatively, they voted for a minority in this party that still tries to bring balance ? (A good poll requires a focus group.) (And there is more in the world than just Brexit.)
  • The 2016 Labour Remainers are 76.1% loyal to the old point of view. Yet Labour leader Corbyn also prefers a Brexit. It might be the pecularities of the British system of District Representation (DR) that caused these voters not to switch to LibDem. (But the LibDem also have a liberal policy that many voters for Labour dislike. The system of DR doesn’t favour the entry of new political competitors.)
  • The 2016 Leavers have a high loyalty to the old view, ConL 86.8% and LabL 74.4%. Yet this doesn’t diminish the diversity of opinion about how to Leave (though T gets more votes than H).
Comment on uncertainty in this estimate

For n = 4, there are n! = 24 variables, (n-1)^2 = 9 independent equations within the matrix, and there is the addition constraint 1, so that the degrees of freedom are 14. Yet we cannot randomly set weights to zero. If there would be nonzero weights for single-peaked preferences only, then the YouGov ranking matrix would show zeros, which it doesn’t. Thus it takes some arbitration which weights to exclude. There are quite a lot of possibilities, and I can only hope that my choice was wisest. As said, the percentages provided by YouGov have been scaled up to the table given above, and this allows us to determine the error in the estimate. Due to degrees of freedom the calculated error is quite low. The use of an error measure is limited to comparing estimates and not something that is useful to mention here. As said, YouGov have the proper data, and it must be hoped that they will look into this.

Conclusions
  • The ranking matrix is a fine way to summarize results, yet the preference ordering are more accurate on the underlying and relevant orders. This is merely a matter of presentation by the statistical reporter. A person in a poll who can answer on a ranking matrix in fact gives the personal preference ordering. The statistician can compound these data while not losing information on the permutations. From the permutations it is always possible to create a ranking matrix, yet the reverse requires estimation techniques which generate needless uncertainty.
  • Asking for voter preference orderings in a poll is a useful exercise. It is not intended to propose this for general elections. For general elections it suffices that voters exercise a single vote for a party of choice. The condition however is Proportional Representation, otherwise there are serious distortions, see the earlier discussion on this weblog.
  • The information on the rankings and implied preference orderings suggest a rather large state of confusion in the electorate of Great Britain. The notion of single-peakedness appears to be quite useful in highlighting the issue of the preference order.
Appendix July 15 2017

I slightly revised the manner of rounding and included case 16 for all columns. The polished up excel workbook is: 2017-07-15-YouGov-Rankings

Before the UK Brexit referendum of June 23 2016 I warned that referenda can be silly and dangerous, see here in April 2016. I clarified that the Brexit referendum question was flawed in design. I did not look deeper into this, since, like so many others, I had been put on the wrong foot by the 2016 poll average that suggested a continuation of the status quo. After the surprise outcome, I advised the youngsters in the UK to focus attention on this design flaw, as this is the clearest issue and proper reason to argue that the outcome should be annulled, see here in June 2016. When Kenneth Arrow passed away in early 2017, this was an occasion to have a summary text published in the RES Newsletter, which was republished on the LSE Brexit blog. Now, with the 2017 UK general election, I have been looking a bit deeper at these UK election issues.

One result has been the use of the Lorenz curve and Gini coefficient to show the disproportionality in the UK between votes and seats. Almost all EU members have Proportional Representation (PR) with clear exceptions of the UK and France that have District Representation (DR). Apparently, this is a main reason for the influence of populism in the latter two countries. DR allows that politicians are elected with a minority of the vote, which causes a gap with the majority. Politicians like David Cameron can use a referendum to introduce an element of proportionality. Yet referendum questions are quickly flawed.

A main confusion

Another surprise for me was the existence of the Re-Leavers who make up some 23% of the electorate, and who are very likely also a major section in the House of Commons that supported the invoking of article 50.

Apparently many British voters are awfully respectful of democracy, and while they voted for Remain, they accept the referendum outcome, and let their voting behaviour now be guided by Leave. In other words: they no longer operate as voters who are supposed to express their first preference, but they operate as politicians who develop policy using such preferences.

Voters are better not confused about the following angles:

  • It is one thing to accept the Brexit referendum outcome as a fact. Please accept facts.
  • It is another thing to discuss the consequences of that fact.
  • There is always the distinction between your first preference and dealing with new developments.
  • Your first preference can change, but rather only because of arguments, and not just because of a majority view.

For me, it is easy to say this, in a country that is used to PR. In the UK case of DR it may well be that strategic voting requires voters to run with with herd. Nevertheless, the Re-Leavers cause quite a confusion in the voting record. Also for the general elections of 2017 we now can observe that we don’t know what people really want.

The YouGov data of June 12th – 13th 2017

Anthony Wells provided and discussed these data that show the impact of the Re-Leavers. Let me quote the main part, and for this quotation I also moved their copyright sign up.

These early June data are most relevant for judging the June 8 2017 UK general election. Apparently 26% of all adults in Great Britain (UK excl. Northern Ireland), but also 53% of the voters who voted Remain in 2016, reason as follows:

I did not support Britain leaving the EU, but now the British people have voted to leave the government has a duty to carry out their wishes and leave.

I consider this an illogical and rather undemocratic statement.

  • Logic would require the annulment of the referendum outcome, and not to take it seriously.
  • In representative government, it is Parliament that determines policy, not the people by some referendum.

Most of the EU has PR and thus the notion of representative government. The 2016 Remain voters want to remain in the EU, but, 53% apparently also reject the EU notion of representative government, and instead they appeal to the populism of referenda.

More on the design flaw of the Brexit referendum question

A few days ago, I rephrased one aspect as follows: With R for Remain, S for Soft (EEA), for some Tariffs, and N for No Deal (WTO), there are 6 possible strict preferences for a deal, from R > S > T (Theresa May before the referendum) to T > S > R (Theresa May after the referendum). If S and T are collected in L (Leave) then there arises the claimed binary choice between R and L. Voters who are in the categories S > R > T or T > R > would face a hard question. If they expect that R might win, but also that their own preferred option might not win, should they still go out and vote ? They might decide not to turn out, or develop assumptions about what actually might become, given what what they think about future developments. Similarly for the versions of R. See the voting theory about single peaked preferences (and these are not single peaked but double peaked). Overall it is a fallacy that there is a binary choice. Lawyers can argue that one either invokes article 50 or doesn’t invoke it, yet the referendum isn’t such a legal case, for it is an issue of policy preferences.

In fact, above YouGov poll provides us a bit more information on this issue. Look at this section on their page 15:

Look at the column of the total (with 1651 people in the weighted sample). 35% are clearly for Remain, in their first rank. 47% are clearly against Remain, in their last rank. Thus the middle 8 + 9 ≈ 18% (rounding error) is rather confused, for they put Remain between one of the Leave options. How would they have to vote at a referendum that only allows R or L ? We find similar percentages for the subgroups on the right hand side.

Conclusion

The discussion in the UK would be served by greater awareness of these distinctions:

  • The difference between voting for your first preference (setting the target) and trying to second-guess politicians (as if you are in the driver seat).
  • A valid question and an invalid or flawed one, like the Brexit referendum question.
  • The crucial differences between Proportional Representation (PR) and District Representation (DR), linked to the distinction between representative democracy (mostly PR) and populism (mostly DR).
  • There is also something not discussed in the above, but that is the difference between the failing Trias Politica and improved democracy with an Economic Supreme Court.

(Updated July 11  2017) (September 18 2017: Changed “Hard, H” in “No deal, N”)

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.