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Jacob Rees-Mogg had a talk for the Oxford Union, published on YouTube on 2013-11-11. The Oxford Union is a debating society. A debater’s aim is to win the audience over and not necessarily to discuss truth. Rees-Mogg had an entertaining talk but it is not targeted at discerning truth indeed. His presentation comes across as modest and forceful, with the charm of perhaps some old-fashioned style. Who closely considers his words may however be shocked by the unreasonableness and closed-mindedness.

Boris Johnson and Nigel Farage have been criticised for spreading false arguments for the June 23 2016 Brexit referendum. Obviously, these two individuals cannot be held accountable for swinging the views of some 45 million voters. I wondered since the referendum whether they had had some help. Apparently Jacob Rees-Mogg had been giving a helping hand.

To clarify Rees-Mogg’s departure from truth, we first must mention some properties of the European Parliament.

Seat-to-vote ratio’s in the EU parliament

The EU Parliament has 751 seats, distributed over 28 member states with 500 million people. The distribution over countries is not proportional to the populations, since countries are units by themselves, and it is felt that this should have some effect. Thus Germany with its population of 82 million has 96 seats (1.17 seats per million), the UK with its population of 65 million has 73 seats (1.12 seats per million), and Malta with its population of 0.5 million has 6 seats (12 seats per million). There is relatively little tension about this apportionment, since the countries fall in comparable classes (large, medium, very small), and the major political differences translate into political parties. The divisions between Christian Democrats, Social Democrats, Liberals, and what have you, apparently are dispersed over countries in similar manner, or, the political parties are able to create alliances over nations. It is part of the wonder of the EU that nationalism is being channeled and that there is more scope for civil democracy. A recent paper of mine on proportional representation is here.

Jacob Rees-Mogg’s quote on Malta

Jacob Rees-Mogg does not explain above democratic solution for dealing with Member States of different sizes. He criticises the EU that Malta is over-represented compared to the UK. It is a fact that Malta has a higher seat-to-vote ratio, but only pointing to this fact obscures the other considerations. He mentions a perhaps older figure of 15 instead of the current 11, but that is irrelevant here. The demagoguery is that many in his audience apparently are not be aware of the key notions in this apportionment, and he apparently takes advantage of their lack of knowledge to win them over to his own closed-mindedness. The demagoguery is that he creates a suggestion as if Malta has 15 times more influence than the UK, as if 6 is 15 times larger than 73 (as, indeed, 6 = 15 * 73).

The quote at the final minute starting at about 11.30 is, with the abusive “proportionally outvote” and the threat of “spectres”:

“So what is this great experiment doing ? It is helping once again the rise of the extreme right, and in some cases the extreme left. That is the threat to democracy that is there, that is coming, that is deeply destructive. But the fundamental problem, the real issue at hand tonight is that there is less democracy in this country, because of the European Union. Because, Ladies and Gentlemen, however you vote the next general election, 60% of our laws, and some say higher, is made on the basis of European agreements, where the Maltese proportionally outvote us 15 to 1. Whoever you vote for, matters less than somebody in Malta votes for, about the laws of our country. And if you are unsatisfied with that, and you want it changed, I cannot give you any redress, because the United Kingdom Parliament, the most ancient democratic Parliament in the world, has been made powerless. That is the threat to democracy. It is here, but it is on the continent as well. It is a frightening spectre. The best way to deal with it, is to deal with our relationship with the European Union, to put our own democracy first and foremost, and hope that others follow.”

Does it really require a protest ?

It is almost silly to protest to this demagoguery:

  • The situation w.r.t. the UK and Malta in the EU Parliament has been explained.
  • The UK has District Representation (DR) instead of Proportional Representation (PR), which causes that the UK is much less democratic than most countries in the EU or the EU Parliament itself. The PR Gini for the UK of 2017 is 15.6%, but there has been a lot of strategic voting, so that we don’t really know what the first preferences of UK voters are. By comparison, Holland has a PR Gini of only 3.6%, and people in Holland could vote for the party of their first choice. See this weblog text and this paper.
  • I tend to think that Rees-Mogg really worries about the state of democracy, while A.C. Grayling rather sees an elitist or even pecunary motive, see this article, as in “follow the money”. Yet Rees-Mogg doesn’t study the topic, and thus he is condemned to repeat an ideology. He studied history but not science. His voting track record apparently shows that he consistently voted against Proportional Representation. Old-fashioned hypocrisy apparently is also part of his old-fashioned style.

Malta enlarged some 30 x UK, dotted with 15 x UK. Spot the Real Malta

October 18: In memoriam Daphne Caruana Galizia (1964 – 2017), journalist, killed by a car bomb.

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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”.

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