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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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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”.

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

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

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

A persons affiliated with ERS answered to this criticism:

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

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

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

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

Wikipedia follows ERS

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

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

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

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

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

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

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

Scotland is an example

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

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

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

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

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

The current Scottish system

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

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

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

District

Region

Party

Votes

Votes

Con

501,844

524,222

Green

13,172

150,426

Lab

514,261

435,919

LD

178,238

119,284

SNP

1,059,898

953,587

Others

11,741

102,314

Total

2,279,154

2,285,752

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

District

Region

 All
Party

Seats

Seats

Seats

%Seats

%Votes

%S-%V

Con

7

24

31

24.0

22.9

1.1

Green

0

6

6

4.7

6.6

-1.9

Lab

3

21

24

18.6

19.1

-0.5

LD

4

1

5

3.9

5.2

-1.3

SNP

59

4

63

48.8

41.7

7.1

Others

0

0

0

0.0

4.5

-4.5

Total

73

56

129

100.0

100.0

An alternative for Scotland

Let us consider a rough alternative for Scotland:

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

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

District

Region

 All
Party

Seats

Seats

Seats

%Seats

%Votes

%S-%V

Con

1

29

30

23.3

22.9

0.3

Green

0

8

8

6.2

6.6

-0.4

Lab

0

25

25

19.4

19.1

0.3

LD

2

5

7

5.4

5.2

0.2

SNP

26

28

54

41.9

41.7

0.1

Others  0  0  0

0.0

4.5

-4.5

Total

29

95

124

96.1

100.0

A general observation

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

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

The UK Electoral Reform Society (ERS)

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

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

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

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

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

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

The person affiliated with ERS writes to me:

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

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

Missing Scottish voters

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

In an article, Sullivan summarises:

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

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

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

Conclusion

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

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

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

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

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

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

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

There is a bizarre incomprehension of democracy.

I was inclined to say in the English speaking world – UK, USA, India – but there is also France, with the upcoming elections for the French National Assembly 2017. Also France has a system of District Representation (DR) rather than Proportional Representation (PR). Examples of PR are Holland, Germany and to some extent the European Parliament.

Democratic theory favours PR above DR. It is a historical mistake that countries have DR.

The UK Electoral Reform Society (wikipedia) protests about the UK general elections 2017.

Electoral Reform Society, website June 2017

Indeed, there is this difference (wikipedia) between the UK system of DR with the better system of PR. While the popular vote gives a majority to Lab + SNP + LibDem, the majority in seats goes to Con + DUP.

Seats Votes
Con

317

48.8%

13,632,914

42.3%

DUP

10

1.5%

292,316

0.9%

Lab

262

40.3%

12,874,985

40.0%

SNP

35

5.4%

977,569

3.0%

LibDem

12

1.8%

2,371,772

7.4%

Other

14

2.2%

2,047,362

6.4%

Total

650

100.0%

32,196,918

100.0%

There is also the political dynamics of proportionality. Once a proportional system is in place then new parties will have a larger chance to get elected, and then they also have more scope to grow and to challenge the existing parties. We may observe that the UK 2017 outcome may be more proportional than in the past, but this still neglects the dynamics and the build-up of frustration amongst minorities that aren’t represented well.

The UK already has experience with the system of PR, namely for the European elections. While UKIP didn’t do so well within the UK system, Nigel Farage gained the limelight via the elections for the European Parliament.

The UK Electoral Reform Society fails too

Part of the bizarre situation is that the UK Electoral Reform Society (ERS) fails too. They favour the system of “Single Transferable Vote” (STV) and they call this a system of PR while it isn’t PR. It is rather bizarre that they do not comprehend this. The UK had a so-called “referendum on PR” in 2011, but this was actually on the system of “Instant Run-Off” (a.k.a. “Alternative Vote”).

Apparently, the UK has a hangup on DR. They think that districts allow voters to connect directly with the local politicians, and that this reduces the influence of the party bosses. This is a dubious argument. If a representative and party member is out of line with the party then the party might still sack him or her nevertheless. In PR it is easier to start a new political party and be elected (when the issue likely isn’t just local).

Thus the statements by the ERS about district representation derive from historical bias and not from clear theory and practical experience with PR.

Let me give an example how STV favoured by ERS is not PR at all, even though they claim that it would be PR.

Example that STV is not PR

Consider two districts with 30000 voters each. Each district has 2 seats, so that the Droop Quota is 30000 / (2 + 1) + 1 = 10001. Parties contending for these seats are Con, Lab, en LDP. In District 1, the Con are popular, and they present there a list with two candidates. In District 2 the Lab are popular, and they present there a list with two candidates. We consider a rather symmetrical situation as in the following table, also with the STV results.

In STV, voters vote only once, but they can assign a rank order of the candidates.

In District 1, 7503 Con1 voters give Con1 as their first choice and Con2 as their second choice. Also 7501 Con2 voters give Con2 as their first choice and Con1 as their second choice.

  1. In the first round, no candidate meets the quota. LDP1 has the minimal number of votes, 7494, and is eliminated.
  2. In the second round, Con2 has the minimal number of votes, 7501, and is eliminated.
  3. In the third round, the Con2 votes are allocated to Con1, and Con1 meets the quota and is elected.
  4. In the fourth round, Lab3 is the remaining candidate and thus is elected, though the 7502 votes are below the quota.

The situation in District 2 is analogous.

District 1 Votes District 2  Votes
Con1

7503

Elected Con3

7502

Elected

Con2

7501

Lab1

7503

Elected

Lab3

7502

Elected Lab2

7501

LDP1

7494

LDP2

7494

30000

30000

Let us now join the two districts, and look how STV works for the national vote.

There are 60000 voters and 4 seats, so the Droop Quota is 60000 / (4 + 1) + 1 = 12001.

The Con voters put the Con candidates of their district in the first places, and then the Con candidates of the other district. For example, the 7501 Con2 voters have the rank order {Con2, Con1, Con3}.

Because of the symmetrical structure of this example, there are some ties. Rather than using a coin, we use the alphabetical order.

  1. In the first round, no candidate meets the quota, and LDP1 is eliminated.
  2. In the second round, the LDP1 votes go to LDP2, and it is elected.
  3. In the third round, alphabetically Con2 has the minimal number of votes, and is eliminated.
  4. In the fourth round, Con2’s votes go to Con1, and it is elected.
  5. In the fifth round, alphabetically Lab2 has the minimal number of votes, and is eliminated.
  6. In the sixth round, Lab2 votes go to Lab1, and it is elected.
  7. In the seventh round, alphabetically Con3 has the minimal number of votes, 10506, and is eliminated.
  8. In the eighth round, Lab3 remains, and is elected, though with only 10506 votes.

Thus now LDP2, Con1, Lab1 and Lab3 are elected.

Upshot:

  • As the UK Electoral Reform Society (ERS) states that STV would generate proportional results, both {Con1, Con3, Lab1, Lab3} and {Con1, Lab1, Lab3, LDP2} would be proportional results, which however are quite different results, which destroys the meaning of proportionality.
  • With a hangup on DR, there will be little scope for fair representation of the minority LDP.
  • PR would require party representation with {37.5%, 37.5%, 25%} of the seats. Admittedly, this is difficult to achieve with 4 seats, but if the situation persists then one might change the number of seats. This uses the PR criterion rather than the STV criterion.

In these considerations, the notion of PR dominates DR.

Confusing information from Holland

Holland is a small country with some 10 million voters. One might think that its proportional system might not easily scale up to a large unit like the EU. If the EU Parliament would be fully proportional, then Germany might have too large a weight. However, there are also divisions along party lines, and proportionality still would be a fair choice.

Holland had general elections on March 15 2017, and political parties are still negotiating about a coalition government. This is bad advertisement for the system.

There is a confusion in Holland about desiring the minimal majority coalition, that bargains for an agreement that would apply for the next 4 years. It would be more rational to look for a larger majority, and rather set for a flexible agenda, so that issues can be dealt with in varying manner. See this paper of mine. It may also be better to have elections every year, so that Parliament becomes more sensitive to the popular vote. (If you would replace only 25% of the seats, then the electoral quota becomes 4 times larger, and this might be too high again.)

Most bizarre is that the Dutch party D66 wants to change the Dutch PR system into more use of districts … see here. Thus the good news about democracy in Holland is killed again by the campaigners on the D66 hobby horse.

Conclusion

We observe that the UK ERS protests against the failure of the UK electoral system, but we can also conclude that ERS doesn’t comprehend democracy.

We find similar confusions all over the world. The best advice is to change your national electoral system to the PR system like in Holland (or to some extent the EU parliament), yet many campaigners ride their hobby horses of wildly confusing varieties, and calling it “democracy” while it actually isn’t.

PM. A paper of mine on comparing PR and DR is here.

This discussion continues with the exchange of Flassbeck & Lapavitsas versus Storm.

My own position is as follows. Holland creates its own unemployment since 1970 by a wrong policy on taxes and premiums. Holland has the entrenched government policy of “solving” this by wage moderation and exporting its own unemployment to other nations. I present my alternative analysis since 1990. Economists at TU Delft have been arguing against this policy of wage moderation for decades too. They overlook the cause in taxes and premiums, and focus on technology. Schumpeterian innovation requires higher wages to get rid of obsolete technology. Now that Germany has had wage moderation too (because of the fall of the Berlin Wall and the Mark = Mark policy) the discussion on wage moderation moves to center stage for the survival of the Euro. Servaas Storm at TU Delft enters the European discussion again with arguments about technology, and again neglecting taxes and premiums, and neglecting the censorship of science by the Dutch government (what this weblog is about). Storm has an innovation in his analysis by including banking, and how international credits drive international trade, yet, he seems to neglect the phenomenon that trade surpluses generate funds that look for opportunities, often by providing credits that generate more surpluses. Thus Dutch and German wage moderation would be causally more important than bank credits.

PM. See also former IMF director Johannes Witteveen’s lecture on the Dutch export surplus and a need for an investment policy. There is also my discussion in 2009 with a chart of the Dutch export surplus in 1971-2010 (forecast). This is already 8 years ago.

Let me restate some basic economics for some readers who lack this.

Basic macro-economics

  • Let real national output (GDP) be y and the price level be p.
  • Let labour input be x and the wage be w.
  • Then labour productivity is λ = y / x and the Labour Income Quote is LIQ = w x / (p y).
  • Let there be a Cobb-Douglas production function: y = β x^α, with β containing capital and technology.
  • When producers maximize their profits π = p y w x subject to labour input x, then we can derive:
  • The first order condition: dπ / dx = 0 gives p β α x^(α – 1) – w = 0.
  • Or the wage can be set at w = p β α x^(α – 1) = p α y / x = p α λ, since the national labour supply is given as x.
  • This w = p α λ is the rule mentioned by Flassbeck & Lapavitsas: let wages grow with labour productivity and the agreed target of inflation of 2%.
  • From w = p α λ we can derive α = w x / (p y) or α = LIQ.
  • Unit labour costs are ULC = w x / y = w / λ = p LIQ. Thus alternatively w = p LIQ λ or w = ULC λ.

The assumption of the Cobb-Douglas function seems somewhat specific, but given the relatively small changes that we are considering the approximation is often so good that we almost seem to have a definition. The LIQ has the character of a structural parameter α, at least for annual changes.

If prices p and wages w and labour input x remain the same from one year to the other, and productivity rises by rate g, so that  =  (1 + g) y[-1], then α = LIQ = w x / (p y) = w x / (p (1 + g) y[-1]) = LIQ[-1] / (1 + g) = α[-1] / (1 + g). For example, if α[-1] = 80% and g = 2% then α ≈ 78%. In this case α would be stable if wages would rise by 2% too.

The w = p α λ condition is not in the EMU rules. The Eurozone countries apparently are less aware of the notion of “national bargaining” (as in the Dutch Polder model) and have been hesitant to include national wage agreements in the EMU and Stability & Growth Pact (SGP) and its updates. (Check for the word “wage” on this wiki page.)

Another possible rule might be a tax of 5% on the three year cumulative trade surplus (which may be seen as 15% for a single year), to be invested in productive capacity in the deficit countries via national investment banks. Such a tax would not be on export items (like a tariff) but levied on the Eurozone member governments of surplus countries. (At this applet, set the color bar to a score of 0, and slide over the years.)

It is unavoidable to think about such rules. Holland has been moderating its wages long before Germany did. The policy put pressure on the exchange rate of the guilder, but this was resolved by joining the Euro. Holland still is a small country and the impact wasn’t much felt. Now, Europe must explain to Germany that a raise of German wages is required, whatever they fear about inflation. It should help Germany to grow aware that my analysis (see DRGTPE) allows full employment at stable prices, not only by exports but also by stimulating the domestic market.

Shifting the blame

Both North and South Europe deviated from w = p α λ. Some Northerners blame the South, and some accept some blame themselves.

  • Sinn and Schäuble argue that Southern Europe should moderate their wages like Germany.
  • Bofinger and Flassbeck & Lapavitsas argue that Germany (and Holland) should raise their wages.

As Storm states:

“Their main point is that there would not have been large unsustainable current account imbalances within the Eurozone, and consequently no sovereign debt crisis in the deficit countries, if all member states had kept their nominal wage growth equal to labor productivity growth plus 2% (the inflation target). Professor Wren-Lewis (2016) has been making the same point. In this account, this delicate equilibrium has been deliberately upset by nominal wage moderation in mercantilist Germany, with a growing German trade surplus just being the flipside of the growing trade deficit in Southern Europe. It is rather ironic, in my opinion, that a similar logic is used by mainstream observers such as Sinn (2014) or even Mr. Schäuble himself, with this difference: Sinn and Schäuble argue that the current account imbalances were caused by a failure of the crisis countries to follow Germany’s successful example in cutting down their unit labor costs.”

Towards a collapse of the Euro

Sinn and Schäuble want to control inflation and they lack instruments to make sure that Southern Europe adheres to the EMU rules. Thus Sinn and Schäuble take the hard line that it is up to Southern Europe to choose themselves:

  • either unemployment because of high wages
  • or internal devaluation, and subsequent unemployment because of deficient internal demand.

Hence we can understand Flassbeck & Lapavitsas:

“Germans ought to know better than all others about the difficulties caused by wage divergences in a currency union. The deviation of East German wages as measured in international currency, following the German Monetary Union of 1990, destroyed East German industry and forced a transfer union. Unfortunately, for the EU and the EMU the option of a transfer union is simply not available. As long as Germany persists with its policy of wage moderation, the only future for the EMU is collapse.”

Check how I criticised Angela Merkel for her deceit at the German elections in 2013. Given German policies on wage moderation, standard economic theory allows her the choice between a transfer union or a breakup, but she kept silent about this. Of course there is my amendment to the theory of the optimal currency area, see MPRA or RWER, but as long as German policy makers do not indicate that they understand his amendment, we must conclude that they disinform their electorate.

How does Storm handle this ?

How does Storm handle this reference to basic economics ? He misstates the argument, and then rejects it.

“(…) that Eurozone imbalances were driven by (exogenous) losses or gains in unit labor cost competitiveness (…) is a myth (…)”

Storm’s problem is on causality: “what drives what”. Yet this is not quite what this discussion is about. What Storm calls a myth are basically accounting rules.

  • Use GDP = Y = p y = C + I + G + X – M, with consumption C, investments I, government G, exports X and imports M.
  • The current account CA = X – M is also the increase in foreign assets FA = X – M (NY FED).
  • National income, employment and wage translate into LIQ and λ. This is mere accounting.
  • Compare two situations for the same country with only a difference in M. In the first situation there is Y1 with a surplus on the current account, or M < X. In the second situation there is Y2 with a deficit or M > X. Thus Y1 > Y2. Assume the same output price p and working force x so that y1 / x > y2 / x, or λ1 > λ2. The productivity with a surplus is higher than with a deficit. For example, in the second case the country worked as hard as usual, but also imported a car by borrowing from abroad. Mere accounting causes that observed productivity drops. Similarly we have w x / y1 < w x / y2 or ULC1 < ULC2, or that the deficit situation has higher unit labour costs.

Economics is about causality and not about accounting, but it is important to be aware of accounting effects. Regressions with statistical data that contain these accounting effects must be judged carefully.

In above example of importing a car, causality seems to run from first importing to secondly a statistical observation on productivity. This is Storm’s view. But this is not the only causal possibility. Sinn and Schäuble might argue that higher productivity might have been feasible if the car hadn’t been imported but e.g. produced in the country itself with a creditor in the country itself. Thus there seems to be more complexity than Storm allows for (though he already makes a complex case). And Sinn and Schäuble might state more clearly that they also plea for the demise of the German car industry.

Storm’s five arguments

Storm has five arguments that we may indicate shortly. Apparently he repeats himself at points, but this is okay since we look at the arguments and not their number.

  1. Banks in Northern Europe lent to customers in Southern Europe, assuming that loans in Euro were safe anywhere. (Comment: True. However, if there hadn’t been surpluses on the Northern current accounts, then these banks would have had less funds. We are not speaking about a single year, but a prolonged period of surplus funds looking for “investment” opportunities.)
  2. German firms, producing high-tech, high value-added, high-priced and mostly very complex manufacturing goods, do not directly compete with Spanish, Portuguese, Greek or even most Italian firms, which are specializing in lower-tech, lower value-added, low-price and less complex goods (Simonazzi et al. 2013).” (Comment: This is not relevant, since differences in quality are corrected by differences in wages, whence we compare w1 / λ1 and w2 / λ2.)
  3. Four empirical “facts”. (a) Elasticities. (b) In Spain imports grew while exports were unaffected. (c) World income explains exports, and national income explains imports. (Costs might have a one-time effect but then are stable.) (d) There were first the imbalances and only later the worse ULCs. (Comment: Basically agreed on (a)-(c). However, this (d) is the same as (1). We are not speaking about a single year, but about a prolonged period of imbalance and funds looking for profit.)
  4. A more theoretical discussion of (3c), with the example of (2). “These asymmetric growth patterns are the direct consequence of structural differences in productive specialization (Simonazzi et al. 2013).” (However, see (2). Obviously, the EMU doesn’t have an exchange rate regime to correct sustained imbalances. Apparently governments must impose what otherwise would have been done by exchange rate markets.)
  5. “Higher Wages and Higher Inflation in Germany Will Not Help.”

Storm on point 5:

“German exports and imports, as I argued above, are not very sensitive to changes in relative unit labor costs, however, and hence there will be only a limited amount of expenditure switching (away from German products and toward foreign goods), as has also been convincingly shown by Schröder (2015). Let me repeat for clarity’s sake that I am strongly in favor of higher nominal wage growth (in excess of labor productivity growth plus 2%) in Germany. It will definitely help Germany. But it will not help the crisis-countries of the Eurozone.”

“The assumption is that German GDP increases by € 100 billion (which means German GDP is growing at 3.7%). Through global production chains, [my emphasis] German growth creates € 29.5 billion of income in the rest of the world and about € 7 billion in the selected European countries listed in Table 1.”

This looks at production chains (Germany, USA, Korea) ! This may well be. But higher German wages would also mean higher German imports for consumption.

Storm’s view on the real issues (again)

Storm repeats what he regards as the real issues:

“(…) the common currency and monetary unification have led to a centrifugal process of structural divergence in terms of structures of production, employment and trade (as explained in my earlier notes).”

“German wage moderation mattered a lot, not through its supposed impact on cost competitiveness, but via its negative impacts on (wage-led) German growth and inflation, which in turn prompted the ECB to lower the interest rate in the first place.” (Comment: This “negative impact” is TU Delft slang for the idea that low wages reduce the need for Schumpeterian innovation.)

“The consequent crisis of the Eurozone is a deep crisis of inadequate aggregate demand in the short run and unmanageable structural divergence between major member states in the long run.”

I wonder. If Germany provided the European industrial zone and Southern Europe provided the European vineyards, olive trees and universities, then this might still work and everyone might be happy, provided that the prices of cars, wine, olive oil and Ph. D. doctorates would be right. Wage levels in Southern Europe might still be lower, but with a purchasing power parity (PPP) living standards might still be quite comparable. Sinn and Schäuble might like an argument that EU support for investments in Southern Europe should not be competitive to the German car industry (see here on the restauration of the Colosseum).

But this is not the full story. The Po valley has fine cars and machinery too. Italy itself has a North-South problem. Spain has the difference between Catalunya and Andalusia. And Germany has Laender who don’t do as well as Bayern.

Closing this review

This exchange started with Bofinger’s argument that German wages should be raised. This argument is fine. It will stimulate Germany’s domestic economy and imports. The obvious ceiling is provided by risks of unemployment and inflation, but the rule of a wage rise with productivity and the target of 2% inflation is fine too. Germany also has some catching up to do.

It is correct that German exports might not be much affected, and thus neither employment in the exporting sector, because the productivity growth in the exporting sector likely is larger than this growth in the domestic sector. But the rise of imports would still help in reducing the surplus on the external account.

Storm’s arguments on competitiveness & wage moderation are a different subject. This is basically the subject of investments and regional development, and the role of banking. Germany is advised to focus on domestic investments.

Economic analysis would be served by having another indicator alongside GDP, namely a correction of GDP for borrowed funds. The X – M correction works fine for foreign assets, but a correction for domestic borrowing would be helpful too. If one buys a domestic car with credit, then this domestic car really has been produced, but it would be indicative to know whether 10% or 25% of GDP would be from credit.

Overall I can repeat that my analysis of 1990 is still very relevant for understanding and solving the Great Stagflation since 1970. There are DRGTPE dating before the 2007+ crisis and CSBH after it. DRGTPE already has a chapter on the distinction between the exposed and sheltered sectors, and CSBH has a refinement of that argumentation.

It is unfortunate that our fellow economists at TU Delft have been neglecting that analysis since 1990, whence they still lack the full picture. But every day starts with a new sunrise.

Given Kenneth Arrow’s impossibility theorem, it is a fair question to ask what voting system he himself would advise. There is a 2012 interview with him, with a phone recording and transcript, by Aaron Hamlin of the Center for Election Science. Arrow’s advice is:

  • Not plurality and no US Electoral College, with its winner-take-all selection of the US President
  • Not approval voting, since this uses too little information
  • A system that uses more information:

“Dr. Arrow: Well, I’m a little inclined to think that score systems [range voting] where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best. (…) In France, [Michel] Balinski has done some studies of this kind which seem to give some support to these scoring methods.”

His statement about strategic voting – or manipulation:

“Dr. Arrow: There’s only one problem that bothers me about that. And that’s something my theorem really doesn’t cover. In my theorem I was assuming people vote sincerely. The trouble with methods where you have three or four classes, I think if people vote sincerely they may well be very satisfactory. The problem is the incentive to misrepresent your vote may be high. In other words, a classic view is that there’s a candidate I really like, but I know is hopeless. I may put him down at the bottom and vote for the next candidate simply because I feel there’s a chance. Now, if you have a very large electorate you might say no individual has much of an incentive to misrepresent. But I’m not sure. You probably need experience rather than theory.”

Observe that Arrow cautiously states “a little inclined to think (…) probably the best”. His advice to have more empirical research can be supported. The interview touches on some points that call for a closer discussion, also in the light of this earlier weblog text.

Definitions

In plurality, voters only can vote for their best candidate. In a district, often the one with the highest score wins, which is the “first past the post” (FPTP) system. If there are only two candidates, then the winner will also have more than 50%. If there are more candidates, the winner may have less than 50%. There may be ways to assure that a final vote only concerns two candidates. A Putin hack that eliminates a particular candidate will not quickly be accepted, yet, voting theorists still wonder what method would be reasonable. A current example is that Donald Trump got elected with 46% of the popular vote, while Hillary Clinton got 48%. With a turnout of 60% Trump has only 28% support in the electorate, while the House of Congress depends upon district results too. A prime minister who is elected by a coalition in a parliament that has proportional representation (PR) generally has more than 50% support in parliament, and by representation also in the electorate.

In approval voting, voters mention which candidates they approve. The candidate with the highest total approvement is selected.

  • In economics this links up with satisficing (Herbert Simon).
  • Strategic voters will tend not to approve of candidates that might harm their best candidate (even the second best), so that this system devolves into plurality. Steven Brams claims that such fears are overrated but are they ? Brams declines to look into non-satisficing alternatives like the Borda Fixed Point method.

In Borda ranking, each voter puts the candidates in order of preference, and assigns rank numbers.

  • In economics this reflects the notion of ordinal utility.
  • Strategic voters will give a low score to candidates that harm their best candidate (even the second best), which means that “dark horses” (of mediocre approval) might win. See the discussion below.

In range voting, the voters grade the candidates like on a report card, and the candidate with the highest grade point average (GPA) wins. There is the tantalizing but empirically perhaps small complexity of the distinction between a 0 grade (included in the GPA) and a blank vote (not included in the GPA).

  • In economics this reflects the notion of cardinal utility (with voters restricted to the same range).
  • Strategic voters will give a low score to candidates that harm their best candidate (even the second best), which means that the system devolves into plurality. (The use of ordinal preferences and Borda explicitly intends to resolve this again.)

(See also the distinction in levels of measurement.)

Beware of the distinction between cardinal and ordinal preferences

Arrow’s impossibility theorem is about aggregating individual rank orders into a collective rank order. The theorem uses rank orders, or ordinal preferences. Arrow does more than only use rankings. He also defends the “axiom of pairwise decision making” (APDM) a.k.a. the “axiom of independence of irrelevant alternatives” (AIIA) as reasonable and morally desirable (Palgrave Dictionary of Economics).

Range voting allows more information than just ordinal preferences, and it is similar to cardinal preferences (but limiting people to the same range). Cardinal preferences imply ordinal preferences. Yet rank voting doesn’t satisfy the requirements of Arrow’s impossibility theorem, for cardinality violates APDM or AIIA.

One might say that Arrow’s theorem is not about voting systems in general, since it only looks at ordinal and not at cardinal preferences. Instead, Arrow’s position is that he looks at voting theory in general and only proposes axioms that are “reasonable” and “morally desirable”  When cardinality and range voting are excluded from his axioms, then it is because they would be unreasonable or morally undesirable.

These distinctions are discussed – and Arrow’s notions are debunked – in my “Voting theory for democracy” (VTFD). (See especially chapter 9.2 on page 239.)

Arrow’s theorem is only about those voting systems that satisfy his axioms. Since his axioms cause an inconsistency, there is actually no system that matches his conditions. Something that doesn’t exist cannot be reasonable and morally desirable. Arrow’s theorem confuses voting results with decisions, see this earlier weblog discussion.

However, there still remains an issue for voting theory. Range voting allows more scope for strategic voting or manipulation. The reason to restrict votes to rank orders is to reduce the scope for strategic voting.

Gerry Mackie’s “Democracy Defended

A reader alerted me to Gerry Mackie’s thesis with Jon Elster, now commercially available as “Democracy Defended“. I haven’t read this but the blurb seems to confirm what I have been arguing since 1990 on Arrow (but not on Riker).

“Is there a public good? A prevalent view in political science is that democracy is unavoidably chaotic, arbitrary, meaningless, and impossible. Such scepticism began with Condorcet in the eighteenth century, and continued most notably with Arrow and Riker in the twentieth century. In this powerful book, Gerry Mackie confronts and subdues these long-standing doubts about democratic governance. Problems of cycling, agenda control, strategic voting, and dimensional manipulation are not sufficiently harmful, frequent, or irremediable, he argues, to be of normative concern. Mackie also examines every serious empirical illustration of cycling and instability, including Riker’s famous argument that the US Civil War was due to arbitrary dimensional manipulation. Almost every empirical claim is erroneous, and none is normatively troubling, Mackie says. This spirited defence of democratic institutions should prove both provocative and influential.” (Cover text of “Democracy Defended“)

My point however would be that issues of cycling are of concern, like we see with the Brexit referendum question. The concern causes support for representative democracy with proportional representation, rather than populism with referenda.

The key context is switching to parliaments with PR

Discussions about voting theory best be seen in the context of the switch towards parliaments that are elected with PR and that select the prime minister. The president may have a cerimonial role and be elected by parliament too (like in Germany).

It is most democratic when there is proportional representation (PR) of the electorate in the elected body. The more complex voting methods can then be used by the professionals in the elected body itself only. A prime minister is best elected by a parliament with PR, instead of a president by direct elections.

The interview with Arrow contains a criticism on plurality and FPTP compared to PR.

“Dr. Arrow: Yes. I think definitely. I think there’s no question about that. The Plurality system chokes off free entry. In other words, in the economic world we’re accustomed to the virtues of free entry. We don’t want a small number of corporations to be dominate. We favor the idea of new firms entering in order to compete to bring in new ideas, to bring in new products. Well, the same way in the political field. We should be encouraging free entry, I think, in order to have new political ideas come in. And they may flourish. They may fade. That’s what you want, them to be available. So I’m inclined that the Plurality system will choke off by encouraging, the two-party system will choke off new entry. So I’m really inclined to feel that we don’t want Plurality as a voting system. It’s likely to be very stifling.”

“(…) proportional representation [PR] plays very little role in The United States, but they do play a role in a number of countries. And the question of whether single-member districts are appropriate or not. The Germans, for example, have some kind of compromise between single-member and broader districts. (…)”

See my comparison between the Dutch PR and the UK district system.

Proposals that assume that the voters themselves would use the complexer voting systems – perhaps an enlightened form of populism – are complicating election reform, because these methods put too high demands upon the voters and the electoral process.

In the interview, Arrow referred to the proportional systems, but still expressed the idea that voters themselves would use the three or four categories. In this manner Arrow contributed to this confusion on context.

“CES: If you could, just sort of dictatorially, change something about the way that we do voting in the US, something that would make the biggest impact in your mind, what do you think you would do?

Dr. Arrow: The first thing that I’d certainly do is go to a system where people ranked all the candidates, or as many as they wish, and not just two. And that these data are used in some form or another to choose the candidate, say by eliminating the lowest, or some method of that kind. I’d be interested in experimenting with the idea of categorization and creating interpersonal comparisons by that. And those are the things that I would argue for, and certainly the abolition of the Electoral College. It goes without saying.”

In my experience Arrow is often more confused than one would expect. (1) His original theorem confused voting outcomes and decisions. (2) If he really assumed that people would vote sincerely, then he might as well have assumed cardinality, but he didn’t, for then he wouldn’t have had a theorem. (3) He made a theorem on ordinal preferences but now is inclined to cardinality, even though he defends his theorem that cardinality would be unreasonable and morally undesirable since it doesn’t satisfy APDM a.k.a. AIIA. (4) He now mentions PR but doesn’t draw the conclusion of the selection of the prime minister by parliament, and apparently still thinks in terms of a direct election of the president.

Arrow’s contributions to economics derive from the application of mathematics to economics in the 1950s, and not because he was exceptionally smart in economics itself. Paul Samuelson expressed this idea about himself once too, as a physicist entering into economics. If Arrow had been real smart then he also would have had the common sense to see that his theorem confuses voting results and decisions, and that it amounts to intellectual fraud to pretend that it is more than that.

A major issue is that abstract thinking mathematicians can get lost about reality. In VTFD I show that Amartya Sen is confused about his theorem about a Paretian liberal. Sen’s article with Eric Maskin in the NY Book Review about electoral reform also neglects the switch to a parliamentarian system with PR. A major problem in society is that many intellectuals have insufficient background in mathematics and follow such lost mathematicians without sufficient criticism, even when common sense would warn them.

Warren Smith’s parable of the bees

Warren Smith suggests that bees also use range voting to select the next location for their hive. My problem is that bees aren’t known for strategic voting. My VTFD already suggested – as Jan Tinbergen – that aggregation of cardinal utility would be best indeed. Thus I don’t feel the need to check how bees are doing it.

The problem in voting theory is that humans can vote strategically, also guarded by secrecy in the ballot box. Potentially this strategic vote might be less of a problem when votes for the prime minister in parliament are made public, so that people can wonder why a party has a particular vote. But transparency of the vote might not be the key issue.

Smith on Bayesian regret

Smith has a notion of Bayesian regret, as a more objective criterion to judge voting systems. I am amazed by the existence of such a notion for social optimality and haven’t looked into this yet.

Smith is too enthousiastic about Arrow’s support

Smith interpretes Arrow’s “a little inclined to think” as an endorsement for range voting.  Smith provides full quotes properly – and I must thank him for directing me to this interview with Arrow. But I would advise Smith to be more critical. Arrow mainly indicates an inclination, he is also confused and doesn’t repeal his interpretation of his theorem. Also Smith is advised to grow aware and alert readers of his website that the real improvement in democracy lies not in range voting but in a switch to a prime minister selected by a PR parliament. It is another issue how voting mechanisms operate in other situations, like the Eurovision Song Contest.

Smith’s discussion of the dark horse and the war of the clones

To reduce the options for strategic voting, the voters can be restricted to the use of rankings, and then we get systems like Borda, Condorcet, or my suggestion of the Borda Fixed Point method (BordaFP). The latter wasn’t designed to be a compromise between Borda and Condorcet but still can be seen as one. For example, in the 2010 general elections in the UK, with David Cameron, Gordon Brown and Nick Clegg, it appears that Clegg would be a Borda Choice, but Cameron would still be the BordaFP choice because he would beat Clegg in a pairwise contest.

The reader would enjoy Smith’s discussion of the dark horse and the war of the clones, in his criticism of the Borda method. There is no need for me to repeat his short statement, and I simply refer to here. While you are reading, there is also a picture of Frisian horse Fokke of 2013, and we continue the discussion below it. This discussion is not in VTFD since I mainly pointed to strategic voting but didn’t develop the argument, and thus I thank Smith for his succinct criticism.

 

Frisian Fokke 2013

War of the clones

This assumes the Borda system. Smith (point 8) compares the election between Mush (51%) and Bore (49%) with the election between Mush and some clones Bore1, Bore2, Bore3 (leaving unclear who the real Bore is). Supposedly it is publically known that Mush selects Bore1 in second place, so that the Bores can collect all their votes on Bore1 too. Now Mush loses. This criticism is accurate.  With Condorcet’s rule, Mush would beat all Bores, but the idea of Borda is to mitigate Condorcet. With enough Bores, the BordFP method is not immune to this either.

In above key context, the method would not be applied by the whole electorate but only by parliament. The number of parties would be limited, and each party would only mention one candidate. In the current Dutch parliament there are 13 parties, see Bloomberg with a graphical display of the political spectrum and my analysis on an application of BordaFP. Here the problem doesn’t really arise.

In general people might feel that parties and their candidates differ. If not, then this would require attention. For applications of Borda or BordaFP to smaller committees, it would be sensible to be aware of this. Committees might devise rules about when candidates are too much alike, bunch their votes as if they were one (and rerank), and only call for a decision vote between the clones when they would actually be chosen.

The dark horse

Smith (point 2) considers candidates A, B, C and various nonentities. Kenneth Arrow used the more polite term “irrelevant alternatives”. Let me settle for Dark Horse D. Let me also distinguish truthful voting and strategic voting. In a truthful vote there is no difference between the true preference and the ranking submitted to the ballot box. In a strategic vote there is the strategy provided by the truth and the tactic vote submitted to the box. (Potentially one might design a voting system in which a voter submits those two rank orders simultaneously, but then we must relabel between truth and those two submissions.)

A member of parliament (MP) faces a dilemma. If the MP prefers A > B > C > D then giving the ranks 4, 3, 2, 1 will give 3 points to B, which might cause that B is chosen instead of A. This MP has the incentive to shift points to the Dark Horse, as in 4, 1, 2, 3, hoping that nobody else will vote for this dark horse anyway. If all MPs think in this manner, then the Dark Horse will be elected with an impressive score.

Smith provides an anecdote how such an event happened in the selection of a job application, where there was disagreement about an excellent macro-economist and an excellent micro-economist, whereupon a mediocre candidate got the job.

This is the prisoners’ dilemma. (1) If everyone votes truthfully then they all benefit from the true selection. (2) If everyone votes strategically then they all suffer the worst outcome. (3) Each has an incentive to deflect from the true vote.

The BordaFP method is sturdier than Borda but is not immune to this situation.

A prime answer to Smith is that in parliament the rankings for the selection of the prime minister might be public, so that voters and the press can question party tactics. A party that gives so much points to a Dark Horse might be criticised for not appreciating a better candidate.

Looking for balance

For now, I find Smith’s discussion a bit unbalanced. He emphasizes the disadvantages of Borda, but these have the answers above, for the proper context, while the disadvantages of range voting don’t get as much attention. Range voting stimulates the strategy of giving zero points to alternative candidates, whence it reduces to plurality with all its drawbacks. A candidate with 51% of the vote in plurality might not be better, since more extremist, than a candidate with a higher Borda score who is more moderate. The main point remains that the key issue is that countries with district voting like the USA, UK and France better switch to PR.

By way of conclusion

It remains true that Borda has the risk of a Dark Horse, and that the search for better algorithms is open. How can we elicit information from voters about their true preferences ? In the ballot box we might numb their brains so that they vote like bees (perhaps also with the dance) ?

An idea that I already mentioned at another place: MPs might submit two inputs, one with the strategy (supposed to be true) and one with the intended tactic. (One would design a test whether these better be rankings or ranges.) The intermediate result would be based upon the tactics. A random selection of the true preferences then is used to revise the tactics to improve the results for those MPs who have the luck to be selected. This prospect encourages MPs to be truthful about the strategy.

Another possibility for such double submissions: One might first determine the outcome according to the submitted strategies (supposedly true) and then use a random selection to use the allowed tactics, and only uses these if they indeed cause an improvement in the eyes of the MP. This sanctions a moderate degree of unavoidable strategic voting, but reduces the chaos when all do it without information about others.

Such calculations are simple for a partial outcome for a single MP. The problem lies in the aggregation of all MPs. Perhaps money helps in solving this too. Voters in the electorate aren’t allowed to sell their vote directly, with the obvious horror stories, also involving the distribution of income. But in parliament there is coalition bargaining which involves money, i.e. budget allocations. Potentially this helps in designing better algorithms. Perhaps the Bayesian Regret comes into play here, but I haven’t checked this. In Holland there is professor Frans Stokman who studies coalition bargaining with his “Decide” model.

Thus the search for better voting schemes hasn’t ended. Yet the main step for the USA, UK and France would be to accept the choice of a prime minister by parliament selected by PR.

The Theresa May government has adopted Brexit as its policy aim and has received support from the Commons. Yet, economic theory assumes rational agents, and even governments might be open for rational reconsideration, even at the last moment.

Scientifically unwarranted referendum question

Based upon voting theory, the Brexit referendum question can be rejected as scientifically unwarranted. My suggestion is that the UK government annuls the outcome based upon this insight from science, and upon this insight alone. Let me invite (economic) scientists to study the argument and voting theory itself, so that the scientific community can confirm this analysis. This study best be done all over Europe, so that also the EU Commission might adopt it. Britons might be wary when their government or the EU Commission would listen to science, but then they might check the finding themselves too. A major worry is why the UK procedures didn’t produce a sound referendum choice in the first place.

Renwick et al. (2016) in an opinion in The Telegraph June 14 protested:

“A referendum result is democratically legitimate only if voters can make an informed decision. Yet the level of misinformation in the current campaign is so great that democratic legitimacy is called into question.”

Curiously, however, their letter doesn’t make the point that the referendum neglects voting theory, since the very question itself is misleading w.r.t. the complexity of the issue under decision. Quite unsettling is the Grassegger & Krogerus (2017) report about voter manipulation by Big Data, originally on Brexit and later for the election of Donald Trump. But the key point here concerns the referendum question itself.

The problem with the question

The question assumes a binary choice – Remain or Leave the EU – while voting theory warns that allowing only two options can be a misleading representation. When the true situation is more complex, then it may be political manipulation to reduce this to a binary one. As a result of the present process, we actually don’t know how people would have voted when they had been offered the true options.

Compare the question:

“Do you still beat your mother ?”

When you are allowed only a Yes or No answer, then you are blocked from answering:

“I will not answer that question because if I say No then it suggests that I agree that I have beaten her in the past.”

In the case of Brexit, the hidden complexity concerned:

  • Leave as EFTA or WTO ?
  • Leave, while the UK remains intact or while it splits up ?
  • Remain, in what manner ?

Voting theory generally suggests that representative democracy – Parliament – is better than relying on referenda, since the representatives can bargain about the complex choices involved.

Deadlocks can lurk in hiding

When there are only two options then everyone knows about the possibility of a stalemate. This means a collective indifference. There are various ways to break the deadlock: voting again, the chairperson decides, flip a coin, using the alphabet, and so on. There is a crucial distinction between voting (vote results) and deciding. When there are three options or more there can be a deadlock as well. It is lesser known that there can also be cycles. It is even lesser known that such cycles actually are a disguised form of a deadlock.

Take for example three candidates A, B and C and a particular distribution of preferences. When the vote is between A and B then A wins. We denote this as A > B. When the vote is between B and C then B wins, or B > C. When the vote is between C and A then C wins or C > A. Collectively A > B > C > A. Collectively, there is indifference. It is a key notion in voting theory that there can be distributions of preferences, such that a collective binary choice seems to result into a clear decision, while in reality there is a deadlock in hiding.

Kenneth Arrow (1921-2017) who passed away on February 21 used these cycles to create his 1951 “impossibility theorem”. Indeed, if you interprete a cycle as a decision then this causes an inconsistency or an “impossibility” w.r.t. the required transitivity of a (collective) preference ordering. However, reality is consistent and people do really make choices collectively, and thus the proper interpretation is an “indifference” or deadlock. It was and is a major confusion in voting theory that Arrow’s mathematics are correct but that his own verbal interpretation was incorrect, see my VTFD Ch. 9.2.

Representative government is better than referenda

Obviously a deadlock must be broken. Again, it may be manipulation to reduce the choice from three options A, B and C to only two. Who selects those two might take the pair that fits his or her interests. A selection in rounds like in France is no solution. There are ample horror scenarios when bad election designs cause minority winners. Decisions are made preferably via discussion in Parliament. Parliamentarian choice of the Prime Minister is better than direct election like for the US President.

Voting theory is not well understood in general. The UK referendum in 2011 on Proportional Representation (PR) presented a design that was far too complex. Best is that Parliament is chosen in proportional manner as in Holland, rather than in districts as in the UK or the USA. It suffices when people can vote for the party of their choice (with the national threshold of a seat), and that the professionals in Parliament use the more complexer voting mechanisms (like bargaining or the Borda Fixed Point method). It is also crucial to be aware that the Trias Politica model for democracy fails and that more checks and balances are required, notably with an Economic Supreme Court.

The UK Electoral Commission goofed too

The UK Electoral Commission might be abstractly aware of this issue in voting theory, but they didn’t protest, and they only checked that the Brexit referendum question could be “understood”. The latter is an ambiguous notion. People might “understand” quite a lot but they might not truly understand the hidden complexity and the pitfalls of voting theory. Even Nobel Prize winner Kenneth Arrow gave a problematic interpretation of his theorem.The Electoral Commission is to be praised for the effort to remove bias, where the chosen words “Remain” and “Leave” are neutral, and where both statements were included and not only one. (Some people don’t want to say No. Some don’t want to say Yes.) Still, the Commission gives an interpretation of the “intelligibility” of the question that doesn’t square with voting theory and that doesn’t protect the electorate from a voting disaster.

A test on this issue is asking yourself: Given the referendum outcome, do you really think that the UK population is clear in its position, whatever the issues of how to Leave or risk of a UK breakup ? If you have doubts on the latter, then you agree that something is amiss. The outcome of the referendum really doesn’t give me a clue as to what UK voters really want. Scotland wants to remain in the EU and then break up ? This is okay for the others who want to Leave ? (And how ?) The issue can be seen as a statistical enquiry into what views people have, and the referendum question is biased and cannot be used for sound statistics.

In an email to me 2016-07-11:

“The Electoral Commission’s role is to evaluate the intelligibility of referendum questions in line with the intent of Parliament; it is not to re-evaluate the premise of the question. Other than that, I don’t believe there is anything I can usefully add to our previously published statements on this matter.”

Apparently the Commission knows the “intent of Parliament”, while Parliament itself might not do so. Is the Commission only a facilitator of deception, and they don’t have the mission to put voters first ? At best the Commission holds that Whitehall and Parliament fully understood voting theory therefor deliberatedly presented the UK population with a biased choice, so that voters would be seduced to neglect complexities of how to Leave or the risks of a UK breakup. Obviously the assumption that Whitehall and Parliament fully grasp voting theory is dubious. The better response by the Commission would have been to explain the pitfalls of voting theory and the misleading character of the referendum question, rather than facilitate the voting disaster.

Any recognition that something is (very) wrong here, should also imply the annulment of the Brexit referendum outcome. Subsequently, to protect voters from such manipulation by Whitehall, one may think of a law that gives the Commission the right to veto a biased Yes / No selection, which veto might be overruled by a 2/3 majority in Parliament. Best is not to have referenda at all, unless you are really sure that a coin can only fall either way, and not land on its side.

Addendum March 31

  • The UK might repeal the letter on article 50 – see this BBC reality check. Thus science might have this time window to clarify to the general public how the referendum question doesn’t comply with voting theory.
  • The recent general elections in Holland provide another nice example for the importance of voting theory and for the meaning of Arrow’s Impossibility Theorem, see here.
Literature

BBC (2017), “Article 50: May signs letter that will trigger Brexit“, March 29

Carrell, S. (2017), “Scottish parliament votes for second independence referendum“, The Guardian, March 28

Colignatus (2001, 2004, 2011, 2014), “Voting theory for democracy” (VTFD), pdf online, https://zenodo.org/record/291985

Colignatus (2010, “Single vote multiple seats elections. Didactics of district versus proportional representation, using the examples of the United Kingdom and The Netherlands”, May 19 2010, MPRA 22782, http://mpra.ub.uni-muenchen.de/22782

Colignatus (2011a), “The referendum on PR“, Mathematics Teaching 222, January 5 2011, also on my website

Colignatus (2011b), “Arrow’s Impossibility Theorem and the distinction between Voting and Deciding”, https://mpra.ub.uni-muenchen.de/34919

Colignatus (2014), “An Economic Supreme Court”, RES Newsletter issue no. 167, October 2014, pp.20-21, http://www.res.org.uk/view/art7Oct14Features.html

Colignatus (2016), “Brexit: advice for young UK (age < 50 years), and scientific outrage for neglect of voting theory“, weblog text June 29

Colignatus (2017), “The performance of four possible rules for selecting the Prime Minister after the Dutch Parliamentary elections of March 2017″, March 17, MPRA 77616

Grassegger, H. and M. Krogerus (2017), “The Data That Turned the World Upside Down”, https://motherboard.vice.com/en_us/article/how-our-likes-helped-trump-win

Renwick, A. e.a. (2016), “Letters: Both Remain and Leave are propagating falsehoods at public expense“, The Telegraph, Opinion, June 14

From the BBC website