What's fairest for a voting referendum?
This is a little off-topic maybe, but I've been thinking about one aspect of the electoral reform debate which I've not seen mentioned anywhere else.
(If there's a connection with freedom of information, perhaps it's that electoral reform and FOI are both aspects of constitutional reform which some see as part of a democratic renewal process.)
Electoral reform is now rising up the political agenda. It's widely accepted that a new voting system is such a fundamental change that it could only be adopted if a referendum on the idea was held first. But that surely prompts the question: what should be the voting system used in such a referendum?
The outcome could be very different according to that decision.
Suppose there were four options on offer for voting systems - the current First Past the Post system (FPTP), the Alternative Vote (AV) supported by some Labour electoral reformers, the Single Transferable Vote (STV) backed by the Liberal Democrats, and Borda, a points-based system advocated by those who see it as a more consensual approach. (A full explanation of each system is given below).
Suppose also that there are 100 voters and they happen to be divided into four opinion groups, with their order of preference for the voting system as follows:
So what would happen if there was a referendum with all four options on the ballot paper with the votes counted under the various systems (assuming no tactical voting).
If FPTP was used to count the result of the referendum, it would win; if AV was used it would win; if STV was used it would win; and if Borda was used it would win.
Under FPTP only the first preferences matter, FPTP has the most and it wins.
Under AV, the bottom two on first preferences (STV and Borda) are eliminated; FPTP gets no second preferences while AV gets 24 (from those who put STV first) to add to its 27 first preferences, so it scores 51, overtakes FPTP's 28 and wins.
Under STV, just Borda is eliminated on the first round. Since the 21 second preferences of those who put Borda first go to STV, on the second round STV has 45 votes and AV is now bottom as it still has 27. So AV is now eliminated, STV picks up another 27 votes in second preferences, so it now has 72 votes and beats FPTP, still on 28, in the final round.
Under Borda, FPTP scores 205 points, AV scores 257, STV scores 268, while it is Borda which seizes victory with 270.
Thus under this distribution of public opinion, each system wins if and only if the votes are counted in line with that system.
So what would be the fairest system for a referendum on electoral reform? Maybe what we need is a referendum to decide which voting system should be used in a referendum...?
Notes on each voting system:
• First-past-the-post (FPTP), the system currently used for UK general elections. Voters have one vote and the candidate with the most votes wins.
• Alternative vote (AV), as used in Mayoral elections, also known as the Supplementary Vote. Voters mark a first and a second preference. The first preferences are counted and all except the top two candidates are eliminated. The second preferences of the eliminated candidates are examined and where they are for either of the top two they are added to that candidate's total. The candidate from the initial top two with the highest total of first preferences plus second preferences transferred from eliminated candidates wins.
• Single transferable vote (STV). Since the point of such a referendum would be to choose one voting system, this case would be like STV in a single-member constituency where it works as follows. Voters list candidates in order of preference. After the first preference count, the bottom candidate only is eliminated, and his/her second preferences are added to the totals for the other candidates in line with those preferences. After this the candidate who is now bottom is eliminated, and more second/third preferences are transferred. Then the bottom candidate is eliminated and this process continues until only two are left and the candidate with the higher total of votes including transferred preferences is elected.
• Borda count - as with STV, voters list candidates in order of preference, but unlike STV Borda is a points-based system. If there are four candidates and the voter puts them all in order of preference, a first preference is worth four points, a second is worth three points, a third is worth two, and a fourth is worth one. The candidate with the highest points total wins.
A 
© MMIX~RS~q~RS~~RS~z~RS~18~RS~)
Comments
Sign in or register to comment.
There is another way of making a good choice though and it suggests that AV should win in this experiment:
If you conduct a series of pairwise elections, then AV narrowly beats every other option.* It is therefore the 'Condorcet' winner, and it's pretty difficult to argue that it isn't the best compromise. Trouble is that sometimes there isn't a Condorcet winner because A is preferred over B, B preferred over C, and C preferred over A. Oh well...
* AV beats FPTP and Borda by 1 vote and STV by 5
Complain about this comment
I apologise if the following comment is too long. Please feel free to delete it if it is.
With the approach set out here you suffer from two problems.
The first is Arrow's Impossibility Theorem. This states (very roughly) that no method of aggregating preferences that satisfies four reasonable conditions (non-dictatorial, able to handle any number of options, pareto efficient, and not sensitive to irrelevant alternatives) can be guaranteed not to produce a cyclic ordering of aggregate preferences. A majority (for example) may prefer option A over Option B, Option B over Option C, and Option C over Option D, and Option D over Option A.
The actual result can depend on the actual aggregation device used, and in particular on who chooses (or pre-vets) the options.
The second problem is related to the first. It is that you've already limited the option set to the four voting systems described.
But who decided that??? What if the People want some other option entirely - a dictatorship, or a direct democracy, or a lottery?
In other words, when deciding upon a decision-making system, how do you decide which decision-making system to use.
We may observe that - in deciding upon a decision-making system - there is no self-evident principle by which the preference of one individual may be privileged over the preferences of others a priori (i.e. without reference to a previously chosen decision-making system).
(That is not to say that some people do not believe that their own preferences should prevail. But such a belief is itself nothing but a preference, and - by application of the foregoing observation - there is no known means by which it may be privileged.)
Secondly, there is only one method of aggregating preferences that does not require the a priori privileging of some over others. That is an aggregation in which all preferences are aggregated with equal weight (so that none is privileged) and in which the options to be voted upon are not pre-vetted by a subset of individuals (since pre-vetting would privilege the preferences of the subset).
A series of referendums in which the citizens themselves can initiate options allows reforms to be decided without a priori privileging. Such a system operates (as an ongoing system) in a country such as Switzerland where the People enjoy the right of initiative. It provides a basis for continued legitimacy, in the sense that the People - if they do not approve of the way in which their government is constituted - may call for it to be changed at any time
In this case Arrow's Theorem does not apply. Rather than trying to find an aggregation device which can handle any number of options while satisfying Arrow's conditions, this approach identifies the aggregation first, and tests successive options until one of them satisfies the conditions of that aggregation device.
No doubt if there is an error in this logic, one of your readers will point it out!!
Complain about this comment
The difference between FPTP and other systems is for me very simple.
1. Under FPTP voters vote "for" something - of course the disadvantage is that the number of people who vote "for" the winner need only be very small if everyone else has a very diverse range of views.
2. Other systems produce results which can best be described as that which the voters disliked least. Of course the winner has a genuine majority of votes but most of the votes would have been at best half hearted.
Most PR/AV systems encourage tactical voting - if you can not get someone to vote for you then get them to vote for you second, almost guarantees politics goes into stasis as no party would ever suggest radical ideas, they might keep their core vote but lose all those vital second preferences.
FPTP produces 2 party politics, relatively stable govts, that are usually reasonably easy to kick out and an absence of single issue MPs and extremists - overall not a bad system although could do with some tweaks.
PR based systems tend to produce - extremists or single issue politicians getting seats (see EU election) and either totally unstable govt (eg Italy) because there are too many parties in coalition, or incredibly stable govts where it takes 20+ years to change (for which of the post WW2 era, Germany and Sweden are good examples). The first ensures pork barrel politics and corruption (whether you do a good job or not does not matter because the govt will change within months, so you might as well go on the take) and the latter as UK local politics has shown time and again, guarantees corrupt politics because you will not lose your job even if you are corrupt.
Complain about this comment
I have to agree with your second commentator that the selections being offered are too limited.
However we are talking about a vote on how to elect 400+ people to Parliament and so we should not confuse the matter by applying the voting principles to the referendum.
With approximately 40 million votes being cast in a referendum with only one outcome then the option of voting in a FPTP way is perfectly legitimate. However what all the 4 options suggested have in common is that they are non proportional. In fact FPTP can actually be more proportional than the other options as they are geared towards limiting the voting power of minority groups. AV was suggested as an option for the Scottish Parliament until it was pointed out that it gave too much emphasis to Labour. The sudden interest in electoral reform is geared towards a single outcome, Labour's self interest in creating a system that prevents the Conservatives from gaining an overall majority. However their preferred methods will also reduce Democracy in this country by making it much harder for independents to get elected while also diminishing the Lib Dems's share of the vote. Currently nearly a 3rd of the country could vote Lib Dem and they still get less than 10% of the seats, Labour's plan could actually reinforce this bias.
Complain about this comment
Donatio: I've seen a set of preferences for five candidates that gives five different results under FPTP, Supplemental Vote (that Martin calls AV), Alternative Vote (that Martin calls STV), Borda and Condorcet
MorrisStephen: In that situation, you're allowing voters to vote on sequential 2-option votes (by any voting system, it doesn't make a difference) to either change or not change. This is identical to "pairwise voting with a fixed agenda", which fails the "independence of irrelevant alternatives" Arrow criterion. Consider the situation where you have three options in a Condorcet cycle (A > B > C > A)
Complain about this comment
There should never be more than two options yes or no simples.
Complain about this comment
It would be helpful if rather than give academic examples, real life voting figures were used. I nice exercise for someone to go through the published voting figures for the last x elections and use them in the various methods and compare the results they produce compared to actual results.
Complain about this comment
JonAxtell: Unfortunately, because proportionality systems other than list systems (as used in the EU elections) rely on rankings rather than just putting a cross in a box, it is virtually impossible to use those results to translate to a propertionality result.
The only recent election that could yield data is the London Mayoral election which uses the Supplemental Vote (here called AV) system. The downside of that is only first preferences are recorded unless the first preference is knocked out and the second preference is for one of the top two candidates. Even then we can't tell which votes went to which second preference. As ballot papers are destroyed a year after the election there would not be enough raw data out there anyway.
If any option other than FPTP was chosen, we'd be going in fairly blind as to the outcome.
Whichever is chosen, *all* the new alternatives a pain to count by hand...
Complain about this comment
In response to _cim_, last night's comment was written very late and very quickly, and I may not have explained myself very well.
You are indeed correct that theoretically this might give rise to a aggregate cyclic preference ordering.
I actually intended to make the point that - in realistic situations - the available options are not simple and mutually exclusive - unlike the examples given here. In practice, the "options" that form an actual constitution are complex compromises that may be tailored (the process of "horse-trading" or just "trading") until one is devised which satisfies the conditions of the previously identified aggregation device.
Arrow's Theorem always has the potential to hold. But that doesn't mean it must actually arise in every circumstance.
It is a theoretical possibility that certain features may be so important and so mutually exclusive that they could form a cycle in which the People keep going to a referendum choosing first A, then B, then C, then A again, and so on.
However, in practice, this is very unlikely. In practice, it is more likely that someone will devise a compromise that satisfies the device and is stable over time . . . if for no other reason than the People get fed up with voting!! In practice, we might reasonably expect the system to settle down into a stable equilibrium.
The interesting thing about the equally-weighted aggregation device without pre-vetting is that it provides a logical means of choosing a device that relies only on the condition of universalisability (i.e. it makes no difference how one changes the labels of the individuals involved) rather privileging the preference of any labelled individual.
Complain about this comment
JonAxtell/RobT: Additionally, because changing the voting system would change which seats were marginal and which voters were important to the final result, you can't assume that the parties would campaign in the same way (either in their policies or where they concentrate their campaign funding), which means you can't assume that voters preferences would stay constant.
MorrisStephen: For issues of policy, cycles are indeed unlikely, as it's rare that more than two options will get widespread support. For election of representatives, on the other hand, repeated iterations of "would you prefer X to the current incumbent" are unlikely to be satisfactory in practice. Condorcet counting of all options together is a more efficient approach in that case, and doesn't lose anything, but the problem with Condorcet (as with any non-proportional system, such as Borda or AV - but not STV or Lists) is that it means that 51% of the electorate can control 100% of the seats.
Complain about this comment
The benefit (to Labour) of a supplemental vote is that they perceive the majority of the UK as being left-of-centre and that therefore any position where Labour come a close second to the Tories will result in a Labour win as the Lib-dem vote presumably will vote generally for Labour.
However we have to look at the situation where a Government is so despised that large amounts of TV come in - in the 'ABL' - anything but Labour scenario. In this situation the converse would happen - Lib Dems would vote 'Anti-Labour' i.e. conservative in their second votes resulting in Labour losing many seats that they might have won.
Complain about this comment
A Transfer system is essential. So is a mechanism to include disaffected electorate - 60% of the electorate did not vote at the last EU election. Maybe there should be a box on the voting slip to show disaffection with all candidates (rather than vote BNP). An election where the total vote is less than 50% of the electorate should be null and void and repeated!
I feel let down by those who did not vote almost as much as I feel let down by the major parties who prefer to slag each other off rather than work together to solve the problems of the country!
Complain about this comment
In all the media presentations, only the % of those who voted was shown on the graphics. This is statistically incorrect. Especially since 60% of the electorate did not vote at the EU election - this should be shown loud and clear!
Complain about this comment
The Schulze method (http://en.wikipedia.org/wiki/Schulze_method) should also have been included in the list. It's a preferential voting system from 1997 which works by repeatedly removing the weakest defeat until ambiguity is removed. Some will criticise it as being complicated, but isn't that a price worth paying to make sure we get the most democratic system?
Also, we must get rid of FPTP, but it would be a travesty if we were to replace it with the system (Alternative Vote Top-up, or Alternative Vote Plus (AV+)) chosen by the Independent Commission on the Voting System (the Jenkins Commission) which Blair gave certain conditions to to make sure it's conclusions would be favourable to the interests of the Labour party. If we change the system we must do so to benefit the country, not the Labour party.
Complain about this comment
Grrrr! I thought at least when Nick Robinson corrected himself, the misunderstanding regarding AV was over with the BBC. Evidently not.
Martin - AV is not, I repeat NOT, the same system as Supplementary Vote. It is not used for the London Mayoral elections. Wikipedia is your friend. AV is, for all intents and purposes, the same as STV for single-winner elections is.
The reason AV is distinguished from STV is simply one of clarity - STV tends to be associated with the multi-member constituency system.
In short, Supplementary Vote is a distinct, separate system from AV.
Complain about this comment
Even having gone to some lengths to arrange the numbers as you have you seem to accept that the current, in my view corrupt, electoral system would only get the support of about 28%.
Since at the EU elections the Conservatives & Labour, the only parties that gain from FPTP & coincidentally the only ones that support it, got 44% combined I suspect the real figure would not be higher than that. I also think that if the poll were run FPTP on that basis the electorate, who are not as simple as the political classes like to think, would mostly choose to go for the most popular PR system. This is called tactical voting & is common in FPTP elections. That the people feel we have to try & outsmart the system to get near to what we actually want is, itself, strong evidence that the system represents us badly.
Complain about this comment
I've had very similar thoughts about what would happen in a situation where each voting system gives a different winner. It interesting to see an example.
I agree with many of the other comments here, non voters should always be reported in statistics and I really like the idea of "None of the above" option. When I was a Student we always had a reopen nominations option.
Seems to me that no option is going to be perfect but most are better than what we have. So pick something a move forward, rather than being stuck with the status quo because nothing ticks all the boxes.
Complain about this comment
I was under the impression that under the Borda system, each candidate was awarded one point for every candidate ranked below him/her on each ballot paper. In a four candidate election, the candidate ranked first on the ballot paper would receive 3 points, the second candidate, 2 points, the third candidate, 1 point and the last candidate, 0 points. I believe that Professor Michael Dummett explained the system in this way. Understood like this, the Borda system would still leave the possibility open of a candidate receiving no points (if they were ranked last on every ballot paper). Can anyone confirm if this is indeed the case, as the article assumes that Borda awards points to all candidates?
Complain about this comment
Little of Justin's comment makes sense to me
> Under FPTP voters vote "for" something..most PR/AV systems encourage tactical voting
In reality the UK experience is that FPTP produces widespread tactical voting, because so many votes are otherwise wasted
> FPTP produces...govts that are usually reasonably easy to kick out
but sadly a lot of MPs who are more or less safe whatever they do (or don't do)
> PR based systems tend to produce...either totally unstable govt or incredibly stable govts
which suggests that it isn't the PR that's doing the "producing", but the politics and culture of the various countries concerned...
Complain about this comment
I think that voting should be like the census, compulsary and conducted by person, post, electronically, or proxy.
The proxy vote would sort out the local councillors, and make sure they do some work for their individual community.
In person, or by post for people who want to hide their voting preference.
Electronically either at home or at a polling station would also give more speedy results.
There must also be a box for do not agree with any of the candidates or policies, this would indicate satisfaction with the polititians in the arena. Or the general mood of the population as a whole.
Complain about this comment
View these comments in RSS