Tag Archives: voting

Ranked choice and most-least voting

I recently realised that two systems proposed as “PR-lite” or “a step towards full PR” can produce radically different outcomes IN REALITY and not just as a THEORETICAL CURIOSITY. The two are “single candidate ranked choice” and “most-least voting – MLV”, most notably when there are just three candidates.

Here’s the deal. Under ranked choice you must rank all three candidates, 1, 2 & 3 (most preferred to least preferred). Under most-least voting you indicate only the “most preferred” (rank 1) and least preferred (with 3 candidates, rank 3). The OBSERVED set of data should be the same. (I’m not going to get into the issue of why they might not – that gets into complex mathematics and I’ll do it another time).

For those who don’t want to get bogged down in the following discussion of the maths, here’s why the two systems can, given EXACTLY the same observed count data, give a different “winning candidate”. Ranked voting essentially tries to identify the (first or second best) candidate that the people-supporting-the-losing-3rd-party-candidate are “most happy with”. Under MLV, if both “first” and “second” preference candidates are diametrically opposite (and mutually hated) then NEITHER should necessarily be elected. The candidate who came a (very very) distant third can be elected if (s)he is NOT HATED by anyone. Essentially, if you polarise the electorate you are penalised. A “centrist” who hasn’t either “enthused” or “repelled” anyone will win under MLV.

I tended to think this was a “theoretical curiousity”. However, upon looking more closely at the 2016 Iowa Democratic Presidential primary I realised this ACTUALLY HAPPENED. Bernie Sanders and Hillary Clinton were essentially tied on about 49.5% each in terms of their “primary first preference vote”. Hillary had the edge, and the 3rd candidate, O’Malley dropped out (but too late so he got votes). Yet he was actually the key influencer, if either ranked voting or MLV had been used. Under ranked choice, either Hillary or Bernie would have won (determined by who the majority of O’Malley’s supporters put as second preference). Under MLV, and assuming that the “much talked about antipathy between Bernie and Hillary was real” then each candidate’s supporters would have put the other as “least preferred”. The “most-minus-least” counts would have been slightly negative for one and likely both candidates. O’Malley, on the other hand, would have obtained a small positive net most-minus-least vote (getting 1 to 2% of the vote, with few/no people putting him as “least preferred”). MLV simply subtracts the “least preferred” total from the “most preferred” total for each candidate giving a “net support rating”.

Under ranked choice voting either Hillary or Bernie would have won. Under MLV both would have been denied the win in favour of O’Malley, because he “pissed nobody off”.

Here’s the more detailed discussion.

Most-Least Voting (MLV) is a special case of a more general method of “stated preferences” called Best-Worst Scaling (BWS). Declaration of interest: I am a co-author on the definitive CUP textbook on BWS, was involved (along with its inventor) in much of the theoretical development and application in various fields (most notably health). HOWEVER I have had no involvement with the theory, parameterisation or application of MLV. Indeed, once I became aware of this method of voting, on checking the bibliography, it became clear that the authors were not actually aware of BWS and due to the “silo effect” in academia, had come up with it largely independently of what we had already done. Incidentally some of the Baltic States have used or do use MLV in certain instances so it isn’t just a “theoretical curiosity”.

OK, having got that out the way, what do I think of MLV? In short, I think it is worthy of serious consideration and wish we’d thought of it first! Like ranked choice voting with single member constituencies (something in use or proposed in various Anglo-Saxon countries like Australia, the UK and USA), it is not “proper” Proportional Representation (PR). However, it can be considered either as a nice compromise, or as a stepping stone to “full PR”. In terms of its similarities to ranked choice voting: suppose there are 5 candidates in your constituency. Under ranked choice, for the maths to not be horribly skewed and potentially very very gameable, you should be forced to rank all five, 1,2,3,4,5. The problem, known since the mid 1960s, is that people are good at “top” and “bottom” ranks but get very “random” and arbitrary “in the middle”. MLV exploits this. It only asks for top and bottom. Thus it may be considered to be the “minimum change to first-past-the-post – FPTP – possible” so as to “make things easy for people”. You only provide ONE extra piece of information – the candidate/Party you like least. If you do not provide both a MOST and a LEAST choice then your ballot is spoilt. This is IMPERATIVE for the maths to work, and for the system to be demonstrably “equitable”. (Most-minus-least vote totals must sum to zero.)

The common question is “Suppose there are only three candidates – aren’t ranked choice and MLV the same?” NO. See above for a real life example. Ranked choice MIGHT be unconstitutional in certain countries (if the mathematicians and lawyers got together because not everyone has the “same influence” mathematically).

So what is happening in practice?  The authors conclude that if the “FPTP winning” candidate espouses (say) a very extreme policy on (say) immigration or something, that all other parties abhor, then (s)he is likely to lose. All other parties “gang up” and place that candidate as “least”. Most-minus-least vote tally is net (highly?) negative. A more “moderate” candidate likely wins. Indeed, the authors claim that “centrists” likely prevail a lot of the time – though they might be an “O’Malley with 1% primary vote”. Though if a candidate would get a MAJORITY (and not just a PLURALITY) under FPTP, they’ll still win under MLV. So “majority” (non-coalition) governments still can happen – they’re just harder to achieve and “third parties” (etc) much more easily get a foothold. I happen to think that this “centrists rule” conclusion is a little simplistic when you move from a single dimension (left/right) to multidimensional space. Yes, maybe you get a candidate closest to the centroid across all dimensions but “how strongly people regard each dimension” can affect results. So, as they frustratingly say in academic papers, it’s “an empirical issue” as to what will happen. However, I will venture a conclusion that “extremists” will naturally get weeded out. Whilst some extremists might be generally considered bad (consider dictators who were first voted in via pluralities in 1930s Europe), others (painted as “extremists” by the MSM like a Sanders today or an Attlee or FDR of yesteryear) could be considered necessary and without them society would be much worse off. It gets necessarily subjective here…!

TL;DR: Arrow’s Impossibility Theorem still holds. MLV doesn’t solve all problems but it is attractive in addressing a lot of the most commonly made criticisms of voting systems used in the UK and USA. However, it isn’t the ONLY system that can address these criticisms – it is merely the “simplest” in terms of practicality and requiring “minimum extra effort by voters beyond what they do now”. Whether you “like it” depends on your “values”.

 

Labour voting reform?

So. Zoe Williams has thrown the cat amongst the pigeons with a piece attempting to predict the result of the Labour leadership election. She has interesting insights, some obvious, some perhaps less so. One that most would consider obvious is:

There are some known knowns: Thornberry, if trends continue, won’t make the ballot. 

I agree. So we’re probably down to a three horse race, Long-Bailey, Nandy and Starmer. As Williams points out, actually it is pretty difficult to pin down at least the latter two regarding their “true values”. What they’re saying during this campaign is not necessarily the best guide. I’m someone with a multi-decade career in examining preferences; looking at revealed preferences – what a person has DONE ALREADY, is often (though far from exclusively) the best way to understand what they value. Thus Williams has attempted to look at their votes in Parliament, among other actions. It’s still an uphill task but she should be admired for trying.

Her main conclusions:

  • Long-Bailey won’t finish third in the first round of voting so won’t be eliminated;
  • In circumstances where she HAS come third, her supporters’ preferences have almost all gone to Nandy;
  • Supporters of Starmer almost all put Nandy as second preference;
  • Supporters of Nandy almost all put Starmer as second preference.

For those of you who know my background – co-author of the definitive textbook on Best-Worst Scaling, you probably have had the “aha” moment already. However, for others, I’ll guide you through something I freely thought was probably more of a “theoretical curiosity” than a real possibility in a real election. I’m quite fired up!

IN SHORT:

  • UNDER THE (SEMI-PROPORTIONAL) EXISTING ALTERNATIVE VOTE (RANKING – SPECIAL CASE OF SINGLE TRANSFERABLE VOTE) SYSTEM, STARMER WILL LIKELY WIN;
  • UNDER A HYPOTHETICAL (VERY NON-PROPORTIONAL) FIRST-PAST-THE-POST SYSTEM (CURRENTLY USED AT WESTMINSTER), LONG-BAILEY WOULD LIKELY WIN;
  • UNDER ANOTHER SEMI-PROPORTIONAL SYSTEM – MOST-LEAST VOTING – NANDY WOULD LIKELY WIN.

So, using the same set of rankings, 1, 2 & 3 from every Labour voter, we could have ANY ONE OF THE THREE LIKELY CANDIDATES WIN, DEPENDING ON THE VOTING SYSTEM. Voting enthusiasts will have likely watched “hypothetical” cases on YouTube etc showing artificial data that could do this. But I genuinely believe, if Zoe Williams is correct, that we might be about to see real data in a real election that demonstrate this phenomenon!

Before I go any further, I shall make two things clear:

  1. The Labour leadership voting system is established. It is ranked voting (Alternative Vote). This is merely a thought exercise intended to spur debate about the Labour Party’s policy for electoral reform at Westminster.
  2. Plenty of people have discussed the existing FPTP used at Westminster, and AV (as a “compromise” measure between FPTP and “full Proportional Representation – PR”). Unfortunately AV lost the referendum on electoral reform – badly – several years ago. Thus I want to illustrate another “semi-proportional compromise” that might prove more acceptable to the British public – Most-Least Voting.

2020 LABOUR POSSIBLE RESULT

CLICK ON IMAGE TO ENLARGE.

Understandably, there are NO hard data on the relative percentages of support for the (assumed) three candidates likely to qualify for the final round involving the general membership of the Labour party. I’ve used some, I hope not unreasonable, guesstimates, based on YouGov figures (when there were 4 or 5 candidates, but the bottom two together accounting for <10%).

THESE FORM THE FIRST PREFERENCE (ROUND ONE) PERCENTAGES FOR THE THREE CANDIDATES.

For round two, it is pretty obvious Nandy will be eliminated.

The question becomes, “To whom do her supporters’ votes go?”

For that, I use the information from aforementioned article by Zoe Williams in the Guardian. Unless Long-Bailey has a MUCH bigger lead over Starmer than seems reasonable at the moment, and unless Zoe’s finding that Nandy’s supporters are likely to put Starmer as 2nd is totally wrong, then Starmer is likely to win after redistribution. End of story. RED FIGURES.

Under a hypothetical First-Past-The-Post (FPTP) system (as used for Parliamentary constituencies at Westminster) there’s a good chance Long-Bailey would have won – with probably a plurality but not majority (i.e. not >50% but beating the other two). BLUE FIGURES.

Most-Least Voting (GREEN FIGURES) may require some exposition since only regular readers will be familiar with it. M-L voting works on the principles that:

  • Voters MUST, for a “valid, non-spoilt ballot”, indicate their MOST PREFERRED and LEAST PREFERRED candidates.
  • So a voter gives just TWO pieces of information, “most” and “least”. Clearly, as the number of candidates increase, this becomes MUCH easier than AV, involving a “full ranking”. Oodles of research (see aforementioned textbook co-authored by me) demonstrates that people are TERRIBLE at full rankings and that this has VERY REAL problems in terms of producing a candidate that is mathematically “the best” – the statistical rules that MUST hold for the AV algorithm to “work” almost never hold. This might be why Aussies are increasingly disliking AV – I lived there for 6 years and saw it in action. Believe me, I’ve seen the stupid results it can produce.
  • Now, with only three candidates, like here, giving ranks 1, 2 & 3 seems identical to just selecting “most” (rank one) and “least” (rank three). Yes, the information is identical – ASSUMING THE FORMAT OF THE QUESTION HAS NOT INDUCED DIFFERENT “GAMING OF THE SYSTEM i.e. tactical voting.
  • What differs is the MATHEMATICS OF WHAT IS DONE WITH THESE THREE RANKINGS.

Under M-L voting, “more weight is given to people’s degree of dislike” – to be more precise, THE EXACT SAME WEIGHT IS GIVEN TO WHAT THEY LIKE LEAST/HATE AS TO WHAT THEY LIKE MOST/LOVE. This doesn’t happen under AV. Why? And how?

  1. “Most” votes for each candidate are added up, just as under FPTP.
  2. “Least” votes for each candidate are added up, separately.
  3. Each candidate’s “least” total is subtracted from their “most” total.
  4. This produces a “net approval score”. If it is positive, on average the candidate is “liked”, if negative, on average “disliked”.
  5. The candidate with the highest net approval score wins.

Note some important properties of M-L voting:

  • If you have majority support (>50%) then it becomes increasingly difficult to “knock you out” – so the British people’s oft-stated desire for “strong single party government” is not sacrificed, merely made a little more difficult.
  • For those (LOTS) of candidates in British elections winning with a plurality but not majority (i.e. winning but not obtaining 50+%), often getting low 40s, then they have to be a LOT more careful. The opposition might be divided upon their “preferred” candidate, but if they all agree you have been obnoxious to their supporters they will ALL PUT YOUR CANDIDATE AS “LEAST PREFERRED”, PUSHING THAT CANDIDATE INTO NEGATIVE TERRITORY. He/she won’t win.
  • The strategy, if you don’t have a strong majority in your constituency, is to offer a POSITIVE VISION THAT DOESN’T ENGAGE IN NEGATIVE CAMPAIGNING AGAINST YOUR OPPONENTS. Candidates who are “extreme” without being constructive LOSE.

So, what’s the relevance for the Labour leadership contest? Well, if it is true that Long-Bailey and Starmer do indeed “polarise” Labour supporters, each having a relatively large, passionate body of supporters who are ill-disposed toward the other, then electing either one could prove toxic for Labour when facing the Conservatives. Maybe the candidate who “comes through the middle by alienating virtually nobody” might be better?

As usual, I will mention Arrow’s Impossibility Theorem. There is NO FAIR VOTING SYSTEM. You must decide what are the most important targets for your system, then choose the system that best achieves these. You won’t achieve EVERY target. However, you can achieve the most important ones.

So Labour, what do you want?

  • The possibility of single-party power but, given current population dynamics, something that seems a LOT more difficult than it was in 1997 under Blair, or
  • A system which preserves the single-member constituency and which cannot be fully proportional, but which is semi-proportional and which is very very close to FPTP…..maybe close enough that it would WIN a referendum, unlike AV?

MOST-LEAST VOTING WOULD NOT BE FULLY PROPORTIONAL. BUT, GIVEN A DESIRE FOR SINGLE -MEMBER CONSTITUENCIES, IT WOULD BE SEMI-PROPORTIONAL, THUS:

  • The percentage of seats in the House of Commons per party would be MUCH closer to their percentage of the popular vote;
  • HOWEVER, it would NOT be EQUAL. Parties offering popular manifestos that did not vilify others and which commanded support in the 40-something range, could STILL get an overall majority in the House of Commons.
  • Whilst those in favour of “full PR” could still complain, I’d argue this is a pragmatic compromise between two fundamentally incompatible aims – Proportionality and Single Member constituencies. Furthermore, if a majority government DOES emerge, it’s unlikely to have done so via vilifying minorities. There will be no tyranny of the majority.

FINALLY, PLEASE DO NOT TAKE ANY OF THIS AS AN ENDORSEMENT FOR A PARTICULAR CANDIDATE. I AM IN NO WAY SEEKING TO “CHANGE THE RULES” TO GET WHO I THINK WOULD DO BEST. I MERELY USED THE LABOUR CAMPAIGN AS AN EXEMPLAR BECAUSE IT HAS SOME (SORT OF) REAL NUMBERS THAT MAKE THINGS INTERESTING!!!!

I think there’s debate to be had here.