Tag Archives: most-least voting

Most_least Voting(2)

Most-Least Voting – Questions raised – some of which were serious, some I suspect were “rabble-rousing”. I’ve edited to reduce snark and generally tried to give benefit of the doubt, even though I know some people really should just go out more……

Arrow’s Theorem only applies to generic voting. Fair results can be obtained if particulars are taken into account. When you only have a few candidates MLV is not what you’d go for. With a huge pool of eligible candidates, say 1000, all available for say 9 seats, then Cumulative vote tallying is ideal.

Reference please.

“Also something polsci experts often fail to consider is degree of polarization. You don’t have to have just “like” vs “dislike”, you can have a Likert scale on degree of like/dislike, and use it to weight the votes, so that a polarizing candidate who is less polarizing than the other still has a chance to be ahead of the milquetoast centrist. I know, I know, requires fairly sophisticated voters, but worth a shot some time in experimental research trials.”

Likert scaling assumes distances between each choice (answer option) are equal. Please provide references from the mathematical psychology literature showing this to be true. (I’ll save you time – there are none. My co-author was editor of the top journal –JMP – for almost 40 years and never encountered a study showing this. He is AAJ Marley.).  I could quote you amusing anecdotes like the fact traditional Chinese older people associate the character for number 4 with death so avoid it. Statisticians then spend yonks trying to work out if dips at number 4 are “real” or “due to cultural stuff”.  Please stop throwing up new terms like “likert” when it is merely expressing a phenomenon I discredited in my postings before.

San Francisco city government, supervisors, sheriff and district attorney are chosen by ranked choice voting. That, combined with district elections for supervisors, has resulted in a parade of ineffectual, sometimes dangerous, political mediocrities, a chaotic disaster, controlled by the Democratic County Central Committee. If a voter fails to choose three candidates, their vote is thrown out.

You say ranked choice choice voting – I’m not defending that – so your point is?

Some supervisors have been elected with less than 25% of the vote.

Choose from Hillary, Trump and any run of the mill US politician in the centre. Why does LESS THAN 25% “MEAN THEY ARE ILLEGITIMATE”?  – “Top” candidatees don’t matter under MLV if they also disgust a huge number of the rest of the population. This is NOT ranked voting (which YOU talk about). Please actually address my discussed voting system and don’t straw man.

It’s horses for course to get around Arrow. In other words, you select the most appropriate voting system for the size of the candidate pool and the seats being vied for.

I said your latter statement at the start. Why are you presenting this as a “new insight”? Arrow always said you make your moral judgments, based on “values” and the “system”, THEN you can choose the system that best achieves these. As to “get around Arrow”. Nope.

While it is an interesting fad, there is no real guarantee that rigging elections to favor centrists will get you better government. As it happens, I am a Libertarian. Some of my ill-advised fellow party members argue vociferously for ranked choice voting or the like. I attempt to point out to them that RCV tends to guarantee that my party will never win elections, but the RCV faithful will not listen.

Where did I say that MLV rigs elections in favour of centrists? I merely quoted an observation from the Dutch/Belgian researchers that centrists probably stand a better chance of being elected. If you have data showing that MLV disproportionately benefits centrists at the expense of others please quote it – PARTICULARLY in a multidimensional format (which even the continental Euroepan authors do not). Note I also said that in a MULTI-DIMENSIONAL world, the concept of a “centrist” is less meaningful. MLV could get you your libertarianism (in getting govt out of the bedroom). Please stop putting words into my mouth.

There’s a lot of talk about candidates and parties, but not a lot of talk about policy.

One way to create significant momentum to deal with global climate change is to place high taxes onto fossil fuels. As Illinois recently demonstrated, this is highly unpopular.

In either Ranked Choice or Most-Least systems, how do necessary but unpopular policies get enacted?

I’m not going to claim miracles. Just as under ANY other voting scheme, there must be a critical mass of people who “see the peril” and vote accordingly. MLV at least allows these people to “veto” candidates who totally dismiss the environmental issues. So it isn’t “the solution” but it may be “ a quicker solution.” One big benefit of MLV is that it is probably the system that gives the greatest “veto power” to any majority of the population whose candidate(s) didn’t make it into government. So in the UK, the strong environmental lobby crossing all the “progressive parties” who keep losing elections could start exercising real power via their “least” votes.

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.

 

Most-Least Voting redux

Just a quick repeat of the logistics and mathematics of Most-Least Voting. This is a type of voting that:

(1) Satisfies an apparent desire by British people to “change the voting system by the minimum amount”;

(2) Is NOT perfectly proportional, BUT tends to produce outcomes that are far closer to the proportionality in the proportional systems endorsed by a lot of parties on the European mainland than existing First-Past-The-Post (FPTP).

Thus, it is a practical compromise that I believe would be acceptable to people whilst giving smaller parties greater enfranchisement. Crucially, the often 60+% of people in many constituencies who didn’t vote for the “winner” and feel disenfranchised, become RE-ENFRANCHISED by getting to veto candidates that are widely regarded as unacceptable.

STEP 1:

This works EXACTLY as at present. It is First-Past-The-Post, with a voter indicating that candidate they like MOST. Most totals are tallied, like now. But that is no longer the end of the story. A second step is conducted.

STEP 2:

Voters must, for their ballot to be valid (and the mathematics to work) cast a second ballot. This can be considered the “reverse” to Step 1: they just indicate the candidate they like LEAST. Think of it as “which candidate do I consider totally unacceptable?”. Least totals are tallied.

COUNTING AND THE WINNER:

“Least” totals are subtracted from “most” totals. Thus if the Conservative candidate under FPTP would “win” with 45% (and the remaining 55% of people spread too thinly across Labour, LibDems and Greens) then things might change. If all supporters of those three “anti-Tory parties” put “Conservative” as “LEAST” then that is 55%. The Net Approval Rating of the Conservative candidate is 44-55=-10%.

Suppose Labour got 40% of “most” votes (coming 2nd under FPTP). Suppose all Conservative voters put Labour as “Least”. That’s only 45%. 40-45=-5%. There are no more “least votes” left – they’ve all been used to veto the Tory.

Labour gets -5% so beats the Conservatives. What about the minor parties? Well these must add up to 15% (100-45-40). The Conservatives and Labour shot each other down. So, one of the minor parties (let’s say the LibDems) got all those remaining 15% most. There are no least votes to knock them down.

RESULT = Lib Dem win.

TACTICAL VOTING:

Of course the public ALWAYS learn how to “game” any voting system. It’s likely some strongly BREXIT tories would put LibDem as “least”. It is not necessarily the case that the Lib Dems will “always come through the middle as the party nobody hates”.

Indeed down south the Conservatives and LibDems will likely try to knock each other out, potentially letting in Labour. Further north the Conservatives and Labour might attack each other, allowing Lib Dem wins (as illustrated above).

You can ALWAYS construct – under ANY voting system – a set of figures that gives a “weird” result – this is inevitable given Arrow’s Impossibility Theorem (no voting system is fair).

But I personally believe that the tendency of M-L voting to stop extremists is a good property at this place and at this time. It’s worthy of consideration. The Baltic states have used or in one case do use it.

Mathematically, M-L is the system that is least likely to give an incorrect “ranking” of all the candidates in a constituency, after taking on board “degree of like and dislike” of EVERYONE.

 

M-L voting has been/is used in some of the Baltic States so is not “just a mathematical curiosity”. There are some peer-reviewed articles (which alas I no longer have access to, not being in academia anymore and with which I had no connection) which have illustrated that M-L voting tends to penalise extremists who adopt negative campaigns and conversely benefit centrists who are penalised under systems like First-Past-The-Post.

 

M-L voting is thus something for which I have no “dog in the fight”, although I approve of it, with it being a SPECIAL CASE OF BEST-WORST SCALING, for which I am co-author of the definitive textbook.