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.

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.