Tag Archives: most-least voting

most-least pt 2

One good thing about Twitter is getting some feedback on things you propose. OK we know most of Twitter is like a swamp, but I’ve had the benefit of some excellent, constructive comments, in the light of my discussion of most-least voting.

The discussion has revolved largely around “how to present, or “sell” it to the public”.

This is a valid question. In the UK we are used to a system that very transparently rewards a single winner in a constituency – the person getting the most votes. For all the flaws in FPTP it is at least clear and transparent what’s going on.

Changing the system runs into various issues that have been raised:

  1. Many proportional systems used across the EU use “multi-member constituencies”. You no longer have a single MP to bring concerns to.
  2. The system used to count is very opaque to the average member of the population. Even someone like me can get bamboozled.
  3. Ranking systems SOUND attractive. In practice they are both theoretically and practically awful.

Multi-member constituencies

Having several members is attractive in one sense – there’s likely to be an MP “close to” your views. However, constituencies are large and GETTING to your preferred MP’s office might be a much bigger journey.

Opaque system

We might know how to physically rank candidates, but the system of how votes get translated into seats necessarily involves equations. Most people’s eyes glaze over.

Ranking is bad m’kayyyyy

Ranking candidates from (1) (top) downwards sounds intuitive. In practice it is riddled with problems.

First, mathematically, for a ranking to properly represent Mr Smith’s preferences, he MUST be equally “certain” of his “top candidate”, his “2nd best”, his “third best”….down to his “bottom” candidate. We rarely get the data to test this. But when we have done, we almost inevitably find it fails. Mr Smith is pretty sure of his top (most preferred) candidate. He is also pretty sure of his bottom (least preferred) candidate. But middle candidates? Nope. Quite frequently he fills them in almost randomly.

Yet in counting, if Mr Smith’s top choice gets eliminated (due to too few votes overall), then his 2nd and lower preferences then become absolutely KEY. They are redistributed. Which is how nonsense candidates like the Monster Raving Loony Party candidate might get through.

Theoretically two things have gone wrong:

First, rankings in the middle are very unstable but mathematically are treated as if the person was “just as certain” as they were with their top and bottom ranks. This is bogus.

Second, redistributing the votes from people whose preferred candidate has been eliminated in effect gives them two or multiple “bites of the cherry”. This is undemocratic. Whether you get “one bite” or “several” depends on whether you happened to choose the eventual “winner” as top rank. Challengers get a shedload of attacks on the front-runner, even if they’re a demonstrable loonie.

Most-Least – what is ITS problem?

ALL democratic systems fail at least one key criterion of fairness (Arrow’s Impossibility Theorem). Most-least’s is not entirely clear. But as a Twitter colleague said, it may be a hard sell, because if (say) Labour and the Conservatives “knock each other out” then a candidate with few “most” votes (but few least votes) may win. This “looks bad”.

I agree, from the perspective we hold at the moment, it does indeed look odd.

However, I’d argue we need to change the narrative. We have to start thinking about “which candidate is the most unifying in terms of being least polarising?” Now, the Monster Raving Looney candidate won’t win. It’ll be a more well-known party candidate. But maybe we should also be taking a leaf out of the book of countries like the USA – with the possibility of recall elections. If a nonsense candidate does get through, it won’t be hard to get a recall election to get rid of him of her in favour of a serious person.

But the bottom line is I believe we must stop thinking that “the winner” gets to ignore the (often 50+% of)  electors who didn’t vote for him or her – and indeed might ALL have agreed he/she was the WORST person on the ballot.

It is all about the terms of the debate and how we define “winning”.



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.


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.


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.


“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.


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.

Most-Least Voting Would have Killed Brexit

I’m looking at the results for England and Wales from the 2019 European Parliament election. Scotland and Northern Ireland are yet to declare (though we pretty much know the Scottish result already). The percentage votes are really rather remarkable if you are interested in Best-Worst Scaling, or the branch of it known as Most-Least Voting. I couldn’t have made up more interesting figures if I’d tried. Here are the percentages from the Guardian as at 09:55 BST on Monday 27/05/2019.


Brexit: 33.3%

Lib Dem: 20.9%

Labour: 14.6%

Green: 12.5%

Conservative: 8.8%

Change UK: 3.6%

Ukip: 3.5%

Plaid: 1.0%


Now, let’s do a little thought experiment. It is pretty subjective since we have no data on what party any individual liked *least*. But given the nature of this election, we can make some pretty informed guesses. And if we’d had Most-Least Voting, particularly if coupled with the most common constituency format across the EU (national), rather than regional, the pattern of MEPs elected would have been RADICALLY different.


Here are some interesting titbits to inform my counterfactual:

Extreme “Leave” support = 33.3%+3.5% = 36.8%

Extreme “Remain” support = 20.9%+12.5%+3.6% = 37.0%

Pretty similar, huh?

Under Most-Least Voting you get two votes: the party you like most (just as at present) but you must also declare the party you like least (for your ballot to be valid – else the mathematics doesn’t work). At the counting stage the total number of “least” votes is subtracted from the total “most” votes to give a “net approval rating”. It doesn’t take a genius to work out what would have happened in England and Wales, given these figures.

ASSUMING the Brexit + Ukip supporters had perfect foresight (snigger, bear with me), then they could have knocked out the three strong Remain parties. But those three parties would have knocked out Brexit + Ukip. IF the Brexit (being the big group) people didn’t concentrate their fire so perfectly they could have more easily knocked out one or two of the three Remain parties. BUT then the third would have got through easily.

So, what would we have likely ended up with? Most MEPs being ones who “didn’t articulate an EU policy very well” (if you want to be polite) or “who didn’t know the f*ck what they thought about the EU” (if you want to be less polite). In other words, most MEPs would have been Labour or Conservative (with Labour beating the Conservatives). They would have “come through the middle” of the debate.

Would this have been a “good” thing or a “bad” thing? I can’t answer that. Indeed if Arrow (“Nobel” prize-winner) couldn’t show the existence of a “fair” form of democracy then I bloody well can’t.

I will venture a thought, however. It is that such a hypothetical outcome would have shown what many of us who have done survey work already know: most people cannot possibly provide a properly informed view on EU membership – whether being instinctively “Remain” or “Leave”. The referendum had little to do with the EU (except for some racists and some greedy gits who used freedom of movement and capital to exploit people). Plots of the Index of Multiple Deprivation against Leave/Remain votes in Nottingham are almost a perfect straight line. If you felt left behind by 40 years of Westminster crappiness from both Tory and Labour governments then you tended to vote Leave. It’s really pretty simple.

Most-Least Voting would at least have nullified the issue that isn’t the real issue. The two main parties might – just might – have then been forced to start addressing the real issues going on across this country. Food for thought.

(NB I left out Plaid merely because their effect would have been marginal. If you want to include them in your own calculations feel free – it bumps up Remain vote a little).