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.
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.
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.