You support nuclear power??? Ooooh, now there’s a discussion for the future…..

]]>“Why do we never hear mention of the consequences of Arrow’s theorem and the Gibbard-Satterthwaite theorem in the political discussion of voting systems? A great deal has been compromised to get the AV referendum. Mathematics won’t end the political arguments, but it would certainly prevent much wasting of time.”

It is unfortunate and frustrating* that we live in a world, where despite advances in mathematics, science and technology, all we hear in this debate is mindless celebrity endorsement of either voting systems. I am not saying everyone should look at the proofs of those theorems but just be made aware of the statements.

*Well, I can hardly say I am surprised though.

]]>http://www.guardian.co.uk/commentisfree/2011/apr/22/formulas-for-fair-voting?INTCMP=SRCH

“Actually, the question is mathematical rather than political, and mathematicians have discovered several fundamental facts that severely limit what a voting system can achieve. Think of the voting system as an algorithm that takes all the personal preferences of voters (it is assumed that each voter has an order of preference of the candidates or parties) and produces the election result, which is a single preferred ordering of the candidates or parties that, in some sense, summarises the views of the whole electorate.

A theorem (proved by Allan Gibbard and Mark Satterthwaite) tells us about elections designed to find a single winner, as is the case when a constituency elects its MP. The theorem says that, if there are three or more candidates, any voting system which is not a dictatorship and which allows the possibility of any candidate winning, is susceptible to tactical voting (where voters have an incentive to vote in a way that doesn’t reflect their personal preferences).”

]]>Under AV the scope for tactical voting is extremely limited (as was argued at length in the blog post). As for not wanting to state a second or third preference, that is also permissible under AV. I guess I would need to better understand your reasons for never wanting to give a second or third preference.

(In a rush – might be back later).

]]>“The problem with that analysis is that it assumes everyone acts rationally and has done the maths before they vote. People don’t.”

This assumption (beloved of economists everywhere until recently) is never made in Tim Gowers’ post, the analysis merely compares the two systems. No ‘rationality’ or intelligence is accorded to the voter whatsoever. Where did you see this? I admit I have not fully read Alan Renwick’s article.

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