Re: [EM] Majority Criterion, hidden contradictions

[Chris Benham]

Abd ul-Rahman Lomax wrote: As written, AV satisfies the MC, and the arguments I see on this, so far, do not really address the issue. What issue? Since you don't support the "MC", why do you even care if it does or not? Show me a proof that AV does not satisfy the MC, but Plurality does. To do so, you must define "strictly prefer." "Strictly prefer" means exclusively prefer. The "Majority Criterion" (I don't like this name because Woodall uses it to refer to Majority for Solid Coalitions. I prefer "Majority Favourite" or "Majority for a single candidate") means that if more than half  the voters prefer X to all other candidates, then X must win". What Approval in effect does is ask the voter to divide the candidates into two sets at his/her discretion (technically one of these sets may even be empty) and then tell us which set s/he prefers to the other. Only if the voter's preferred set happens to have one member can we infer which candidate that voter prefers to all others. So really since the method doesn't ask the voter which candidate is their exclusive favourite, it has no way of  "knowing" who is the favourite of the majority is and so of course can't and doesn't  meet Majority Favourite/MC. Abd isn't the first sophist to try to argue that if a voter puts more than one candidate in his/her preferred set, that must mean that he/she means to rank them all equally in first place and so therefore if a majority don't put X alone in their preferred set X can't be the majority favourite. (But that is like me gluing your legs together and then pretending that you only have one leg.) These voters, who have elected to use Approval in this way, have abstained from indicating the "strict preference" which is part of the Criterion, and therefore they are not party of the "majority." The criterion doesn't stipulate that the majority have to be willing to pay a price or engage in some perhaps risky strategy to express their strict preference for X above all others. It is not accurate or honest to ignore voter preference or treat it as irrelevant when the ballot does not allow it to be expressed! Does Plurality allow the _expression_ of preference? How? The only "preference" the criterion is concerned with is the first one, and that is the one that FPP allows voters to express.  Making the comparison with Approval, if the voters are constrained to put a single candidate in their "preferred set", then of course that candidate is their clearly voted strict favourite. Chris Benham

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