Kevin: You wrote:
You say it is inelegant to specify assumptions about methods to which criteria apply. [endquote] Yes. You continue: But your alternative is criteria that have to discuss not just sincere preferences but also the degree to which voting may be insincere. [endquote] Some of my criteria stipulate sincere voting by some or all voters. Some of them stipulate other preference/vote relations, such as not having to vote someone equal to or over one's favorite; or not having to vote someone over one's favorite; or not having to vote a less-liked candidate equal to or over a more-liked one. However my criteria don't discuss degrees of insincerity. My criteria use one, and only one, definition of sincere voting. You continue: And you need to define these concepts in a universal way, irrespective of ballot format. [endquote] I have. I posted that definition years ago. I re-posted that definition within the last few weeks. Sincere voting: A voter has votes sincerely iff s/he doesn't falsify a preference or fail to vote a genuine preference that the voting system in use would have allowed hir to vote in addition to the preferences that s/he actually did vote. [end of definition of sincere voting] To falsify a preference is to vote x over y without preferring x to y. To vote a genuine preference is to vote x over y when one prefers x to y. [end of definitions of falsifying a preference and voting a genuine preference] I defined voting x over y in a wordy way that spoke of an election with arbitrarily many candidates and voters. But someone else suggested a much briefer definition: A voter votes x over y iff the relation of x's and y's status on hir ballot is such that, if s/he were the only voter, and if x and y were the only candidates, then, with that relation of x's and y's status on hir ballot, x would win. [end of someone else's brief definition of voting x over y] I don't know if I like that as much as my longer definition, because of the awkwardness, and possible ambiguity, of speaking of a relation of 2 candidates' status on a ballot. Well, the relations described in the following paragraph are such status relations. Of course, in Approval, that means approving x but not y. In Plurality it means voting for x, which implies not voting for y. In a rank method it means ranking x over y. In Range Voting, it means giving a higher rating to x than to y. Explicitly specifying those things would be a perfectly adequate definition too, but I prefer a completely method-disregarding definition. You continued: I don't feel this is more elegant. Possibly better-def... [the rest of what you said didn't copy] [endquote] What don't you feel is more elegant? Using one universal definition of sincere voting that applies to all ballot-formats and methods? Or do think that it isn't more elegant for a criterion to apply seamlessly to all methods? Mike Ossipoff
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