At 08:35 AM 11/7/2006, Michael Poole wrote: >Abd ul-Rahman Lomax writes: > > > No voting method can use preferences that are not expressed. > > > > Linguistically, the Criterion contains a lost performative -- or > > something like that. *How* do the voters answer affirmatively. It > > could only mean that they so answer on the ballot. Which in Approval > > *requires* that they vote for X and not for any other candidate. And > > if a majority of voters do this, that candidate cannot lose. So why is > > it said that Approval fails the Majority Criterion? > >Nothing in the MC talks about what the ballot contains, only about how >voters answer a specific yes/no question.
A question which is not on the ballot. If the Majority Criterion is held to apply to Approval Voting, and it is held that Approval Voting fails the criterion, it must be that the "question" asked the voters is *not* what is on the ballot, it is some theoretical question that seeks to discover any preference at all, no matter how weak. *Where is this question?* Is it on the ballot? Now, it is possible for voters to answer the question posed in the MC, using an Approval ballot. Same as a plurality ballot. Simply vote for the candidate preferred and for no others. Here is another statement of the Criterion, from Wikipedia. The one I quoted before is from the same article, but is not, formally, the definition. The "question" was mentioned in an explanation. Mr. Poole fell into the same trap, he also referred to "how voters answer a specific yes/no question." >if a majority of voters strictly prefers a given candidate to every >other candidate (i.e. the given candidate is the first preference of >more than half the voters) and they vote sincerely, then that >candidate should win. What does it mean to "strictly prefer?" And which is the Criterion, "a majority strictly prefers" or "the given candidate is the first preference"? The latter is clearer, but the former is the language I'll use. Now, Approval is not a ranked method, exactly. I'd call a ranked method any method which allows the ordering of candidates by preference where there are more than two ranks. I.e., it becomes possible to express "strict preference" for more than one candidate. Approval allows the expression of "strict preference" for only one candidate. If one votes for more than one, it is no longer, under Approval, an expression of a strict preference. So: what does it mean that the voters "strictly prefer." Given that this is an election criterion, using ballots, it *must* mean that the voters express this preference on the ballot. If the method does not allow this expression, then we must also say that it does not satisfy the Majority Criterion. But Approval *does* allow the expression of strict preference. In exactly the same way as Plurality. The appearance that Approval does not satisfy the MC is caused by the fact that voters may express a *group* preference, if they so choose. This is no longer a strict preference on one over all others. But if a majority *expresses* a strict preference, which Approval *allows* them to do, they cannot fail to elect that candidate under Approval. Approval satisfies the Majority Criterion. I have stated that Range does not satisfy the Criterion. That may not be the best analysis. If a Majority expresses a *strict* preference for one candidate over all others, by bullet voting that candidate at max rating, -- what else would "strict preference" mean? -- again, that candidate cannot fail to win. This is exactly the same as with approval. It is only if some of that majority does not express such a strict preference, but, instead, a weak preference, i.e., less than the full strength, that the candidate could fail to win. It's been argued in these posts that "But this is not Approval if they vote for only one, it is Plurality." No, it is not. In non-Approval plurality, without that strange no-overvote rule, a voters' ballot is disregarded if the voter votes for more than one. That is, Plurality *only* allows the expression of strict preference. That Approval allows something else does not cause it to fail the majority criterion. Let me go over this with Range: A majority votes: A 99 B 10 C 0 With this vote, A *might* fail to win. It's unlikely, but possible. But this is not the expression of strict preference, there has been a verbal slight of hand here. Here is strict preference, where in every pairwise election, the majority *fully* prefers A over every other candidate: A 99 B 0 C 0 Yes, *for these voters*, Range has reduced not only to Approval, but to Plurality. But that does not make the method Range or Plurality, for other voters may vote differently, and their votes will be counted as cast. Michael made this argument: > Approval does not ask >voters to answer according to that question. It fails the Majority >Criterion because if you add the constraint that each voter only >approves of one candidate, the system stops being Approval voting. There need be no such "constraint." Again, this extra condition has been supplied. *Approval allows the expression of "strict preference," and if a majority so expresses a strict preference for one candidate over all others, that candidate must win. If voters, on the other hand, approve of more than one, they have failed to express a strict preference between the candidates so favored. They have expressed *no* preference between these candidates. So they don't count as part of that majority that has expressed strict preference. They are irrelevant to whether or not the method satisfies the Majority Criterion. Frankly, it's become utterly obvious to me. There has been a lack of solidity in considering the meaning of the Criterion. I made that same mistake myself for a long time, I readily accepted the claim that Approval failed the criterion. It was a lack of rigor, a mushing together of ideas about preference and Approval Voting, and recommended strategy for Approval, etc. Indeed, the recommended strategy for Approval *for some voters* is not to express strict preference. Those voters are giving up their right to express preference between multiply-approved candidates. >I am not arguing that Range creates the use of extreme scores (zero >and maximum), only that it encourages it to an extent that the result >is likely to be technically hardly better than Approval and >practically more likely to polarize factions. It only seems to "encourage it" in a context where people are focused on winning, on getting their preference. But my point has been that this *is* extreme preference, and if that is how people see the situation, it is *correct* for them to vote that way. But Range *allows* voters to move away from that. >The US currently has extremely polarized factions, and most of my >criticisms apply to plurality voting as well as to Range, but I would >rather replace the current system with one that seems robust in >practice rather than one that merely allows higher resolution of >polarization. I see no reason to believe that Range would "encourage" polarization. Given the status quo, the introduction of Range would certainly not *increase* polarization, since the present system *depends* on full polarization. Neither would Range, by itself, eliminate polarization. It just makes it possible. Systems that don't allow the expression of preference strength are inherently flawed. But the real problem is attempting to cram what would intelligently be a deliberative process into a single election. The designers of democracy quite well knew that majority rule properly applied to single questions. Approval actually begins to restore this, by effectively asking the question, one question for each candidate: "Is this candidate acceptable?" The most broadly acceptable candidate wins. sStandard Plurality asks a complex question: which of these candidates is the most acceptable? Thus it explicitly disallows the separate question for each candidate. In my view, *whatever* election method or methods are used, there is not full democratic process if the election is not explicitly accepted by a majority. The identity of a Condorcet winner is certainly of interest, but the Condorcet winner could fall far short of being accepted by a majority. Approval and Range can as well, but are much more likely to find the candidate who will be most broadly accepted and for whom, thus, the "shall we elect this candidate" would prevail by a majority. If a majority don't want a candidate to take office, why do we presume that the election should be considered complete? It is blatantly undemocratic, violating the most basic principle of democratic decision-making, majority rule. Yet this is exactly what we can get with single-ballot, get-it-over-with elections. Having a top-two runoff (which can be variously defined, and some ways of doing it are clearly better than others) is closer, and if NOTA was on the ballot as well, it would be complete. (NOTA: None of the Above, a common Libertarian proposal.) ---- election-methods mailing list - see http://electorama.com/em for list info
