<DIV>>Message: 1<BR>>Date: Sun, 29 Aug 2004 19:03:58 +0100<BR>>From: "James Gilmour" <JGILMOUR@GLOBALNET.CO.UK><BR>>Subject: RE: [EM] recommendations<BR></DIV>
<DIV>>The facility for party voting in the Australian Federal Senate STV-PR elections is a </DIV>
<DIV>>gross perversion of STV. It has reduced STV to just another party list PR system.</DIV>
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<DIV>Correct me if I'm wrong, but my understanding is that people have the option of voting either their own preference order, or else a preference order that a party decided upon in advance. I was under the impression that it was a response to the complexity of the system.</DIV>
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<DIV>I understand all of the principled objections to party list systems, but in practice I think that the open list methods (especially the Swiss version) are good enough. Or, put another way, I'd regard an open list system as a huge improvement over what we currently have in the US. Progress is about improvement, not perfection.</DIV>
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<DIV>As to Steve Eppley's comments on resolvability:</DIV>
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<DIV>I like the definition from the social choice literature, but sometimes I prefer to work with continuous models rather than discrete models. The definition that you posted really only works for discrete models. Here's what I mean by a continuous model:</DIV>
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<DIV>For N candidates I will consider an N!-dimensional space where each coordinate corresponds to the fraction of the electorate voting with a given preference order, and I'll restrict my analysis to an affine N!-1 dimensional manifold in that space where all of the coordinates are non-negative and sum up to 1. I find that it makes a geometrical approach easier.</DIV>
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<DIV>To ensure resolvability, I stipulate that the method must yield a definite result for every point on that manifold except a sub-manifold of N!-2 dimensions or lower. Or, I'll use a short-hand that the method must give a definite result except "on a set of measure zero", with all necessary caveats and definitions implicit in that short-hand.<BR><BR></DIV>
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<DIV>Date: Sun, 29 Aug 2004 11:46:25 -0700<BR>From: "Steve Eppley" <SEPPLEY@ALUMNI.CALTECH.EDU><BR>Subject: Resolvability (was Re: [EM] Re: Election-methods Digest, Vol<BR>2, Issue 42)<BR>To: election-methods@electorama.com<BR>Message-ID: <4131C211.25986.5D9890@localhost><BR>Content-Type: text/plain; charset=US-ASCII<BR><BR>Alex S wrote:<BR>>> Steve Eppley wrote:<BR>>>> Aren't all the voting methods we've been promoting <BR>>>> both anonymous and neutral? Doesn't that mean<BR>>>> none of them are entirely non-random?<BR>><BR>> My understanding is that anonymous and neutral methods only <BR>> need a non-deterministic component to break ties. When I <BR>> analyze methods mathematically (e.g. my never-ending quest <BR>> to prove that Strong FBC is impossible) I simply leave aside <BR>> the issue of ties by specifying that the method yields a <BR>> definite winner determined uniquely and deterministically <BR>> from t
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ballots submitted except "in rare cases", <BR><BR>It can be misleading to leave aside the issue of ties<BR>and tiebreaking. There may also be negative consequences<BR>if, as a result, a poor tiebreaker is chosen. In <BR>particular, suppose the tiebreaker is not independent<BR>of clones. Even though ties will be rare, it won't be <BR>known at nomination time whether the vote will be a tie, <BR>so it would be rational for every faction to nominate <BR>a slew of clones just in case there's a tie.<BR><BR>> where "rare cases" is made more precise depending<BR>> upon the mathematical framework that I'm using. <BR>-snip-<BR><BR>There's a criterion in the social choice literature, <BR>resolvability, that's defined precisely and is useful for<BR>distinguishing which methods rarely involve randomness. <BR>(For instance, Tideman provides a definition in his <BR>1987 paper on clone independence.)<BR><BR>Resolvability<BR>-------------<BR>A voting method is resolvable if and only if
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<BR>for each possible collection of votes, <BR>one of the following two cases holds:<BR><BR>1. There exists a candidate that would be <BR>elected with certainty given those votes.<BR><BR>2. There exists a candidate x and an expression v<BR>such that v would be an admissible vote if <BR>some voter voted v, and x would be elected<BR>with certainty given the votes with v added.<BR><BR>In other words, if the voting method is resolvable, <BR>then every election is at most one vote away from an<BR>election that would be tallied entirely non-randomly. <BR>It follows that if the number of voters is large,<BR>then the fraction of possible elections that would<BR>require some randomness to elect a single winner <BR>is very small.<BR><BR>I slightly prefer a slightly different definition <BR>of resolvability, changing the wording of case 2:<BR><BR>2. For each candidate x that has a non-zero chance<BR>of being elected given those votes, there exists <BR>an expression v that would be an
admissible vote <BR>if some voter voted v, such that x would be elected<BR>with certainty given the votes with v added.<BR><BR>>>> Man, this stuff has got me really worried. It's just <BR>>>> scary how unconcerned the Republicans seem about <BR>>>> having a verifiable vote-counting process. <BR>-snip-<BR><BR>I didn't write that. Alex must have quoted someone else.<BR><BR>--Steve<BR><BR><BR><BR>------------------------------<BR><BR>_______________________________________________<BR>Election-methods mailing list<BR>Election-methods@electorama.com<BR>http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com<BR><BR><BR>End of Election-methods Digest, Vol 2, Issue 44<BR>***********************************************<BR></DIV><p>
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