At 01:47 PM 5/13/2006, Steve Eppley wrote: >Abd ul-Rahman Lomax wrote: > > At 10:38 PM 5/12/2006, Simmons, Forest wrote: >-snip- > >> So most of the time, in the context of Candidate Published > Orderings, Concorcet will > >> yield an unambiguous social ordering of the candidates, with no > cycles to resolve. >-snip- > >> I would say that's amazing, and extremely relevant to the topic > of this thread. >-snip- > >I think an assumption undergirding that conclusion is questionable.
Note that Eppley is answering Simmons here, not me. > Given a voting method >that tends to elect a candidate within the sincere top cycle, >candidates trying to win >will tend to position themselves more closely on more issues than >they do under existing >voting methods. This is speculative, isn't it? > With smaller distances between candidates, other quirky effects that are >hard to predict or analyze will become relatively stronger. If the analysis was correct, the absolute value of the distances, I'd think, would not be important. Further, if we assume that candidates are elected based on their "positions" on issues, then, if they position themselves identically, *it does not matter which one is elected.* Of course, there are other considerations. The analysis presumed some kind of space occupied by candidates, with a distance from each candidate to another. This may have nothing to do with "positions" on issues. Or it may have everything to do with them. The assumption is that preference between candidates is based on n-space distance. It's a loose concept, but got one better? Simmons wrote: >Actually, I did not assume that there was any linear or two >dimensional relationship. You can use any measure of closeness that >you want, linear, non-linear, ten dimensional, or infinite >dimensional (for example the norm of the difference of the quantuum >mechanical wave functions of the candidates, if you like). > >My only assumption is that there is some measure d of distance that >(for each pair of candidates A and B) satisfies d(A,B)=d(B,A) , and >that when d(A,B)<d(A,C), consistency requires that candidate A rank >candidate B ahead of candidate C . > >These distances are numbers, so they can be linearly ordered. Eppley continues: > If candidates (and their >supporters) do not agree on the importance of the issues--for >example, some may care much >more about abortion, some may care much more about taxes, some may >care much more about >health care, some may care more about corruption, etc.--then cycles >may not be so rare. Justification for this claim? >-snip-- > > I'd prefer the flexibility of Asset Voting to the fixed process > of Candidate Published > > Ordering, for the latter could still create a minority winner, > unless the rules > > prohibited that. >-snip- > >I'm unsure what the writer meant here by "Candidate Published >Ordering" and by "minority >winner." Candidate Published Ordering is a standard fixed election method (assuming that the method used for counting is one that always -- exact ties excepted -- produces a winner. Any fixed election method, necessarily, can create a minority winner, which means a winner not approved by a majority of voters. "Approved" is a rather loose concept, but one measure would be that a majority of voters would prefer an immediate rerun of the election, with new debate and preferably new candidates (but including the previous 'minority' winner.) If the voters were presented with a separate question, after the election, "Shall the results of the election be accepted and the winner take office?", a majority would vote No. That's a "minority winner." > When I wrote weeks ago about candidates' publishing pre-election > orderings, I >didn't specify how the votes should be tallied, so in my mind we're >writing about a family >of voting methods. Technically, yes. But the method assumes that it is a ranked method. It *could* be IRV, but given the nature of the process, which is much simpler to count than standard full-Condorcet methods, because of the limited number of ballots in the final tallying process, there would seem to be no reason not to use a fully-Condorcet qualified method. And what Simmons claimed was that his analysis shows that cycles would be quite rare. If cycles are quite rare, it is reasonable to use Condorcet alone, with no cycle resolution process within the method, dealing with cycles as an election failure. Election failures happen even with plurality. (Things happen, such as the loss of a large number of ballots, the discovery of massive fraud, etc. Courts have been known to order elections to be held all over again.) > I wrote then that tallying by MAM would be good, and in some later >messages mentioned a simple system using candidate withdrawal and >plurality rule. On the >other hand, some methods in this family would be quite poor, such as >tallying by Borda, >which would encourage nomination of a farcically large number of >inferior clones. Perhaps. It is not clear what would happen with Candidate-List. But there is no reason to use Borda. >I don't know where the dividing line is between "rules prohibiting a >minority winner" and >rules that define a member of this large family of voting methods. Under plurality, a rule prohibiting a minority winner would be a rule that requires that the winner obtain a majority vote to win. It gets more complicated with, say, IRV or Condorcet methods, but a requirement might be, for example, that ballots only be analyzed, say, two or three candidates deep. If there is no majority winner with such a truncated set of ballots, then the election has failed. (But if there is such a majority winner, the ballot analysis would be continued...} But more direct would be an Approval cutoff on the ballots, common with some Condorcet methods. >Is a "minority winner" a candidate not in the sincere top cycle? Top cycles, I think, imply that at least one, if winning, would be a minority winner. But the definition is not clear from a simple ranked ballot, there would have to be an approval cutoff. 5: A>B>C>D 4: B>C>D>A 3: C>D>A>B 3: D>A>B>C A:B 11:4 A beats B A:C 8:7 A beats C A:D 5:10 D beats A B:C 12:3 B beats C B:D 9:6 D beats B C:D 12:3 C beats D If we look at these ballots truncated, assuming only the top two ranks are approved: 5: A > B 4: B > C 3: C > D 3: D > A A is, of course, the plurality winner, based on first choices. A is the first or second choice of 8 voters, B of 9 voters, C of 7 voters, and D of 6 voters. Under the assumption above, A and B would be "majority winners," and C and D would be "minority winners." I'm not familiar with the various methods of cycle resolution that have been proposed. Pure Condorcet winners have an appeal, the only negative aspect to them would come from the fact that the best candidate, theoretically, may not be on the ballot at all. We should select executives by a search for the best, which is essentially a parliamentary system. And I'd prefer to move away from standard election methods in selecting the parliament. I'd prefer a proxy parliament, or the peer-parliament equivalent, Multiwinner (single district) Asset Voting. >Assuming he was referring to tallying using candidate withdrawal and >plurality rule, I >believe I understand his point: Some candidates might "perversely" >refuse to withdraw >even though staying in elects an inferior or extremist candidate. Under Asset Voting, candidates don't necessarily withdraw, rather they recast some or all of the votes they have received. They may distribute these votes as they choose, and I presume that there would be deliberative process or, what some political scientists consider a separate process from deliberation, bargaining. > Although we could >abandon the simplicity of "withdrawal//plurality rule" for something >like MAM (under which >candidates wouldn't need to withdraw to defeat inferior or extreme >candidates) or >"withdrawal//Instant Runoff" (under which only some major candidates >would need to >withdraw), I don't see this as a big issue. The incentives on the >candidates to do the >right thing look fairly strong. If exceptions will be few, why >worry? A legislature >composed of a supermajority of centrists ought to perform well; a >few extremist >legislators would be irrelevant. Actually, there should be extremist legislators, as long as they are not incapable of participation in the process, if there are extremist voters. >I apologize for not knowing what Asset Voting is. It's Warren Smith's invention: http://www.math.temple.edu/~wds/homepage/multiwin.pdf My own simplification I called FAAV: Fractional Approval Asset Voting. The ballot is a standard list of candidates, vote for one or as many as you like. If you vote for one, that candidate gets one vote. If you vote for N candidates, each gets 1/N votes. A quota is required to win. I've assumed that a quota Q for an assembly intended to have at most M members would be exactly V/M, where V is the number of valid ballots cast, with at least one vote on them. If a candidate receives X votes, and X = Q, then the candidate is elected. If X > Q, the candidate is elected, and has X - Q votes which can be allocated to another candidate. The redistribution of votes would continue until M-1 members have been elected. There are theoretically enough votes left to elect an Mth member, but that would require a consensus of those holding all remaining votes. Unless there is a plurality election held with those votes. There are other contingencies to be considered. Bottom line, though: election failure, which in this case would mean the failure to elect M members (and which might be relatively common), can be specifically attributed to candidates holding votes who did not recast them. The system could, and should, allow the election of candidates not on the ballot, if there are sufficient votes given to them. This would allow those holding votes who were unable to agree as to who to elect when restricted to the set of unelected candidates, to find an acceptable compromise. > I can glean something from the context, >though. So, let me say this: A positive aspect of the "fixed >process" of having >candidates publish orderings of the candidates prior to the election >is that it will help >focus attention on the candidates' and voters' relative preferences >regarding the various >compromise positions on the issues. My own view is that issues are almost irrelevant. "Almost." Issues serve as a way to measure candidates, but positions on issues are so hopelessly manufactured in order to gain votes that they become more of a smokescreen than real information. Asset Voting could actually become quite similar to Delegable Proxy simply by it becoming common to use write-in votes for candidates personally known to the voter. However, back to Published Ordering and fixed process. Published Ordering does provide some information to the voter about the candidate. If a candidate publishes an ordering which displays, say, some party line, this is information. If a Democrat were to have as a second or third choice a Republican, it would show an ability to think and act across party lines. I personally would value that. > I think it's more important to elicit this info, when >making collective decisions, than to elicit the candidates' and >voters' favorite >positions. Elections should be about making decisions in the near >term; there are plenty >of other forums in which current minorities can argue that the >elected compromise >positions are inferior, to try to make their preferred positions >popular enough to be >adopted in the future. If I were choosing a proxy to represent me, >I'd want to choose >someone who would relatively order the plausible compromises >similarly to how I would, >since ultimately one of the compromises is going to be chosen. Personally, I'd want to choose a proxy who would order the candidates *better* than I could. Why not? Am I perfect in my knowledge of the candidates, so that someone else could not do a better job. The *critical* action is the act of trust involved in choosing a proxy. Choose well >Contrast candidates' published orderings with a more familiar >method, parliamentary >proportional representation systems (PPR). In PPR, each party or >candidate adopts >positions favored by a significant segment of the voters, to win >some seats. (Typically a >minority of the seats.) After the election, the elected >representatives negotiate to pick >the governing executives; assuming no faction won a majority of the >seats, some sort of >compromise will be reached. My (limited) understanding of the >behavior under PPR is that >how the parties/candidates will negotiate after the election is not >scrutinized much >during the period prior to the election, when the focus is more on >preferred positions. This is party-system PR. Multiwinner Asset Voting can create non-party PR. More accurately, the voter can choose a preferred representative, or can choose a committee, which might all be members of the same party. Candidates can distribute votes within their party, or outside it. The key thing about Asset Voting is that no votes are wasted unless there is a publicly identified person who does the wasting.... ---- election-methods mailing list - see http://electorama.com/em for list info
