At 11:21 PM 3/23/2008, Dave Ketchum wrote: >On Sat, 22 Mar 2008 19:35:13 -0400 Warren Smith wrote: > > The "YN model" - a simple voting model in which range voting behaves > > optimally while many competing voting systems (including Condorcet) > > can behave pessimally: > > > > http://rangevoting.org/PuzzAggreg.html > > >When I stare at this all I get is headaches: > >Why would Plurality voters be attracted to candidates with 3 Ys, or no Ys >- yet reject 4 Ys?
Okay, candidate YYYY holds the majority position on every issue. However, individual voters may have different positions. The example given by Brams, on the site, does not spell out the voting strategy followed in trying this with Plurality. However, it is pretty obvious. As a voter, you have one of the sixteen positions, so you will vote sincerely for that candidate. So the table provided from Brams is a voting table that shows that there are this many voters who hold each position described. It's arbitrary, in this case, the example is constructed. If there are these many voters, with these positions, and there are none with the position YYYY, all of these voters will vote sincerely for a candidate other than YYYY. Q.E.D. And that this problem seems hard shows how deeply ingrained are some of our habits. To directly answer Mr. Ketchum, suppose you are one of these voters, and your personal position on the issues involved is YYYN. That means that you agree with the majority on three out of four of the issues involved, in that order. There is a candidate with this exact position. So you vote for him or her. In the example, only three other voters are exactly like you. No voters vote for YYYY because, in this example, no voters have that exact position, and because every position is represented in this 16-candidate election, they all have another candidate whom they prefer. If you look at each issue position in the chart, you will see that a majority of voters would approve of each "motion" if presented individually. (I have not verified this, but if it isn't so, a serious mistake was made either in the model or in presenting it.) >Why would Condorcet voters seem to be attracted to Ns? If the answer is >that they truly are, why should Condorcet be blamed as if a bad method? Read the thing again. The chart is a table of positions in the electorate, which then, by the terms of the problem, can be used to predict votes. With Range, an assumption was made that you would vote according to how much you agreed with the candidate. Apparently all issues were considered equally important. With Plurality, you would vote for your favorite only, which is simple, because there is exactly one such candidate, there being only one candidate holding each exact position. The question about Condorcet winners being "attracted" to Ns shows that the point has been entirely missed. Voters are attracted to candidates who agree with them. If your position on an issue was, for example, NNNN, you would vote for that candidate. Voters are not "Condorcet voters," rather, a Condorcet method takes a ranked ballot and translates in a certain way, IRV translates it differently, Borda differently, etc. In any case, to study how a ranked method will apply to this situation, we simply assume that each voter votes first rank for the candidate with an exact match to the voter's position. The voter is going to have exact agreement with no other candidates. This is enough, first of all, to tell us that YYYY will not win under IRV, because all lower rankings will be moot, that candidate is the first one eliminated. "Core support" criterion, that lovely creation of Rob Richie, requires this as if it were desirable, when this example shows a case where a representative -- say it is a rep being elected -- agrees with the electorate majority on every issue, possibly, cannot win. Is this a common case? That is not asserted; for starters, the 16-candidate field is pretty unusual. Except in San Francisco. So we eliminate, for the individual voter, the exact match candidate. We now have a choice of candidates who agree with the voter on three out of four issues. The problem, you will note, isn't solved on that web page. We could make a nice neat assumption that somehow these issues have been arranged in a universal sequence of importance, so that agreement in the first position is more important than that in second, and so on. The effect is that the fourth issue is dropped, there are now eight unique positions, each held by two candidates; one of these, however, was in first rank, so the other one is now the second choice. And, by recursion, we can determine the vote of each voter. I haven't done it. Once upon a time, I would have. Life moves on. ---- Election-Methods mailing list - see http://electorama.com/em for list info
