On Tue, 18 May 2004, Ken Johnson wrote: > > >Message: 2 > >From: =?iso-8859-1?q?Kevin=20Venzke?= <[EMAIL PROTECTED]> > > > >Ken, > >... > >I did not test Plurality. I think it is very strange that you found it to > >be better than Approval. ... > > > >Kevin Venzke > >[EMAIL PROTECTED] > > > > > >Message: 3 > >From: [EMAIL PROTECTED] > >... > >That's odd. Approval turned out pretty well in my sims. > >... > >Brian Olson > >http://bolson.org/ > > > > > > > Here's an example of the kind of Bad Thing that can happen with > Approval. There are 3 candidates (A, B, C) and 10 voters. I am using > signed CR's in the range -1 to 1 (CR>0: approve, CR<0: disapprove). > Following are the sincere CR's: > 9 voters: A(-1), B(0.1), C(1) > 1 voter: A(-1), B(1), C(-0.1) > avg CR: A(-1), B(0.19), C(0.89) > approval: A(0), B(10), C(9) > plurality: A(0), B(1), C(9) >
It is interesting that when we measure CR, we always assume that it is average or total CR that is relevant. If we were to erase the "avg CR" line in the above tally and replace it with "min CR" or "lowest percentile CR" we would get A(-1), B(.1), C(-.1) and then declare that B does "best with respect to CR," since B sports the largest number on the "min CR" line, the only line dealing with CR. In fact, arguably "consensus" is more about finding the candidate that maximizes minimum CR than about finding the candidate that maximizes the average CR. That's why getting consensus is so difficult: if one voter holds out, then the consensus isn't perfect. Approval is a kind of compromise between perfect consensus (which gives too much control to the picky, and may be impossible) and average CR maximization, which gives too much credence to the idea that one voter's satisfaction completely makes up for another voter's dissatisfaction. Approval tends to elect the alternative that is tolerable for the greatest number of voters (at least in the zero info case), which is more in the spirit of consensus (where the concerns of minorities cannot be ignored). Digression*********** "One man's good fortune compensates for another's misery" might make more sense in a country where goods and burdens were distributed equally throughout society, but not in any actual capitalist, socialist, or communist country of modern history. If there were such a country, then in that society it would make sense to try to maximize total or average CR. Such a society would also ameliorate the "tyranny of the majority" problem. NAFTA has raised the GNP of both the USA and Mexico, as predicted. But within both countries the rich have gotten richer, and the poor have gotten poorer, because the leaks that used to give some trickle down have all been efficiently caulked. In neither country has a majority of citizens increased in prosperity, but note that it would be possible for the majority to increase in prosperity while the lowest quartile of the poor moved downward. **********end of digression Approval does best at maximizing the number of voters that can live with the winning result in the zero info case. As information increases, Approval moves away from this kind of consensus winner towards the CW if there is one. If that were the whole story, then (in my opinion) Approval would be better than Condorcet, since Approval would always give a result between the Condorcet Winner and the consensus winner (in the above sense) which is the kind of consensus winner most needed in actually existing societies (in my opinion: see above digression). Unfortunately, at least in the USA, moving away from zero information means moving in the opposite direction ... the direction of decreasing information towards more disinformation. "The more you watch, the less you know." As far as I'm concerned, that's the only reason that Condorcet might give a more satisfactory result than Approval in the USA presidential election. But is that possibility worth the extra baggage of ranked ballots? When answering this question keep in mind that Approval elections tend to correct the disinformation, so the dynamics of Approval tend to be self correcting in the long run. Forest > > ---- > Election-methods mailing list - see http://electorama.com/em for list info > ---- Election-methods mailing list - see http://electorama.com/em for list info