Juho, thanks for your insights. In your excellent example, candidate D appears to be the IA-MPO winner, especially if we define implicit approval as "ranked above bottom." Forest On Fri, Jun 5, 2015 at 12:03 AM, Juho Laatu <juho4880@yahoo.com> wrote: > One solution for this problem would be to use some rated method. If every > voter votes according to his travel distances to each candidate center we > could get ideal results. I mean that actually we are discussing here > indirectly whether to use ranked or rated methods. > > (In the example one could mandate each voter to vote based on the distance > (in the rated method based election), or calculate the results based on the > addresses of the voters, i.e. without having an election. This way we could > get rid of any possible strategies. :-) ) > > When compared to the rated methods, (plain) Condorcet methods focus only > on counting the majorities, not the strength of opinions. In this example > any two 33 voter groups could form a clear majority. They could agree to > vote together to make the center between them the winner. Any sensible > argument against the third 33 voter group could be a sufficient reason (for > the two 33 groups) to do so. > > One could say that Condorcet methods aim at electing stable winners. They > try to seek a winner that will not be disliked by some clear majority. (I'm > vague here because the behaviour of different Condorcet methods is somewhat > different.) If you would elect C, there could easily be some majority > alliance that would be interested in trying to change the elected center to > another center. If you elect Mx, the outcome is probably more stable. > > One can study this example also from strategic voting point of view. I > guess the given votes are quite stable and there are no obvious strategies > to improve one's (distance based) expected outcome. Condorcet could however > make it possible to strategically make the result worse in the sense that > the voters could reduce their expected outcome in terms of distance but > make the expected outcome better in the sense that the whole society would > benefit of it. I mean that many voters could see that C is obviously in > some sense best for the society, and they could therefore rank C first in > their ballots. No harm done and no risks doing so, if the voters truly > prefer a solution that is good for all, and not just good for them > personally. The point here is that Condorcet does not force them to make > decisions that they consider stupid. If some solution looks stupid to us in > some example, maybe the voters would see that stupidity too, and vote > accordingly (changing their preferences to something more sensible). > > Juho > > P.S. I'm ok with electing Condorcet losers in some (extreme) scenarios. As > I already said, Condorcet methods tend to seek stable solutions. In the > following example the Condorcet loser (D) is disliked only very mildly in > the pairwise comparisons, while all the others have a strong opposition > against them (in favour of changing them to some other candidate). > 17 A>B>D>C > 16 A>D>B>C > 17 B>C>D>A > 16 B>D>C>A > 17 C>A>D>B > 16 C>D>A>B > > > > On 05 Jun 2015, at 05:11, Forest Simmons <fsimmons@pcc.edu> wrote: > > > Suppose that a town with 100 voting citizens has 33 voters residing at > each of the three vertices of an equilateral triangle (with two mile sides, > say), and one voter residing within two hundred yards of the the center of > the triangle. > > > Proposed sites for the new community center are M1, M2, and M3, at the > respective midpoints of the three sides of the triangle, as well as site C > at the center of the triangle’ a couple of hundred yards from the lone > voter that we just mentioned. > > > Assuming that voters prefer closer sites over more distant sites the > preferences are > > > 33 M1=M2>C > > 33 M1=M3>C > > 33 M2=M3>C > > 01 C > > Note that C is the Condorcet Loser, since each of the M’s beats C pairwise > by almost a two-thirds majority, 66 to 34. > > > On the other hand, C is the IA winner with 100 percent implicit approval. > > > Candidate C is also the IA-MPO winner with a score of 100-66, compared > with 66-33 for the other alternatives. > > > How about average distance of voters from each of the alternatives? > > The average distance to alternative C is 0.66 times the square root of > three miles, or about 1.14 miles. > > > The average distance to any of the M’s is about 1.24 miles. > > > If the M’s were moved directly away from their midpoint positions to a > position nearly twice as far from the center as the midpoint position, the > preference schedule based on distances would not change, but the average > distance from voter to any of the M’s would go up from about 1.24 to > about 1.52 miles, more than 33 percent farther than the average distance to > C. > > > Think of it: the center location is about 33 percent better on average. It > cuts the distance in half for the faction that ends up furthest from the > winning M, and doesn’t give a lopsided solution where 33 voters have to go > twice as far (forever after) as the other 66 voters on the vertices of the > triangle. It is the geometrical center solution and the approval > solution, but it is the Condorcet Loser. > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > > >