I don't recall using the term "average ranking". My focus was on average (or total) point counts (i.e. Borda scores), as a way of showing the practical and strategic equivalence among the Borda variations mentioned.
Steve Barney wrote: > > Bart: > > OK, I get it now. When I see the term "average ranking" I think of something > other than what you describe. I think you get a more intuitive, and perhaps > more descriptive sense of "average ranking" if you do as follows. You average > the RANKINGS for each candidate by dividing the sum of the rankings of each > candidate by the number of voters. For example, if there are three candidates > and two voters, one voting for A>B>C and the other voting for A>C>B, it goes > like this: > > 1 1 > A A 1st > B C 2nd > C B 3rd > > A: (1+1)/2=1 > B: (2+3)/2=2.5 > C: (3+2)/2=2.5 > > That makes more sense to me, on an intuitive level, than averaging the total > point scores. Don't you agree? > > Steve Barney > > PS: Thanks for the reference. That will help my education along. > > --- In [EMAIL PROTECTED], Bart Ingles <[EMAIL PROTECTED]> wrote: > > > > Steve: > > > > I agree with your Saari results, if the two voters are ignorant enough > > to actually bullet vote (even though this may accurately represent their > > preferences). > > > > One of the ways to defeat Saari's variation is for the two voters to > > collaborate: One voter agrees to rank A, B, and C in order, while the > > other ranks A, C, B. So the individual ballots are worth (2, 1, 0) and > > (2, 0, 1). The combined total is (4, 1, 1), hence the per-ballot > > average (2, .5, .5) I claimed below. > > > > Thus the suggestion that Saari's variation could function as a sort of > > voter intelligence screen, since a potential bullet voter who doesn't > > understand the above strategy has his voting power reduced by one-third. > > > > Samuel Merrill III (Making Multicandidate Elections More Democratic, > > 1988) includes the following citation: > > Black, D. (1958) *The Theory of Committees and Elections*, Cambridge > > University Press. > > > > I haven't read Black's work. But the issue seems moot to me, since with > > the voter strategy above (or the equivalent coin-toss strategy), the > > three variations we have discussed (Borda, Black, and Saari) are all > > equivalent. > > > > Bart > > ===== > "Democracy"?: > http://www1.umn.edu/irp/images/postcardAd2.jpg > AR-NewsWI, a news service for Wisconsin animal advocates: > http://groups.yahoo.com/group/AR-NewsWI/ > > __________________________________________________ > Do You Yahoo!? > Send your FREE holiday greetings online! > http://greetings.yahoo.com
