Saari and Cyclic Ambiguities
atarr at purdue.edu
Fri Mar 29 12:37:13 PST 2002
The only ranked method discussed here that does NOT hand this election to E
Borda count reduces this to
And the Borda scores are 20, 15, 15, 17, 30, for A, B, C, D, and E,
respectively. E wins by a huge margin.
In Condorcet voting, the Smith/Schwartz set is every candidate, there are
no ties, and every voter expressed a full ballot. So all the Condorcet
methods are pretty much the same. Ranked pairs overturns D>E and C>E (in
that order). SSD drops C>E, B>D, D>A, A>C, E>B, and D>E, (in that
order). Both results leave E unbeaten.
In IRV, A is eliminated first, then C, then E (by a count of 11B 15C
9E). E gets screwed by having the wrong votes transfer. B wins the
election, even though B finished dead last in Borda Count and only beats
one candidate pairwise.
If the Approval cutoff is consistent, then Approval elects E as
well. Plurality of course elects E as well. So really, only IRV can screw
this one up. It's not tremendously illustrative (sorry).
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