[EM] favorite betrayal in Condorcet(wv, =permitted, no partial votes)
Warren Smith
wds at math.temple.edu
Wed Aug 31 17:51:24 PDT 2005
The original general-purpose 19-voter FBC example from the Center for Range Voting web page
http://math.temple.edu/~wds/crv/IncentToExagg.html:
8:B>C>A
6:C>A>B
5:A>B>C
B wins under Condorcet Voting [Ranked Pairs variant, winning votes,
equality-ranking permitted] according to Eric Gorr's calculator at
http://www.ericgorr.net/condorcet/. (Incidentally, I think this is also
the same as what has been called "Steve Eppley's MAM method.")
Modification I: In original, 3 of the 6 C>A>B voters switch to A>C>B:
8:B>C>A
3:C>A>B
3:A>C>B
5:A>B>C
New result: AB tie. This is an improvement from the switched voters' point of view.
Modification II: In original, 3 of the 6 C>A>B voters switch to A=C>B:
8:B>C>A
3:C>A>B
3:A=C>B
5:A>B>C
B wins. (This is no change.)
CONCLUSION: these 3 voters, by "betraying" their favorite third-party candidate C
so that they could strategically exaggerate the major-party candidates A and B
to "top and bottom", with C "middle", caused the election result to improve.
But if they had only partially betrayed C by voting A=C>B, then that would not
have provided enough power to change the election result. A full-power betrayal
was necessary.
I conclude from this, that either
(1) Adam Tarr's contention that the "winning votes"
and "permit equalities" enhancement of Condorcet, could avoid this kind of
2-party-domination-inducing problem, was wrong.
or
(2) Eric Gorr's calculator program is wrong.
-Warren D. Smith
[let me know n which of 1,2 you think it is.
let me know if this is really the same thing as Eppley MAM. Thank you.]
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