[EM] RE : [Fwd: Condorcet and the later-no-harm criterion]
Kevin Venzke
stepjak at yahoo.fr
Fri Dec 22 12:30:40 PST 2006
Michael,
--- mrouse1 at mrouse.com a écrit :
> According to wikitest.electorama.com, later-no-harm is incompatible with
> the Condorcet criterion. Is there a general proof or a set of examples
> illustrating this? Plus, are there any examples not involving circular
> ties?
Douglas Woodall showed this in "Monotonicity of single-seat preferential
election rules," Discrete Applied Mathematics 77 (1997), pages 86-87.
3 a
3 b
3 c
2 a>c
2 b>a
2 c>b
Under Woodall's assumptions there must be a scenario "arbitrarily close"
to this one which is not a tie. So suppose that A is the winner in such
a scenario. If the 3 "a" voters instead vote "a>b," then B is the CW.
Alternatively you could say that the original scenario is a tie that is
won by each candidate 1/3 of the time. Then still, when the B preference
is added, A is harmed by having his win odds go from 1/3 to 0.
There is no example not involving circular ties. If you can be assured
that every election will have a CW, there won't be any LNHarm problems.
Also, you can modify this proof to make a similar demonstration about
Condorcet and (my interpretation of) FBC.
Kevin Venzke
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