[EM] extension of proof

[Kevin Venzke]

Warren,

--- Warren Smith <wds at math.temple.edu> a écrit :
> the LNH & condorcet incompatibility proof may also be done
> WITHOUT assuming anonymity & neutraily by a 3-case argument

By the way, Woodall 1997 proved that Condorcet is incompatible with either
Later-no-harm and Later-no-help. In fact, I consulted his proof in order
to come up with my FBC demonstration. Woodall's scenario only assumes that 
truncation is permitted, since Woodall doesn't consider Later-no-harm to be 
meaningful when truncation isn't permitted.

This is his proof, from "Monotonicity of single-seat preferential election
rules," Discrete Applied Mathematics 77 (1997), page 86:

3 A
3 B
3 C
2 A>C>B
2 C>B>A
2 B>A>C

According to Woodall, there must be some profile arbitrarily close to this one
which results in A winning. But if, in this profile, the A ballots are placed by
A>B>C ballots, the winner must change to B due to Condorcet, so that LNHarm is
violated.

Kevin Venzke



	

	
		
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