[EM] LNHarm performance; majority rule definitions

[Kevin Venzke]

Dear Markus,

--- Markus.Schulze at alumni.TU-Berlin.DE wrote:
> I suggest that (for the sake of completeness) you should also
> indicate in how many cases ranking the additional candidate A
> changed the winner from one of the other unranked candidates
> to candidate A.

That will be easy enough to find. The only unranked candidate would be 
B, though. I'll post some statistics later.

>Then I proposed the following criterion in 1997:
>
>   If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2,
>   then candidate B must be elected with zero
>   probability.
>
>Steve Eppley proposed the following criterion in 2000:
>
>   If d[A,B] > V/2 and p(wv)[B,A] < V/2,
>   then candidate B must be elected with zero
>   probability.

That's interesting. The CDTT contains each candidate who is not disqualified
by your criterion. My failed attempt to improve on the CDTT contained each
candidate not disqualified by Steve Eppley's version of the criterion.

(I posted this before, but the latter wasn't monotonic: Suppose majority-strength
defeats are A>B>C>A and D>B. Eppley's criterion says B can't win. But adding some 
preferences for A so that a majority votes A>D results in B no longer being
disqualified, which is harmful to A.)

It seems that the CDTT is mostly equivalent to the "Smith//Truncation set" you
defined: 
http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-May/001483.html
Except that you wanted it to be somewhat easier to reach a "majority."

I don't remember you mentioning this set again. I wonder if that's because the
Smith//Truncation set is not necessarily a subset of the Smith set.

Kevin Venzke



	

	
		
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