[Election-Methods] Elect the Compromise (correction)

[Forest W Simmons]

Below where I said "unlike Borda" I should have said "unlike D2MAC."  
Neither the Borda solution nor the reverse plurality solution requires 
anything other than the ordinal preferences.

So the deterministic solutions that do not depend on some form of vote 
trading are insensitive to whether or not the voters are inclined to 
approve C.

Perhaps we could refine the challenge to ask for methods that elect C 
with near certainty when the two factions are

55 A 100 C 80 B 0
45 B 100 C 80 B 0

but almost surely do not elect C with when the two factions are

55 A 100 C 20 B 0
45 B 100 C 20 B 0

assuming throughout optimal strategical voting under near perfect 
information.

It seems to me that vote trading and/or randomness are needed to solve 
this challenge.


Forest W Simmons wrote:

>
>I was thinking of "vote against one," which could be called Reverse 
>Plurality, the base method for each step of the Coombs sequential 
>elimination method. Equivalently, it could be described as, "vote for 
>exactly two candidates."
>
>This method would elect C because the 45 in favor of B would have no 
>reason to vote against B or C, so they would all vote against A.  If 
>the other 55 voted more against C than B, then B would win, so they 
>will vote more against B than C, which allows C to win.
>
>Unlike Borda, this solution works even if the ratings for C are low:
>
>55 A>>C>B
>45 B>>C>A
>
>I'm not advocating Reverse Plurality, but it is perhaps the simplest 
>deterministic solution to the challenge.