[Election-Methods] Elect the Compromise (correction)

[raphfrk at netscape.net]

 Forest W Simmons wrote:

> 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.
> 

What about using a clone elimination stage to allow Borda be used.

For example, select 3 candidates using a PR method.   This is basically
a clone elimination stage.

The winner is then determined using Borda where all 3 candidates must be
ranked.

The problem is that A can still be cloned into A1 and A2 as the A faction has a majority and
so can ontain a majority under any reasonable PR method.  However, at least there would be 
a choice between A1 and A2.  The B faction would get to decide which of the 2 A's would 
win.  The end result could easily be that C is A2 (i.e. the 2nd candidate from the A faction 
... which isn't likely to be infinitely cohesive).  

Also, the more candidates that are passed through the first stage the better.  If 4 candidates
were passed, then a faction with 40%+1 of the vote can get 2 candidates to the 2nd stage.

This would yield

A: 2
B: 2

If A and B factions both ran clones, then the result is:

55:  A1>A2>B2>B1
45:  B1>B2>A2>A1

A1 gets 3*55 = 165
A2 gets 2*55 + 45 = 155
B2 gets 55 + 2*45 = 145
B1 gets 3*45 = 135

This assumes perfect strategy.  The A faction is exactly countering
each B faction vote.  However, it is unlikely that the B faction could
coordinate all to vote the same way without the A faction winning.

It still doesn't solve the problem, but at least it gives the voters more choice and they 
aren't likely to be party fanatics in general.  Also, if there are lots of candidates
through the first stage, maintaining party uniformity would be alot harder.





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