[EM] RE : Combating the Approval Burr dilemma

[Kevin Venzke]

raphfrk,

--- raphfrk at netscape.net a écrit :
>  As a quick recap, the Burr dilemma is where there is an incentive for
> voters from 
>  the same faction/party not to approve all members of that party.
>  
>  So, what about something like this:
>  
>  A ballot counts as approving a candidate if 
>  
>  - the voter selects approved
>  - the voter selects favorite
>  - the voter selects conditional and the candidate got more favorite
>  votes than the voter's favorite.

This is rather IRVish in how it plays out. Unlike IRV there would be
less incentive for the supporters of the less popular of the two 
candidates to lie about their favorite, since the win is determined on
approval. But on the other hand this is worse than IRV in that one
*can* cause their favorite to lose by listing conditional choices.
(Your favorite could be leading in approval, but poor in first 
preferences, causing your ballot to approve some conditional choices.)

Here are the treatments of this scenario that I'm aware of, where B
is short a majority, and A1 and A2 supporters debate whether to defect
or cooperate, and B voters have no lower preferences:

IRV:
A1 and A2 both loyal: the preferred of A1 and A2 wins
A1 and A2 both disloyal: B wins
A1 loyal, A2 disloyal: A2 wins if he would have, otherwise B wins

Problem: This can violate the only expressed majority preference in an
election like 49 B, 24 A2, 27 A1>A2, in which B is elected and the A1
supporters' compromise choice is ignored.


Approval or Schulze(wv):
A1 and A2 both loyal: the preferred of A1 and A2 wins (or approval tie)
A1 and A2 both disloyal: B wins
A1 loyal, A2 disloyal: A2 wins

Problem: Burr dilemma, as you notice.


MinMax (pairwise opposition) with ties broken by first preferences:
A1 and A2 both loyal: the preferred of A1 and A2 wins
A1 and A2 both disloyal: B wins
A1 loyal, A2 disloyal: the preferred of A1 and A2 wins

Problem: In an election like 49 B, 24 A2, 27 A1>A2, A1 wins despite
the possibility that A1 and A2 are not even aligned, and A1 doesn't
appear to deserve to beat B.


I have a simple method called "vote for and against" (VFA) which is 
similar to the latter. The voter votes FOR one candidate and AGAINST 
one candidate. If any candidate receives AGAINST votes from more than 
half of the voters, this candidate can't win. Subject to this, the 
candidate with the most FOR votes is elected.

So in our scenario, there is no such thing as defection unless A1 or
A2 supporters decide to vote against a candidate other than B (which
would make no sense if they're aligned). If A1 and A2 supporters make
up a majority, B will be disqualified, and the plurality winner between
A1 and A2 wins.

Something I like about this method is that if there are three candidates,
Left, Right, and Center, and it is assumed that either Left or Right
will be receiving a majority of the AGAINST votes, then those voters
who prefer Center have no incentive to not vote for him.

Kevin Venzke


	

	
		
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