[EM] About Condorcet//Approval

[Kristofer Munsterhjelm]

Diego Santos wrote:
> Many members of this list prefer a Condorcet method to any other voting 
> method, especially if it meets Smith. But how vulnerable are ranked 
> methods to strategic voting?
> 
> Consider these two assumptions:
> 
> 1. Sincere Condorcet cycles would are too rare if used in real elections.
> 2. Strategies are somewhat common in contentions elections.
> 
> Compromising is almost unnecessary in River, Schulze or Ranked Pairs, 
> but these methods are vulnerable to burying. And still if a sincere 
> Condorcet winner exists, these methods have a possibility to elect a 
> Condorcet loser, because only rankings don't provide enough information 
> to find the sincere winner in all situations.
> 
> I don't have a proof, but I think that if a sincere Condorcet winner 
> exists, Smith//approval is the only method  resistant to both 
> compromising and burying strategies. This property is valid in all 
> 3-candidate scenarios.
> 
> Because Smith is more complex to explain, my current favorite election 
> method is Condorcet//Approval. We don't need complex algorithms to find 
> a winner.

You could also have the approval version of Smith,IRV. Call it 
Condorcet,Approval. I think it's Smith (so it would be Smith,Approval), 
but I'm not sure. The method is this: Drop candidates, starting with the 
Approval loser and moving upwards, until there's a CW. Then that one is 
the winner.

Is Condorcet,Approval (Smith,Approval?) nonmonotonic? If not, and it is 
Smith, then you have a simple Smith-compliant Condorcet/approval method.


These methods would obviously need approval cutoff ballots (unless you 
go with the MDDA assumption, that the approval cutoff is where the voter 
truncates, but I don't think that would be a good idea here).