[EM] CD, briefer, better-workng, and with Juho's clarifications

[Juho Laatu]

Some comments on the CD criterion itself.

I see CD as a situation where there is a group of voters (V) that has majority and whose members all prefer certain set of candidates (C) over all other candidates. With sincere votes one of the C candidates is guaranteed to win (it may be unclear which one of them). Some V voters can improve the expected outcome by voting some C candidates "lower". The Chicken Dilemma emerges when multiple members/subgroups of V (with different preferences within C) follow this strategy, and as a result some candidate outside C wins.

This is not an exact definition yet, but you can see what I mean. Should we assume that in CD there are multiple strategic groups within V? Should we assume that one of the candidates outside C will win?

Juho


On 11.1.2014, at 16.26, Michael Ossipoff <email9648742 at gmail.com> wrote:

> I've added Juho's clarifications to CD's definition.
>  
> Additionally, I noticed that, not only didn't CD apply to Plurality, but it didn't apply to Approval either, for the same reason. That wasn't acceptable, when a criterion can't compare, to other methods, a method widely agreed to be a contender for one of the best.
>  
> I'd felt that the premise stipulation that A would win under sincere voting might not be necessary, but I was leaving it in because, it seemed desirable. But when I found that it made the criterion apply to neiithr Plurality nor Approval, I deleted that condition from the premise.
>  
> That was where it was necessary to speak of sincerity. Without that stipulation, it's no longer for CD to speak sincerity or preferences. That means that the sincere voting definition can be removed from the Preliminary Definitions.
>  
> All this makes CD considerably briefer.
>  
> Now CD applies to Plurality. (Plurality doesn't pass), and to Approval.
> Chicken Dilemma Criterion
> 
> From Electowiki
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> Definition
> 
> Supporting definition:
> 
> The A voters are the voters who vote A over everyone else. The B voters are the voters who vote B over everyone else. The C voters are the voters who vote C over everyone else.
> 
> 
> Premise:
> 
> 1. There are 3 candidates: A, B, and C.
> 
> 2. The A voters and the B voters, combined, add up to more than half of the voters in the election.
> 
> 3. The A voters are more numerous than the B voters. The C voters are more numerous than the A voters, and more numerous than the B voters.
> 
> 4. The A voters vote B over C. The B voters refuse to vote A over anyone.
> 
> 5. None of the C voters vote A or B over the other.
> 
> Requirement:
> 
> B doesn't win.
> 
> [end of CD definition]
> 
> 
> 
> In the chicken dilemma scenario described in the premise of the Chicken Dilemma Criterion (CD) defined above, if B won, then the B voters would have successfully taken advantage of the A voters' co-operativeness. The A voters wanted to vote both A and B over the candidates disliked by both the A voters and B voters. Thereby they helped {A,B} against worse candidates. But, with methods that fail CD, the message is "You help, you lose".
> 
> Some methods that pass the Chicken Dilemma Criterion:
> 
> ICT, Symmetrical ICT, MMPO, MDDTR, IRV, Benham's method, Woodall's method
> 
>  
>  
> ----
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