Re: [EM] IIDA: IIA and SODA delegation

2012-03-29 Thread Ted Stern 
It is my impression that the only situations in which IIAC fails is
when there is no majority.

Would it be possible to get around IIAC by adding a two-candidate
runoff?

Ted

On 29 Mar 2012 05:35:47 -0700, Jameson Quinn wrote:

 The Independence of Irrelevant Alternatives criterion (IIA, also sometimes
 abbreviated IIAC) is a bit of a silly criterion. Arguably, no system really
 passes it. For any ranked system, just take a simple ABCA 3-candidate
 Condorcet cycle, and then remove the irrelevant candidate who loses to the
 winner; any system which reduces to plurality in the 2-candidate case must now
 fail IIA. Rated systems can pass, but that means assuming that people will 
 vote
 silly ballots. For example, in approval, ballots with all candidates approved
 or all candidates disapproved; or in range, non-normalized ballots. (Majority
 Judgment is the only commonly-discussed system where a non-normalized ballot
 might not be strategically stupid; but even there, voting all candidates at 
 the
 same grade seems pretty dumb.)

 But of course, because of its role in Arrow's theorem, and because of the
 simplicity of definition, it's not a criterion we can entirely ignore. For
 instance, it's always going to be a part of the comparison table in wikipedia.
 (Which has gotten some updates recently; check it out)

 When it comes to delegated systems like SODA, it becomes even crazier. Is a
 candidate irrelevant even though their use of the votes delegated to them 
 was
 what swung the election? So, just as Condorcet advocates have defined
 Independence of Smith-Dominated Alternatives (ISDA), I'd like to define
 Independence of Delegation-Irrelevant Alternatives (IIDA). A system is IIDA
 if, on adding a new candidate, the winner either stays the same, changes to 
 the
 new candidate, or changes to a candidate whom the new candidate prefers over
 the previous winner.

 Unfortunately, SODA isn't actually 100% IIDA. The scenario where it fails is a
 chicken dilemma where the new candidate pulls enough votes from one of 
 the??two
 near-clone chicken candidates??to shift their delegation order. But it does
 meet this criterion for three candidates; that is, a third candidate does not
 shift the balance of power between the first two unless they choose to. And I
 suspect that you could define a SODA-like system which would meet IIDA, if you
 didn't mind adding complications.

 Jameson


 
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Re: [EM] IIDA: IIA and SODA delegation

2012-03-29 Thread Kristofer Munsterhjelm 

On 03/29/2012 09:41 PM, Ted Stern wrote:

It is my impression that the only situations in which IIAC fails is
when there is no majority.

Would it be possible to get around IIAC by adding a two-candidate
runoff?


I don't think so. In a subset of all possible two-round elections, the 
voters are perfectly consistent in the second round. That is, all the 
people who prefer A to B votes A above B if A and B are the second round 
candidates, and so for any and all pairs of candidates.


For these perfectly consistent scenarios, you can define a virtual 
one-round method that determines the winner and second-place finisher 
according to the original method, then determines how the voters would 
have voted in the second round according to the pairwise preferences 
submitted in the first round.


This virtual one-round method is an one-round method like any other. If 
it passes IIAC, then it serves as a one-round method that passes IIAC. 
So if a ranked two-round method passes IIAC, then there also exists a 
ranked one-round method that passes IIAC -- and if a rated two-round 
method passes IIAC, then there also exists a rated one-round method that 
passes IIAC. Runoffs by themselves don't grant IIAC where it otherwise 
wouldn't exist, because the runoff method has to be irrelevant of 
independent candidates in every single situation.


(Runoffs have other things going for them. They make strategy harder to 
pull off because strategists have to focus on two candidates, not just 
one; and the second round is always honest.)



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