[EM] IIDA: IIA and SODA delegation

[Jameson Quinn]

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 A>B>C>A 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

[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 A>B>C>A 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
>
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info

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Re: [EM] IIDA: IIA and SODA delegation

[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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