[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
>
>
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