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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