[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<http://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29>.
(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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20120329/cd987345/attachment-0003.htm>