[EM] Spoilers

[MIKE OSSIPOFF]

Anthony wrote:

>This brought up a question for me.  Suppose a
>purely hypothetical Approval election in which
>there are two major parties, with candidates
>Mickey and Goofy.  A third party candidate,
>Roadrunner, is very popular, but is not expected
>to win.
>
>Roadrunner voters feel they should vote for
>Mickey in addition to their own bird, since if
>Roadrunner doesn't win, they absolutely don't
>want the election going to Goofy.  So most
>Roadrunner voters vote for Mickey too.
>
>On the other hand, Mickey voters think that if
>support for Goofy is so strong that he beats
>Mickey, then for sure he will beat Roadrunner
>too.  Thus, they figure that they shouldn't vote
>for Roadrunner, since that could build up support
>for Roadrunner to the point where, if Goofy
>doesn't win after all, the election could go to
>Roadrunner.

Yes, if Mickey is the perceived alternative to Goofy, and
appears to be the compromise that Roadrunner voters need, then
the Mickey voters shouldn't vote for Roadrunner. It should be
understood by both the Mickey voters and the Roadrunner voters that
Mickey is the compromise for beating Goofy--if that's how it
looks.

>
>The end result is that Mickey's perceived
>advantage over Roadrunner might get him elected
>even though Roadrunner might actually have more
>sincere approval than Mickey.
>
>Doesn't this sound a lot like the way Plurality
>and IRV suppress support for a third party by
>forcing voters to be insincere?

Only somewhat. First of all, what this means is that Approval needs
predictive information and strategy. But it doesn't need the kind
of drastic favorite-dumping strategy that Plurality & IRV need.

This reply won't be limited to repeating this statement, but
there are degrees of suppressing support for a 3rd party: Approval
makes it necessary for the Roadrunner voters to not cast a pairwise
vote between Roadrunner and Mickey. Plurality, and often IRV, make
it necessary for the Roadrunner voters to insincerely vote Mickey
_over_ Roadrunner.


Myerson & Weber have written about "voting equilibria". A summary
of what that means is: An outcome that confirms the predictive beliefs
that led people to vote as they did.

They point out that, in Plurality, nearly _any_ 2 parties can be
the top 2 votegetters at equilibrium, if it's perceived that they're
"the 2 choices".

That isn't true of Approval. If Roadrunner could win pairwise against
Goofy, then Goofy won't get more votes than Roadrunner. If the
Mickey voters don't vote for a 2nd choice, then Roadrunner will get
more votes than Goofy if he has more 1st choice support. If they all
do vote 2nd choices, then Roadrunner will outpoll Goofy if Roadrunner
has a sincere pairwise win against Goofy.

If there's a party at the voter median position, in Approval, then
it's the only party that can win at equilibrium.

Approval quickly homes in on the voter median point, and stays there.

Myerson's & Weber's definition doesn't apply to rank methods, but it's
evident that a method like IRV that will sometimes make people vote
a compromise over their favorite can make it appear, in the election
returns, as if those voters' favorite isn't winnable.

That's a big qualitiative difference between Approval, vs Plurality
& IRV.

Additionally, Approval passes the Unanimously Unpreferred Candidate
Criterion, but Plurality & IRV fail it. If everyone prefers X to Xc,
and if Xc wins, and if a certain voter has voted Xc over X, then
it shouldn't be that there's no way that he can change his vote so
as to no longer vote Xc over X without causing the election of someone
whom he likes less than Xc.

Approval meets that criterion, but Plurality & IRV don't.

The "c" in "Xc" stands for corrupt. UUCC is a simplification &
extension of Myerson's corruption test for voting systems. Incidentally,
Borda does even worse than Plurality & IRV by Myerson's test.

I've posted more elaborately scrupulous definitions of UUCC, and they're
in the archives. I can find them if you'd like. Wordings written so
that there can be no 2 ways to interpret them.

But yes, Approval does have things in common with Plurality, strategically:

The way you can go wrong in Approval or Plurality is if you think
Favorite will get fewer votes than Worst, when actually Favorite
has a majority--or if you think that Favorite has a majority, but
he turns out to get fewer votes than Worst.

A majority vs fewer votes than Worst. That's a big mis-estimate, isn't
it. Let's not exaggerate how easy it is to make that mis-estimate.

Especially if all 3 candidates are anywhere near equal. The way
that mis-estimate would be easier would be if Middle had very little
1st choice support. But typically the median is also near the mode,
and so that isn't so likely. Also, of course, that's also the guaranteed
IRV failure example.

Another thing: Say everyone mistakenly believes that Worst will outpoll
Favorite. The Worst Voters won't vote for Middle, but the Favorite
voters will.

Say everyone mistakenly believes that Favorite will outpoll Worst.
The Favorite voters won't vote for Middle, whom they need, but the
Worst voters will.

Approval, even when everyone has the same misinformation, errs
middle-ward, not to the extremes, which is where IRV will be regularly
jumping to.

If it looks like Worst will or won't outpoll Favorite, that information
will be available to everyone.

Now, you might say that these advantages are shared with Plurality.
Sure. The strategy aspects that Approval shares with Plurality aren't
the worst thing about Plurality. The worst thing about Plurality is
the way that it makes people dump their favorites, and conceals
those favorites' support, and can stick away from the voter median
at equilibrium.

Mike Ossipoff

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