[EM] Margins' 0-info insincerity

[MIKE OSSIPOFF]

EM list:

Blake pointed out that, with 0-info, in an election where A
has a utility of 1, C has a utility of 0, & B has a utility
inbetween, with Condorcet, a voter could sometimes have incentive
to rank B equal to A, in 1st place, even though he likes B less
than A.

That's true. If B's utility is greater than .8, then it's to your
advantage to rank B in 1st place, with A. That means that you'll
have that incentive about 1/5 of the time, 20%.

So you can have incentive to not vote your AB preference.

And with Margins, it's to your advantage to not vote your BC
preference if B's utility is less than 5/16. So you'll have
that incentive about 31.25% of the time.

So, with both methods, it will sometimes be to your advantage
to not express a preference. But with Margins you have that
incentive about 1.5 times as often.
I'd say that means that Margins is about 1.5 times as insincere
as Condorcet, even with 0-info.

***

If anyone requests it, I'll post the way I got those results
when there's time to, in a few days. If you doubt those results,
you could ask me to posts how I got them, or you could start
by calculating your own version of those answers, and then,
if they differ from my answers, we should both post our derivations.
Either way.

***

Mike Ossipoff



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