[EM] Approval errs toward middle. IRV errs toward extremes. Which is worse?

[MIKE OSSIPOFF]

Some of us have posted many examples of how IRV eliminates a middle CW and 
jumps to an extremist as the winner. IRV errs toward the extremes.

Approval, when it errs, tends instead to err toward the middle. Middle in 
the sense of inbetween.

Say it's Favorite, Middle, & Worst.

Middle is the CW. Worst has a 1st choice Plurality.

Inaccurate polling results make it look as if Favorite has a 1st choice 
majority. So the Favorite voters don't vote for Middle. The result? Does 
Worsts win because Middle doesn't get support? No. The Worst voters, 
believing that Favorite will outpoll Worst, if they vote at all, might as 
well hope that Favorite doesn't reallly have a 1st choice majorilty, and 
vote for Middle, in hopes of keeping Favorite from winning. So Middle isn't 
unsupported. Middle wins.

Sure, if Favorite does have a 1st choice majority, and inaccurate polling 
information makes it look as if Worst will outpoll Favorite, then of course 
the Favorite voters will vote for Middle, and will give the election away to 
hir. So Approval can err toward the Middle.

As I said, IRV errs by electing extremists, and Approval, when it errs, 
tends to instead err toward the middle. Which is more dangerous? Which is 
more likely to result in there not being a next election?

By the way, the likelilhood of Approval's error has been exaggerated. How 
likely is it really that, if Favorite has a 1st choice majorilty, it will 
appear that Worst will outpoll Favoarite? That's quite a big mis-estimate, 
isn't it.

Unless, of course, Middle has very little 1st choice support. But that's the 
most familiar (but not the only) IRV failure example. IRV's simple 
3-candidate failure example.

So I've discussed several reasons why Approval is better than IRV:

1. Asymmetrical pair correspondence of examples where IRV beats Approval by 
ICC & MMC, with examples where Approval beats IRV by WDSC & FBC.

2. The fact that ICC & MMC are fortuitous special case criteria, while WDSC 
& FBC have more general applicability.

3. Merrill's SU results, in which Approval is significantly better than IRV 
by SU.

4. Approval always has Nash equilibiria in which no one reverses a 
preference. But IRV has situations where the only Nash equillilbria are ones 
in which people bury their favorite to elect a CW.

5. IRV errs by electing extremists. Approval, when it errs, tends to err 
toward the middle.

Mike Ossipoff

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