[EM] Juho--about unreversed Nash equilibria

[Michael Ossipoff]

Juho said (about margins poor properties with regard to unreversed Nash 
equilibria):

This one did not change my feelings much. If you'd say something similar 
about sincere votes

I reply:

Here I believe that you’re saying you want something said about complete 
sincerity rather than just the absence of order-reversal. That would be 
nice, but no non-probabilistic method would comply. With even our best 
methods, if everyone is voting sincerely, sometimes someone can gain by 
order-reversal, and so it won’t be a Nash equilibrium.

So we talk about whether, when there is a CW, there are always un-reversed 
Nash equilibria. And with margins there often are not.

Juho continues:

, and would provide examples

I reply:

Ok, I’ll provide examples. But the margins order-reversal example that I 
already posted is an example. With wv, the order-reversal is thwarted and 
regretted merely by the B voters truncating. With margins it takes more than 
that. Often it takes order-reversal to protect the CW. But, if that isn’t so 
in that particular example (sometimes equal ranking will do it, sometimes it 
takes order-reversal in margins), then I’ll post an example tomorrow or soon 
after. But, for now, do you seriously think that there isn’t an example?

Juho continues:

that demonstrate that this can happen in real life

I reply:

And in what sense do you claim that I haven’t shown that it can happen, when 
I’ve posted an example of it happening? You’d have to tell what is 
improbable about my example.

Juho continues:

and that the game theoretic choices would be obvious to the voters

It’s well established that, if there’s a Nash equilibrium, people will find 
it.

Juho continues:

maybe then. But now this seems a bit like one addition to the long list of 
theoretical claims about the properties of different methods.

I reply:

No. Demonstrated facts about what can happen, and sometimes will happen.

Juho continues:

This criterion sounds a bit tailored to me.

I reply:

first described that test several years ago.

Juho continues:

I find the "no strategies"/"sincere" border line more interesting target of 
study than the "no reversal" border line.

I reply:

But we don’t choose the border line. You’re not going to find a 
non-probabilistic method for which, when there’s a CW, there are Nash 
equilibria in which the CW wins and everyone votes sincerely (as I define 
sincere voting).

The best that can be done is to separate methods according to which ones, 
when there’s a CW, always have a Nash equilibrium in which no one reverses a 
preference.

But you’re the one who chose to post an order-reversal example first, you 
know. So how come now you don’t consider it as important? <smiley>

In any case, the fact that, with margins, there are situations in which the 
only Nash equilibria involve order-reversal says something about margins and 
its stability and its strategy ridden-ness.

Juho continues:

I also don't like the Nash equilibrium game in the sense that approach seems 
to indicate that requiring strategic changes in the ballots is ok.

I reply:

It isn’t ok with me either. That’s why I don’t like margins. If it isn’t ok 
with you, then drop margins.
Juho continues:


I'm trying to stay and keep the voters within the sincere voting model.

I reply:

That’s a coincidence--so am I. Some methods do that much better than others.

Juho continues:

In the subsequent mail you discussed the name of the criterion: > Sincere 
Nash Equilibrium Criterion (SNEC), or > the Unreversed Nash Equilibrium 
Criterion (UNEC). Using some variant with word "unreversed" sounds more 
exact to me than a variant with word "sincere".

I reply:

Yes. I’ll call it the Unreversed Nash Equilibrium Criterion (URNEC).

Juho continues:

Juho P.S. Just an observation, in case you are interested. Few months back I 
wrote on this list about "Ranked Preferences". One reason behind discussing 
such methods was to see what alternatives there are to truncation and 
winning votes (for situations where strategic threats are _considered_ so 
bad that basic Condorcet methods without any protection methods (e.g. 
mm(margins) ) are _considered_ not to be enough).

I reply:

If you’re suggesting anti-strategy enhancements for Condorcet, please specif 
them in a current posting. I’ve suggested a few such. Like ARLO and power 
truncation. But we aggee that Condorcet doesn’t really need them. At least 
wv Condorcet doesn’t need them.

Mike Ossipoff


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