[EM] Juho--about unreversed Nash equilibria

Mon Feb 26 12:56:07 PST 2007

On Feb 26, 2007, at 3:42 , Michael Ossipoff wrote:

> 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.

I didin't take position on what to prove, just wanted to say that the  
factors that take an election from sincere voting to strategic voting  
are interesting. In most cases going to strategies and counter  
strategies makes the usability of a voting system poor. There may be  
exceptions but I assume poor usability until I see the opposite  
demonstrated. (You can fix my problem by giving good general rules on  
how voters are supposed to vote. One answer might be that they are  
not supposed to think but just vote as told by the party strategists  
(not a perfect one).)

> 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?

An example of what?

> 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.

I think I already replied to the examples and commented e.g. that  
with the given numbers they need a lot of strategic voters to  
succeed. That would make their success less probable at least in  
large public elections.

> 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.

You should maybe describe how you expect the correct voting patterns  
to be found in real elections (by regular voters).

> 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.

There are some scenarios that can be said to never happen if the  
probability is low enough. Much depends on the assumptions (number of  
voters, recommended strategies, level of sincere/strategic  
orientation,...). For example making all the voters of a large group  
vote strategically according to some plan sounds quite theoretical to  
me (in most environments).

> Juho continues:
>
> This criterion sounds a bit tailored to me.
>
> I reply:
>
> first described that test several years ago.

This wouldn't make it less tailored.

> 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).

Sincerity is an interesting border line since voting methods behave  
nicely when we are above that border line. I'd be more interested in  
strategic voting below that line if the method in question would fail  
in keeping sufficient part of the voters sincere and there wouldn't  
be any better methods available. I mean that I'd first like to check  
the assumption that voters would stay sincere enough, and if needed,  
alternative methods that can do it.

> 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>

I think those were studying the borderline between sincere and  
strategic voting, and margins and winning votes.

> 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.

I'd still appreciate the "no Nash equilibria problem" to be  
demonstrated as a real life example. Well, maybe you think you  
already did this :-).

> 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.

Yes, also I lean in the direction that Condorcet doesn't normally  
need any that powerful methods. Maybe also use of winning votes is an  
overkill and "sincere margins" are good enough :-). I also used  
related methods like tied at the top/bottom. A link to one of the  
mails is given below. But these are just FYI in case you are interested.

Juho

http://lists.electorama.com/pipermail/election-methods-electorama.com/ 
2006-November/018855.html

>
> Mike Ossipoff
>
>
> ----
> election-methods mailing list - see http://electorama.com/em for  
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