[EM] Names for equilibria. Principled voting. Our 0-info elections.

MIKE OSSIPOFF nkklrp at hotmail.com
Fri Nov 26 02:36:04 PST 2004


OK, so there are many different ways to generalize/extend/apply/whatever the 
concept of Nash equilibrium to voting, and my preferred formalism is hardly 
the only way to do it.  I am no longer interested in the issue of who gave 
what name to what.

I reply:

  That was evident from the fact that you were calling voting Nash 
equilibrilum "Mike's equilibriuim", "Mike's definiltion", and "Your 
equilibriuim" after I'd told you that I wasn't the first to propose it. But 
if, now, not being interested means that you won't continue to press the 
topic, that's great.

You continued:

I will, however, observe that it is probably not a good idea to apply the 
name "Nash" to an equilibrium that doesn't always exist.

I reply:

I don't know if objective statements can be made about whether a name is a 
good idea, unless one name is briefer than another, or one uses offensive 
language, etc.

You continued:

One of the beautiful things about Nash's result is that his equilibria 
always exist as long as some fairly non-restrictive conditions are met.

I reply:

In other words, it doesn't always exist. But it always exists under certrain 

Of course you'd agree that what you're talking about is a matter of 
individual taste. I've been interested in the actual use of these 
definitions, and issues of taste or aesthetics in naming were never the main 
thing for me.
And I don't deny the usefulness of a variety of definiltions. Of course it's 
good to say something about equilibria of voting systems in 
cyclical-public-preference situations in which there are no voting Nash 
equilibria. But it wasn't I who was criticizing other definitions.

Voting Nash equilibrium was what I was most recently using, because it was 
more useful. If I do more comparison of Nash-like equilbria for voting 
systems, it's a sure thing that I'll use voting Nash equiilbrlium, because 
of its briefest, cleanest definition, and because of previous usefulness.

When using something in public argument, if two definitions apply usefully 
to the situation you're discussing, and one of them has a briefer, neater 
definition, then it's more effective to ouse that one.

But no doubt I'd use others too. For instance, surely I'd also use  ones 
like yours and the one that
I proposed, when I was the one who first used Nash-like equililbria for 
comparing voting systems on EM.

  I'd use those others so that I could also compare voting systems in 
situations with cyclilc public collective preferences in which there are no 
voting Nash equilibria, as I've been deining that term.

But of course situations where there is a CW are much more important.

You continued:

The ubiquity of his equilibria is what makes his concept so broadly 
applicable and important.

I reply:
The equilibrium that was proposed on EM some time ago, which I call voting 
Nash equilibriuim,  was the one that was useful for what I was discussing at 
that time, though I had previously considered one similar to yours.

Saying that one kind of equilibrium is the useful or applicable one  for 
voting systems would be an overly sweeping and premature statement. But I 
realize that you didn't say that.

You continued:

If one uses the word "Nash" in the name for an equilibrium condition that 
can't always be met, it deviates from the original spirit of the term.

I reply:

Often the "spirit" of a term is debatable and individual and subjective, 
especially since different people could judge by different considerations.

You continued:

However, that is purely a matter of taste, and not something that I have any 
more desire to argue over.

  I reply:

  Thank you for taking the higih road :-)  ...after being the one who was 
pressing the "incorrect-name" issue over several e-mails..

You cointinued:

Of course, if we have other goals, such as sending messages to influence 
parties over the long term, then obviously things become more complicated.)

  I reply:

  Maybe principled voting, voting as if one has even a little respect for 
honesty, can send a message to parties, but, the thing is-is, I doubt that 
that's why people vote that way. I didn't vote for Nader to influence the 
Democrat party. They're a lost cause. I simply didn't want to vote for 
dishonest candidates, or for hurting people overseas who haven't done 
anything to us, and that left only Nader & Camejo. People voted for Nader & 
Camejo because they chose to vote for the policy-proposals that they 
actually like.

But it could also be argued that voting for Nader was good 0-info strategy, 
because the information from the media  is so unreliable, so biased toward 
their owners'  interest, that our elections are really 0-info elections. In 
Plurality, the correct 0-info strategy is to vote for one's favorite.

Good, let's agree that the Nash-like voting equilibria issue is completely 
concluded. Is that a deal? It's much more productive to discuss method merit 
than to debate names.

Mike Ossipoff

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