[EM] Alex, the arbiter of equilibrium-naming

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Nov 25 02:32:44 PST 2004


You've answered my question: You really don't have anything better to do.

You said:

I think the reason why I called it "vague" is that at some point in that 
thread the subject of debate was Nash equilibrium, a very particular type of 
equilibrium.  Due to the way the discussion had been going, I assumed that 
you were trying to define Nash equilibrium for voting, instead of some other 
type of equilibrium.  That was my mistake.

I reply:

Oh I forgive you for that, Alex. Your mistake is excusable,  considering 
that I call it voting Nash equilibrium, and repeatedly point out that it's 
the obvioius generalization of Nash equilibrium from the case where only one 
individual changes their strategy. :-)

In fact I still call it that. And it is the obvious generalization of Nash 
equilibrium from the case where only one individual changes their strategy.  
  So it would be perfectly excusable even if you still continuied to make 
your mistake.

You continued:

The great thing about Nash equilibrium is that if everything in your game is 
suitably specified (and the criteria aren't all that strict) then at least 
one Nash equilibrium is guaranteed to exist.  Your equilibrium obviously 
isn't a Nash equilibrium.

I reply:

Is supposed to be some  connection between those two statements?

It's great that Nash equilibrium has that great thing about it when only one 
person changes their strategy. So your wishful thinking about what would be 
great, if it were true under very different conditions,  is your basis for 
decreeing what can and cannot be named as a generalization  of Nash 

But things are actually different when a set of individuals  change their 
strategy. Most people wouldn't expect the properties to all remain the same.
There now, I've cleared  up another mistake for you.

Nash spoke of outcomes that no one individual can improve on  for himself.

On EM, we spoke  of outcomes that no set of individuals can improve on for 

That is the obvious generalization of Nash equilibrium from the case where 
only one individual changes their strategy to the case where a set of 
individuals change their strategy.

And let me correct still another mistake of yours. You keep calling voting 
Nash equilibrium "Mike's equilibrium", "Mike's definition", or "Your 
equilibrium". One mighit have thought that I'd made it clear in previous 
postings that I wasn't the first to proposes that Nash equilibrium 
definition on EM.

You continued:

(see my example with Approval Voting and a Condorcet cycle)

Also, I have acknowledged that my formulation of Nash equilibrium for voting 
is not the only valid way to define a Nash equilibrium.

I reply:

...but you seem to havea  forgotten that acknoledgement since then
You continued:

I have always pointed out that you could treat individual voters as players 
instead of factions of voters.  I have gone on to argue, however, that such 
a treatment is not particularly useful, and that my definition of the 
players is the more useful one.  That's all.

I reply:

Are you aware that that was discussed on EM years ago?

Anyway, even if we call a voter a player, that's useful as long as we speak 
of whether a set of plalyers can improve the outcome for themselves. A set 
of players is a generalization of a player. I didn't say that voting Nash 
equilibrium is identical to Nash's definition, only that it is a 
generalization of it.

Or, if you prefer, you can call a player any set of voters who change their 
vote attempting to all improve the outcom for themselves.

The word "player" isn't mentioned in my definition. But if Nash said 
"player", then you can take your pick of those two player-meanings that I've 
just suggested.

You prefer to add a definition that wasn't part of Nash's wording, the 
definition of a player as a set of voters who share the same preferences. 
That unnecessaly adds a stipulation that puts your definition farther from 
what Nash was talking about. There's nothing wrong with inventing, as long 
as you realize that that's what you're doing.

You continuied:

Anyway, I apologize for misunderstanding and thinking that you were trying 
to define a Nash equilibrium.

I reply:

That's ok. Your your error  is entirely excusable, , considering what I've 
been saying all this time :-)

You continued:

I recognize that you were defining a different type of equilibrium.

I reply:

I do believe he's got it.  Yes, we on EM defined an equilibrium that is for 
voting, for when there are many individuals, whole sets of whom can change 
their strategy, rather than just one. That's different from when we're 
talking about only one individual changing their strategy.

You continued:

Also, as to whether or not approval strategy depends on cardinal preferences 
in addition to ordinal preferences:

I completely agree that in the case of incomplete information it is 
necessary to factor in your utilities when deciding how to vote in an 
approval election.  The equilibrium that I was defining, however, referred 
only to hindsight.

I reply:

No, that statement  in your posting wasn't about an equilibrium referring to 
hindsight--You said that cardinal "preferences" weren't a factor in Approval 
strategy, and now you're trying to contort your way out of that 

And here you've been doing so well so far, acknowledging your errors, but 
now you don't want to.

Mike Ossipoff

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