[EM] Alex, the arbiter of equilibrium-naming
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.
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.
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
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.
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.
(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.
...but you seem to havea forgotten that acknoledgement since then
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.
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
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.
Anyway, I apologize for misunderstanding and thinking that you were trying
to define a Nash equilibrium.
That's ok. Your your error is entirely excusable, , considering what I've
been saying all this time :-)
I recognize that you were defining a different type of equilibrium.
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.
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.
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.
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