[EM] group strategy equilibria

[Alex Small]

I subscribe to the digest, so I got James' message, which he cc'd to me, before I got the digest.  Here's my take on group strategy equilibria:
 
Group strategy equilibria are too common to be of much interest to me.  In many voting systems, including Condorcet systems when there's a cycle, it will frequently be easy to find a group strategy equilibrium where some group of people acting in concert change the outcome.  By contrast, individual voter equilibria are too common to be of interest, since any election with a margin greater than one vote will be an equilbrium.
 
The Nash equilibria that I defined in my previous message, where the players are groups of voters with identical preferences, are "just right."  They're common enough that you can always find one to study, but rare enough that they aren't littering the place with trivial examples (any election with margins of 2 or more votes).  That balancing act is one of the many reasons that Nash got his Nobel prize.  He found a phenomenon that's ubiquitous and hence broadly applicable, but not so common as to be trivial.

election-methods-electorama.com-request at electorama.com wrote:

Mike's definition here is incorrect. He gave the 
definition for a "group strategy equilibrium." 
Those equilibria are rarer than Nash equilibria, 
which merely require that no _individual_ voter 
can get an outcome she prefers more by changing 
her vote (holding all the other votes constant).
--Steve



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Message: 6
Date: Mon, 23 Aug 2004 19:36:30 -0400
From: "James Green-Armytage" 
Subject: Re: [EM] equilibria
To: seppley at alumni.caltech.edu,
election-methods-electorama.com at electorama.com
Message-ID: 
Content-Type: text/plain; charset=ISO-8859-1

seppley at alumni.caltech.edu writes:
>Mike's definition here is incorrect. He gave the 
>definition for a "group strategy equilibrium." 
>Those equilibria are rarer than Nash equilibria, 
>which merely require that no _individual_ voter 
>can get an outcome she prefers more by changing 
>her vote (holding all the other votes constant).
>--Steve

That makes sense. I didn't really think it was the right definition for
Nash equilibria. That's why I put "Nash" in quotes in my last posting. So,
the "group strategy equilibrium" is what we're talking about. That's fine.
I think that group strategy equilibria are useful to talk about, probably
more useful than the Nash equilibria... since nearly all Votes in a large
electorate qualify as Nash equilibria, as you defined it above. Let's keep
talking about group strategy equilibria.

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