[EM] group strategy equilibria

James Green-Armytage jarmyta at antioch-college.edu
Mon Aug 23 17:50:19 PDT 2004

Alex, you wrote:
>Group strategy equilibria are too RARE 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.  

	As I understand it, if some people acting in concert can change the
outcome (in a way that favors them), it's not a group strategy
	Let me stick with Mike's definition, although now I'm defining GSE
instead of Nash: "An outcome, and the votes configuration that caused it,
that no set of voters can improve on for themselves by voting differently."
	I think that in many voting methods, almost surely plurality, and
probably other methods such as approval, Borda, various Condorcet
methods... in these methods, all GSE's will elect the CW.
	Do you agree with this?
	If so, GSE's are not especially rare; that is, they exist when there is a
sincere CW... which is not so rare, I believe.
	How interesting are GSE's? Well, basically I'm suggesting that they help
us form an extremely good argument in favor of Condorcet-efficient
methods, because many other methods only reach GSE's when they select a
Condorcet winner anyway. I'm not exactly trying to stir controversy... I'm
more so just trying to nail down this point.

you wrote:
>Anyway, please don't ask me to defend anybody else's definitions.

	Sorry. No offense intended. I didn't realize before that there were
diverging definitions. Hopefully we are clearing them up now.

my best,

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