Michael Allan wrote:
I think it misses the main point. For your part, you and Raph hope to
apply Nash's model within the context of voting. You therefore tweak
that context in vitro by adding a little indeterminacy, such that Nash
can grapple with it for analytical purposes. Alternatively, you look
at adding indeterminacy to Nash itself (trembling hand). This much I
understand (roughly).
For my part, I argue that Nash can *never* be applied within the
context of voting. The reality as evidenced by the empirical data (in
vivo) invalidates the basic assumptions of Nash. Individual voters
are *not* attempting to affect the outcome of elections. As this
reality contradicts Nash, we cannot turn around and look back at it
through the lenses of Nash.
Whether or not that is the case for individual voters, one could still
use purposive-rational models for political parties. This would be
useful in considering what sort of "how to vote" instructions a party
might provide to their voters in order to strategize on a wide scale (in
the vein of vote management under STV).
The parties themselves would face the same (or a similar) problem in
modeling workable strategy, however, because they would have to know how
many of the party voters would use the party strategy rather than voting
independently. Still, we know that this has not been too great a problem
since parties have indeed employed vote management in the past.
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