[EM] extending Myerson's test--more policy positions

[David Catchpole]

On Fri, 17 Mar 2000, Bart Ingles wrote:

> Of course I'm talking about truncation here, and not order-reversal. 
> Also I don't think we can be talking about the same strategy if you are
> not using utilities.

Well, only because I'm generalising and making utilities arbitrary (but I
am setting up the big-middle-small of utilities in the thingummy
below). When I get the time I'll suggest more specific examples-
preferably one that demonstrates collusion as a Nash equilibrium for a and
c and one that demonstrates probabalistic behaviour as a Nash
equilibrium. Both of these will require a choice of Condorcet completion
to resolve the collude/defect situation- because it generates a paradox
of voting.

> > "two big parties' prisoners' dilemma" I mentioned one time aeons ago while
> > I was ranting against Condorcet's tendency to elect "centrists" in a
> > situation of absolute sincerity. My argument went, in the most simple
> > case, that say there were four types of voters ("parties"), such that
> > 
> > real preferences (not expressing utilities, but you get the drift):
> > 
> > a: A>B>C
> > b1: B>A>C
> > b2: B>C>A
> > c: C>B>A
> > 
> > a>b1+b2
> > c>b1+b2
> > a+b1>c
> > c+b2>a
> > 
> > If b1 and b2 are uncertain, and a and c had roughly the same
> > expectations of b1 and b2 as each other, in some circumstances it would
> > be Nash-optimal for a and c to collude to reverse their preferences
> > between C and their second choice- and even, to probabilistically choose
> > between collusion and defection- A prisoners' dilemma.
> > 
> > >
> > > If B wins, the utility of the outcome is only 0.1.   Why would you ever
> > > want to help B win by ranking him sincerely?  The only way I would do so
> > > is if I knew that A had less than a 10% chance of defeating C.
> > >
> > >
> > 
> > --------------------------------------------------------------------
> > "Never ascribe to conspiracy what can be put down to stupidity"- DJ No MC
> 
> 

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"Never ascribe to conspiracy what can be put down to stupidity"- DJ No MC