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

[Bart Ingles]

David Catchpole wrote:
> 
> 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.

I take that last statement back, at least partially.  If you assume
without stating that the voter's 2nd choice utility is 0.5, then the
truncation strategy would make sense so long as the probability of A
defeating C is > 0.5.  Of course this implies information about other
voters' preferences.  To justify the strategy without such information,
you need to look at voters' utilities.

-B


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