[EM] Majority winner set

[Bart Ingles]

Markus Schulze wrote:
> 
> Dear Mike,
> 
> you wrote (29 Nov 2000):
> > I'm sorry! Because Markus had been repeating things, I must have
> > not thoroughly read one of the paragraphs in his most recent posting.
> > I thought that I did, but I must have missed that sentence, where
> > he stated that the assumption is that the voters report vN-M
> > utilities, sincere or not, and then the voting system takes from
> > those that information that it needs, and would normally get from
> > its own balloting procedure.
> >
> > So I take back the statement that Markus didn't explain it.
> >
> > But my criticisms of those assumptions mostly still remain valid.
> >
> > My answers to some of Markus's statements are different based on
> > what I've just noticed, though.
> >
> > I still say that it's a contrafactual assumption. Why assume that
> > people vote ratings, and that the voting system takes from them
> > the information that it needs, when we could instead just say that
> > the voting system collects the kind of input that it actually does
> > collect when in actual use??
> 
> I assume that the voters vote vNM utilities and that the election
> method takes from the reported vNM utilities the information it
> needs to calculate the winner because I define the criteria in
> terms of reported vNM utilities.
> 
> Markus Schulze


I don't see any problem with this, so long as you don't assume that this
is the final word in the behavior of the voting system in question. 
Many voting system analyses start with sincere vNM utilities, and then
try to determine the likely effects of strategy.

Actually, "sincere vNM utilities" is redundant.  I'm not sure what
"insincere vNM utilities" could even mean.  Anything reported by a voter
would be a rating, not a utility, whether sincere or not.  I think
utilities are mainly useful in thought exercises and computer models,
where you can simply generate the numbers and assume they represent
utilities.  The voters don't "report" these -- the modeler "just knows
them", without necessarily even assuming that the hypothetical voters
are able to report them accurately.  Maybe you mean "report" in a
different way -- that the simulator generating the utilities reports
them, for example.


As to criteria, it seems to me that criteria based on utilities, and
criteria based on votes as cast are both useful, but there needs to be
an understanding of which is which.  Maybe some criteria are more
applicable to utilities, and others to votes-as-cast.  For example,
monotonicity by its definition seems to apply to votes-as-cast.  There
is probably a sincere analog using utilities, but I don't know how it
would be useful.

Something like IIA could apply to either, but would have different
meanings in either case (and probably should have different names in
either case).  One might comment on the stability of the system itself
-- for example, would additional absentee ballots for Gore cause Bush to
win -- while the other might comment on the type or degree of strategy
needed to vote most effectively.