Revealing the Majority Winner
Mike Ositoff
ntk at netcom.com
Sun Nov 15 02:29:24 PST 1998
>
> What you appear to be referring to is the infamous Arrow Problem as
> articulated by Anthony Downs in AN ECONOMIC THEORY OF DEMOCRACY. You may
> want to check it out if yo;u havn't already. It is a major peice of theory
> in Political Science.
Arrrow's impossibility theorem says that we can't have the ideal
conditions that could exist if his Indepenence from Irrelevant
Alternatives Criterion (IIAC) and the Pareto Criterion were
compatible. Someone here pointed out that it's worse than that;
IIAC is incompatible with some really basic majority
properties that we expect, making IIAC quite unattainable by
reasonable methods. IIAC is of interest to people interested
in strategy needs, because, turned around, it's a freedom
from spoilers criterion. But there are methods that approach
close to the ideal, even if it isn't quite attainable. And
even the simple Approval method gets us halfway there, and,
as I say, getting off the bottom at all is the main thing.
> >Mr. Ingles wrote in part-
> >
> >How about this -- suppose we allow the voters to rate candidates on a
> >scale, rather than just rank them. Higher score means more highly
> >favored. The same election could come out a couple of different ways (I
Don't expect sincere ratings. Voters wanting to get the best
they can for themselves will vote as in Approval, giving
maximum points to some candidates, & minimum points to the
rest.
Mike
> >hope you are using a fixed font):
> >
> >Rating: 100 80 60 40 20 0
> >----------------------------------------
> >45 A B C
> >15 B C A
> >40 C B A
> >
> > -or-
> >
> >45 A B C
> >15 B C A
> >40 C B A
> >
> >Neither IRO nor Condorcet can distinguish between the two cases.
> >
> >I think it would be a mistake to pretend these voter preferences don't
> >exist, just because relative ranking doesn't measure them. After a
> >(ranked) Condorcet election where voters' real preferences are like the
> >second example, imagine the backlash when some enterprising pollster
> >reports that when asked to rate the candidates on a 100-point scale,
> >voters gave the winner a median rating of 10, while one of the losers
> >had a median score of 90! (Highest median score -- now there's a
> >method. :-)
> >-----
> >D- Another example of why I suggest a YES/NO vote on choices (along with
> >number votes). Scale rankings are +100 percent to -100 percent (or the
> more
> >common 100 to 0). A majority YES vote means a majority of the voters
> rank
> >the choice above zero (or the more common above 50).
> >
> >Only B in the top example and C in the bottom example would appear to be
> >getting above 50 acceptability.
> >
>
>
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