[EM] [OT] Kenneth Arrow theory... anyone?

[Sampo Syreeni]

On 2003-11-21, Alex Small uttered:

>Is this "single-peakedness" the same as saying all voters fall on a 1D
>ideological spectrum?

Basically yes.

>e.g. if all voters and candidates fit on the left-right spectrum, then all
>voters will have one of these preferences:
>
>Left>Middle>Right
>Right>Middle>Left
>Middle>Left>Right
>Middle>Right>Left

Precisely. In the words of Buchanan, in
http://www.econlib.org/library/Buchanan/buchCv3c22.html :

"Thus the problem stood when Black took it up. Although he made some
improvements in the analysis so far described, and produced the first
comprehensive presentation of the matter, his principal contribution was
his discovery of the "single-peaked preference curve."[93] It may be that
the possible choices can be arranged on a single line in such a way that
any individual will always prefer a choice which is closer to his own to
any that is farther away. It seems likely that a good many of the issues
in active political life are of that sort, particularly those that are
involved in the familiar "left-right" continuum. Black demonstrated that
in this situation no paradox develops. Voting on the issues in pairs, the
normal parliamentary manner, simply leads to the alternative preferred by
the median voter. Again, it is not obvious that this is "the will of the
majority," but at least it is nonparadoxical."

So I was wrong about Tullock&Buchanan's treatment in the previous post --
they actually refer to Black.

>Or is single-peakedness more complicated than that?

Only in the sense that it also generalizes to more than three
alternatives.
-- 
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
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