This stuff on voting is nothing new. Donald G. Saari has been at this one for over a decade now. A good discussion is in his _Geometry of Voting_, 1994, Springer-Verlag, or his article, "Erratic Behavior in Economic Models," _Journal of Economic Behavior and Organization_, July 1991, vol. 16, nos. 1-2, pp. 3-35, in which he reviews earlier stuff going back to the mid-80s. There are links between this and both the Arrow social choice paradox and also the Sonnenshein-Mantel-Debreu Theorem. Barkley Rosser On Mon, 17 Aug 1998 07:42:56 +0100 Chris Burford <cburford at gn.apc.org> wrote:
> This week's New Scientist has a clip in its In Brief section.
>
> In their 4 July issue they had a piece that computer modellers have
> predicted that electronic stock trading could cause chaotic market swings
> if large numbers of computer program are allowed to decide which stocks to
> buy.
>
> They draw an analogy with voting, and now report a claim by a physicist and
> a political scientist that the same thing happens in all group decisions:
> 'almost any voting rule gives you chaotic outcomes'. The paper by Meyer and
> Brown has been accepted by Physical Review Letters but is not published yet.
>
> It gives a mathematical proof, that even if the preferences of a group of
> voters change only very slightly, the results will be completely
> unpredictable a few elections down the line. Such sensitivity to initial
> conditions is a defining feature of chaos [theory].
>
> What is more interesting is how the existence of such proofs will shape the
> management of bourgeois democracy.
>
> Business in Britain does not seem to be complaing about the costs of the
> 5,000 strong focus panel set up by Tony Blair to manage the subtleties of
> public opinion. It is rather similar to what big corporations try to do
> themselves.
>
> Chris Burford
>
> London.
>
-- Rosser Jr, John Barkley rosserjb at jmu.edu