Re: poly: Re: Arrow's Social Choice Theorem / Borda count

I wrote:
> .... I'm far from certain that our constitutional structure
> [as opposed to one with PR] would defeat a clever President
> who might manufacture a pretext to seize dictatorial power.

There's a story that Kurt Goedel, applying for US citizenship, studied
the US constitution and found a flaw that would allow dictatorship; and
when the INS examiner said "Of course you know that our Constitution
makes dictatorship impossible," Goedel opened his mouth to tell about
the flaw but stopped when his eminent friend (Einstein?), who had
accompanied him to the interview, kicked him.

I haven't heard what Goedel found, other than the fact that the "checks
and balances" consist of putting each branch in the others' pockets.

...
One of Arrow's axioms, if I understand correctly, is that the
procedure's output ought to be not just a winner's name but a complete
ordering of all the candidates. This condition is too tight. On
another hand, I guess it follows from the independence criterion and the
elementary requirement of a winner. (Note that in an election for
multiple seats, such as the San Francisco County Board, the number of
candidate outcomes is N!/S!(N-S)!, where N nominees seek S seats.)

-- 
Anton Sherwood  *\\*  br0nt0@p0b0x.com  *\\*  http://ogre.nu