[EM] G-S theorem and random ballot

[Forest Simmons]

On Sat, 13 Mar 2004, Markus Schulze wrote:

> Dear Forest,
>
> in the probabilistic context, a single-winner election
> method is "dictatorial" if there exists a probability
> distribution p[1],...,p[V] on the set of voters so that,
> independently on how the voters vote, this method can be
> described as follows: Voter i is chosen with probability
> p[i] and the winner is chosen from the top-ranked
> candidates of this voter.
>
> So random ballot is dictatorial.

So this is one of those cases where the technical meaning of a word is not
as bad as it sounds.

A dictator in this context is just someone who gets to have his turn at
choosing ... a far cry from the dictators that are conjured up in the
popular mind when it first hears of the "Dictator Theorem."

When we, as children, drew straws to decide who would choose the next game
for our little group to play, we had no idea that some folks would
consider the practice so undemocratic as to think of us as little
dictators in the making.

He who chooses the terminology may have undue influence on the
popular interpretation of the result.

Suppose that the randomly chosen voter were called the "representative"
instead of the "dictator."  Then the Dictator Theorem would be called the
Representative Theorem.

But of course it would lose all of its sex appeal, and would be buried in
the annals of voting theory without ever coming into public notice.


Forest


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