In message 13820 (Sat. 13 March 2004), Markus Schulze wrote:
"...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, ... 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."
In message 13860 (Mon. 15 March 2004), Forest Simmons responded:
�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.�
Yes, and there are some ironies which strengthen Forest's point.
Suppose the contested office is one which has reserved to it some unique decision powers - as here in California for each of the elective executive state offices. Regardless of whether the election method is �dictatorial� or not, the winner of the office then gets to play dictator over his reserved domain. So it seems that ALL single-winner election methods can be viewed as 'dictatorial'.
There�s more. Consider a jurisdiction dominated by a single political party which in turn is dominated by one or a few party bosses. Or, suppose - as here in California - the major parties agree on safe-district redistricting plans which preserve advantages to incumbents and to locally majority parties. In either case, a sexy non-random �non�-dictatorial method will nicely suit the actual dictator(s), whereas an unsexy �random dictator� method will frustrate them.
That�s right: a non-�dictatorial� method can guarantee dictatorship, and a �dictatorial� method can frustrate it.
Joe Weinstein
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