[EM] G-S theorem and random ballot

[Joe Weinstein]

Re:  G-S theorem and random ballot

	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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