Jobst,
In answer to a question from Mike Ossipoff
About the part about equal ranking resulting in candidates having the
same probabililty of winning:
It's impossible for me to give two candidates equal probability of
winning by ranking them equal. Did the question mean "equal effect on
their win-probabilities"?
you wrote:
What I meant was this: When a voter expressed that s/he prefers A to B, we
interpret this to mean that if s/he could choose between A and B, she would
choose A. Now what do we think the voter would choose when s/he put A and B
at equal ranks? Do we assume that s/he would delegate the decision by, say,
asking a friend to decide, or do we assume that she would throw a coin?
I must say that I find this a very odd question, which only seems
relevant if instead of an election method we're talking about Random
Dictator. I prefer Mike's suggestion.
An interesting question might be: "Should equal-ranking a set of
candidates instead of strictly ranking them consecutively cause the
probability that one of those candidates be elected to change?".
Related similar questions are:
(1) "Should equal-ranking a set of candidates at the top make it more
likely that one of those candidates will be elected than if they were
all strictly ranked at the top?"
(2)"Should equal-ranking a set of candidates at the bottom make it less
likely that one of those candidates will be elected than if they were
all strictly ranked at the bottom?"
(Should truncated candidates be treated the same as if they were
explicitly ranked equal-last?)
Chris Benham
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