Russ Paielli wrote:
Russ Paielli 6049awj02-at-sneakemail.com |EMlist| wrote:
It occurred to me a while back that the two criteria may be equivalent. That is, if a method passes monotonicity, perhaps it must also pass summability, and vice versa. That's just a hunch. Can anyone prove (or disprove) it?
Let me partially answer my own question. It just occurred to me that summability cannot imply monotonicity because it says nothing about how the final array sum is interpreted to determine the winner. However, the converse could perhaps still be true. Does monotonicity imply summability?
No. A Median Ratings election in which ratings can be any real number between 0 and 1 passes monotonicity but fails summability.
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