On 02/12/2013 12:24 AM, Jameson Quinn wrote:
What does monotone even mean for PR? You can make something that's sequentially monotone, but it's (I think) impossible to avoid situations where AB were winning but changing C>A>B to A>B>C causes B to lose (or variants of this kind of problem). That's still technically "monotone", but from a voters perspective, it's not usefully so.
I was thinking of a one-candidate generalization to monotonicity, yes. That is, say that X is on the council. Then if some voters raise X on their ballots, that should not kick X off the council.
But wouldn't this imply the more strict monotonicity you're talking about? Say A and B are in the council. Then you raise B, changing C>A>B into C>B>A and then into B>C>A. By monotonicity, B shouldn't stop winning. Now you raise A by changing B>C>A into B>A>C and finally into A>B>C. Again, by monotonicity, A shouldn't stop winning.
I think I've described the method in an earlier post. (Incidentally, it's Bucklin-based.) I could also provide source code if you want to test it on a situation or impossibility proof that Droop proportionality is incompatible with monotonicity. It could use the review :-)
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