matt at tidalwave.net
Tue Feb 11 19:18:52 PST 2003
This would require the voted ballots having an explicit approval cutoff, which neither of the Condorcet methods most popular on this list (beatpath and ranked pairs) include.
My perspective is that the ranked pairs and beatpath methods describe an algorithm for determining contest outcomes independently from the details regarding how equal ranking is counted or ballots are completed or ties are broken or defeats are measured and the like.
It's also worth noting that we're not only talking about truncation here. We're talking about any equal-ranking. Someone could rank, say, A first, B and C second, D third, and leave E and F off their ballot. In this case the presence or lack of an approval cutoff is irrelevant. Then again, if we're using approval-completed Condorcet, then margins vs. winning votes argument is completely irrelevant.
I don't understand your claim that A>B=C>>D makes approval cutoff based ballot completion into A>B=C>E=F>D irrelevant. Do you consider margins vs winning votes irrelevant to approval-completed Codorcet because approval cutoff based ballot completion makes more sense with equally ranked getting 1/2 vote each?
Your argument strikes me as a bit of a bait-and-switch. You suggested that both margins and winning votes options be provided. I point out that margins results can always be generated from winning votes programs. Then you come back with (badly paraphrasing) "if the margins method requires some other information besides the ranking, the winning votes program that only has the ranking information won't be able to duplicate it." Well, sure, but if you give that same information to a winning votes program, then once again you can duplicate the margins result using that program.
Your observation that winning votes can always convert to margins is interesting and helpful.
I initially wrote a whole long tedious and boring explanation here, of how winning votes can be converted to margins, but not vice versa. Upon reading it over, it's pretty poorly written and I think it would be a waste of people's time to read it. If you want to look at it let me know.
Suffice to say that it is essentially impossible to write a winning votes-based program that can't be converted to margins. On the contrary, if a program allows truncation in the ballots, and uses defeat margins to calculate the results, it won't be able to duplicate winning votes results for a number of methods (including most Condorcet methods).
So the only reason to keep margins as a measure of defeat is to accommodate someone who wants margins and unvoted ranked last with 0 votes each for equally ranked? If that really is the only value added to the program by providing margins then we agree - margins doesn't add much.
You could convert winning votes to margins in all fourteen of the ranked ballot variants that are listed on Rob's website
(http://www.onr.com/user/honky98/rbvote/), and that's good enough for me.
Moreover, you could convert to any variant of margins that took the same ballot input as the winning vote method. In other words, if the only way two methods differ is in how they measure defeat-strength, then you can convert winning votes to margins. But not always the other way around.
I will look at the 14 variants. I would appreciate further explanation of the qualification "the same ballot input as the winning vote method". What ballot input is permissable when margins is the measure of defeat that is impermissable for winning votes?
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