Stephane asked: Would you have a web reference for a precise description of the BeatpathWinner method... Is it like Ranked Pairs ? I reply: BeatpathWinner and Ranked Pairs are both considered Condorcet versions. BeatpathWinner is regarded as a Condorcet version because it's equivalent to a method (Cloneproof SSD) that's an interpretation of one of Condorcet's proposals. Ranked Pairs is the best interpretation of one of Condorcet's proposals. BeatpathWinner/Cloneproof SSD and Ranked Pairs are the best rank counts, if we value the standard of getting rid of the lesser-of-2-evils problem. They meet all the criteria that Condorcet is listed as meeting in the criteria compliance table at the top of the technical evaluation page at the website http://www.electionmethods.org , and they're both nonfalsifying, expressive, and conditionally completely expressive, as I've defined those terms here. I don't have a web reference, but I'll give precise definitions here: BeatpathWinner: 1. X beats Y if more people rank X over Y than vice-versa. 2. The strength of X's defeat of Y is measured by the number of people who rank X over Y. 3. There's a beatpath from X to Y if either X beats Y, or if X beats someone who has a beatpath to Y. 4. A sequence of defeats that makes it possible to accurately say that X has a beatpath from X to Y is called a beatpath from X to Y. 5. The strength of a beatpath is measured by the strength of its weakest defeat. 6. If the strongest beatpath from X to Y is stronger than the strongest beatpath from Y to X, then X has a beatpath win against Y. 7. A candidate is winner if no one has a beatpath win against him/her. [end of definition] In other words, a beatpath is a sequence of defeats, so, for example, if A beats B, B beats C, and C beats D, then A has a beatpath to D. Ranked Pairs: 1. In order of strongest defeats first, consider each defeat as follows: Keep it if it doesn't conflict with already-kept defeats. 2. When all of the defeats have been considered in that way, a candidate wins if he has no kept defeats. (Defeats conflict if they form a cycle) [end of definition] Obviously, the strongest 2 defeats will be kept, because there won't be enough already-kept defeats to form a cycle. Let me know if there are any questions about these definitions or about single-winner voting systems in general. Mike Ossipoff _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
