I was browsing around for webpages describing Mr May's theorem of 1952.
It seemed that Mr Kenneth May excluded all 0 winner (2 candidate) elections. Mr Schulze did not get the wording copied right, and introduced all 0 winner 2 candidate elections, for the theorem to fail on. Here is a brief description of the 1952 May 'theorem' I got from the Internet: | May's theorem: When choosing among only two options, there is only one | social decision rule that satisfies the requirements of anonymity, | neutrality , decisiveness and positive responsiveness, and it is the | majority rule. http://216.239.63.104/search?q=cache:gaZP6TtDgy0J:www.dc.eclipse.co.uk/PDF_files/Voting.pdf+%22May%27s+theorem%22+1952+voting&hl=en At a first glimpse the theorem seems to be completely wrong/untrue, since this parameterized method passes but is not the "majority rule": (a0 + t*ab < b0 + t*ba) implies (B wins). (a0 + t*ab > b0 + t*ba) implies (A wins). t is a real number greater than 0. Perhaps Mr Schulze can help out with research into the meaning of those two words: (1) "decisiveness" and (2) "responsiveness", (3) "majority rule" [not ignoring the 2nd preference for some values of "t"] Their plain English meaning and the other words would torpedo and sink the theorem of Mr K. May. At 2005-01-02 21:37 +1300 Sunday, Craig Carey wrote: ... >| Chris Benham wrote (1 Jan 2005): >| > To me, it is axiomatic that a single-winner voting method >| > should, with sincere voting, reduce to FPP when there are >| > only two candidates. >| It is axiomatic until the time when some alternative seems better. >| Mike Ossipoff replied (1 Jan 2005): >| > Axiomatic? You're giving to us a fundamental standard that >| > you have. That's your axiom. You mustn't expect everyone >| > to have the same axioms that you have. >| >| That's not Benham's criterion. That's May's criterion: >| If there are only two candidates A and B and the number >| of voters who strictly prefer candidate A to candidate B >| is strictly larger than the number of voters who strictly >| prefer candidate B to candidate A, then candidate A must >| be elected with certainty. >| > An interesting thing about this mailing list is that the oldies can't learn to stop making thinking mistakes that get exposed in these scenarios: (1) negative vote counts; (2) zero winner elections; (3) Asimov robots instead of voters. (They are not sincere, etc., and they can fill in papers without coughing up info naming the OSSIPOFF "favorite"). --C. ---- Election-methods mailing list - see http://electorama.com/em for list info
