Warren, However, using first-choice plurality to settle Condorcet cycles could easily elect the Condorcet-loser (the candidate who loses in every pairwise match-up). There are many far superior cycle breakers. I personally favor ranked-pairs because it is both reasonable, and relatively easy to explain to lay people (unlike many cycle breakers).
Terry Bouricius ----- Original Message ----- From: "Warren Smith" <[email protected]> To: "election-methods" <[email protected]> Sent: Thursday, May 14, 2009 3:35 PM Subject: [EM] Cramster question Question: Condorcet’s method has many nice properties, and some supporter’s of former Vice President Al Gore pointed out that Al Gore was very likely the Condorcet winner. The problem with Condorcet’s method is that it does not produce a winner often. Thus, let us propose a combination of the Condorcet’s method and the plurality system: This combined system deems the Condorcet winner as the winner. In case that the Condorcet’s method does not produce a winner, then use plurality method to select the winner. Q1) Does the Condorcet-plurality system produce winner more often than Condorcet’s method? Explain. --A1: yes. Every time a Condorcet winner fails to exist (i.e. about 9% of time in random 3-canddt elections), it elects plurality winner. Only fails in cases where BOTH CW fails to exist AND plurality tie. 2) Does the Condorcet-plurality system satisfy the Pareto condition? Explain. --A2: yes. Unanimous first-choices always win. 3) Does the Condorcet-plurality system satisfy Condorcet winning Criterion? Explain. --A3: yes, by defn. 4) We know that both Condorcet and plurality systems are monotone. Is the Condorcet-plurality combined system still monotone? Explain. --A4: Yes. In a rank-order vote containing "A>B" change it to "B>A." Can that ever stop B from winning? Not if B was a CW, and not if B was a plurality winner either. 5) Is the Condorcet-plurality system manipulable? If your answer is manipulable, give an example of an election where manipulation can be done. If your answer is not manipulable, prove it. --A5: manipulable. Example http://rangevoting.org/IncentToExagg.html -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
