James G-A, In this excellent burial/defection example of yours: 46 abc 44 bca (sincere is bac) 05 cab 05 cba
A is the sincere CW and also the sincere (and voted) FPP and IRV winner,and yet all the "defeat-dropping" Condorcet methods (plus SCRIRVE) elect the Buriers' favourite, B. I consider this example to be much more serious and horrific than any 3-candidate example that I've ever seen used to attempt to discredit IRV or DD(Margins).Of this, you wrote (Mon.Mar.14): "This is a hideous result that would shower Condorcet methods in shame for generations to come." So the obvious question I ask you is this: Why then do you reccomend methods that elect B? Or to put it another way: What in your opinion is so bad about the methods that don't elect B? "Like what?" you may ask. Before getting into that, I've a couple of questions relating to the above election: (1)Do you (or anyone) know of any method that doesn't elect B and also meets (mutual)Majority, Clone Independence and Mono-raise (monotonicity)? (2)Do you (or anyone) know of any method that doesn't elect B and also meets Minimal Defense and the Plurality criterion? I've cast "not vulnerable to Burying" into a formal criterion/property: " Burial Resistance: If candidate x wins, and afterwards some ballots that rank any y above x and any z are changed so that z's ranking relative to x is raised while keeping y ranked above both; then if there is a new winner it cannot be y." Unfortunately that is a very strong criterion, and the only methods that I can think of that meet it are IRV and FPP. So how to weaken it so as to usefully distinguish some Condorcet methods from others? With the above scenario in mind I've come up with two "weakenings". "Weak Defection Resistance: If winning candidate x is the CW and the FPW, and xy are a solid coalition with more than 2/3 of the votes; and afterwards some ballots that rank y above x and z are changed so that z's ranking relative to x is raised while keeping y ranked above both; then if there is a new winner it cannot be y." "Weak Burial Resistance: If winning candidate x is the CW and FPW while z is the CL and FPL , and afterwards some ballots that rank any y above x and z are changed so that z's ranking relative to x is raised while keeping y ranked above them both; then if there is a new winner it cannot be y." "Weak Defection Resistance" (WDR) is the Burial-related criterion I referred to in my last message. It is met by Raynaud (GL). I'll give some more method ideas in a later post. Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info
