On 07/13/2016 07:47 AM, steve bosworth wrote: > K: As for the MAM example, it seems that F wins in MAM as well. > > S: Yes, F does win with MAM. I clearly made a mistake when counting. > However, I believe the following new profile does illustrate the point I > was trying to make (see below). This is that MAM (or any Condorcet > method) is less efficient than IRV in discovering the winner with the > highest available average intensity of majority support. This is > because MAM does not count the different intensities of preference as > illustrated by the following calculations: If each of the ordinal > preferences within this profile receive a score out of 10, 10 being > given to each 1^st choice, F receives an average intensity of support of > 9.1 from the majority of 70 that elects her, or 8.47 from all 100 voters. > > This contrasts with N who is elected both by MAM and Majority Judgment > (MJ). N’s average intensity of support from all 100voters is 7.51. > More exactly MJ elects N because she has received the highest > ‘majority-grade’ of GOOD (i.e. perhaps this corresponds to a score of 8). [snip] > *PROFILE: A BETER EXAMPLE:* > 100 CITIZENS RANK CANDIDATES EFGKMNP AS FOLLOWS: I've restated that example into the standard ranked ballot format: 49: F>P>K>N 30: M>E>N>F 21: G>K>N>F And Eric Gorr's MAM implementation http://www.ericgorr.net/condorcet/ says that F wins under MAM ("Ranked Pairs (Deterministic #1-Winning Votes)") as well[1]. According to LeGrand's voting calculator, http://www.cs.wustl.edu/~legrand/rbvote/calc.html the only methods (among those implemented there) that make N win are Copeland (with random tiebreak), Raynaud (ditto), and Small. Note that LeGrand's calculator uses margins, so the defeats matrix will look different. I haven't checked your majority figures yet as I'm not feeling all that well today. I haven't checked your MJ result either; but a very quick and dirty Bucklin count seems to support that N would win under MJ. I would also like to again mention that one can construct examples where IRV does worse by your intensity calculations. I gave one such example in a previous post, and here's another from http://rangevoting.org/CoreSuppPocket.html: 35:A>C>D>B 17:B>C>D>A 32:C>D>B>A 16:D>B>C>A IRV elects B. MAM elects C. Say first preferences are 10 points, second is 9, third is 8, and fourth is 7, then B has an intensity of (35 * 7 + 17 * 10 + 32 * 8 + 16 * 9) / 100 = 8.15 while C has an intensity of (35 * 9 + 17 * 9 + 32 * 10 + 16 * 8) / 100 = 9.16. Come to think of it, any center squeeze example would do. Here's LCR: 48: L>C>R 32: R>C>L 20: C>R>L IRV elects R while every Condorcet method (and Bucklin/MJ) elects C. C's intensity is: (9 * 48 + 9 * 32 + 10 * 20)/100 = 9.2 R's intensity is: (8 * 48 + 10 * 32 + 9 * 20)/100 = 8.84. - [1] It's not strictly speaking MAM because MAM handles ties among majorities differently, but I don't think breaking ties differently would make N win.