As I said, I was tired.
Original example corrected (I hope): 46: A, (B & C tied) 6: B, A, C 4: B, C, A 44: C, B, A Then #(A>B) = 46 and #(B>A) = 54, so B beats A by 54-46 = 8. Also #(A>C) = 52 and #(C>A) = 48, so A beats C by 52-48 = 4. Also #(B>C) = 10 and #(C>B) = 48, so C beats B by 44-10 = 34. C says: "I scored 48 in my only defeat, while A only got 46, and B only got 10. So my worst pairwise defeat was the smallest." B says: "My opponent only scored 44 in my one defeat, while C's opponent got 52, and A's opponent got 54. So my worst pairwise defeat was the smallest." C also says: "I lost by only 4 in my one defeat, while A lost by 8, and B lost by 34. So, again, my worst pairwise defeat was the smallest." Now according to Steve: <<"Try my notation: B beats A by 8 -46 +6 +4 +44 A beats C by 4 +46 +6 -4 -44 C beats B by 34 0 -6 -4 +44 I hope you'll leave it to a method's proponents to teach it, and save the complexities for the rebuttal arguments. :-)">> This seems to me that Steve is saying that C wins according to Condorcet's method since C only loses by 4. Is this correct Steve? But Mike says: <<"Bruce has surely seen my definition of Condorcet's method, and he knows that A's & C's claims, as he writes them, have nothing to do with Condorcet's method's scoring. If his point is that people won't understand why Condorcet scores as it does (instead of counting votes-for, or margins of defeat), I hope I've demonstrated how briefly & simply that can be explained. > This is simple? At best, it's understandable only if it's very carefully No that isn't simple. It's called "obfuscation". But I've answered it. > explained. And the need for such a vary careful explination is part of my > argument for complexity here. My explanation, given above, for why Condorcet counts as it does, isn't complicated. It's brief & simple.">> This seems to me that Mike is saying that B wins according to Condorcet's method because "A's & C's claims, as he writes them, have nothing to do with Condorcet's method's scoring. If his point is that people won't understand why Condorcet scores as it does (instead of counting votes-for, or margins of defeat), I hope I've demonstrated how briefly & simply that can be explained." Is this correct Mike? Either I am missing a whole lot here (which is certainly possible), or Steve and Mike disagree on which of their clearly explained, well understood, and obviously right results is, in fact, the right result--and all I am questioning for now is is the clearly explained and well understood part. A New Example: 48: A, (B & C tied) 6: B, (A & C tied) 46: C, B, A Then #(A>B) = 48 and #(B>A) = 52, so B beats A by 52-48 = 4. Also #(A>C) = 48 and #(C>A) = 46, so A beats C by 48-46 = 2. Also #(B>C) = 6 and #(C>B) = 46, so C beats B by 46- 6 = 40. A says: "I scored 48 in my only defeat, while C only got 46, and B only got 6. So my worst pairwise defeat was the smallest." B says: "My opponent only scored 46 in my one defeat, while C's opponent got 48, and A's opponent got 52. So my worst pairwise defeat was the smallest." C says: "I lost by only 2 in my one defeat, while A lost by 4, and B lost by 40. So my worst pairwise defeat was the smallest." Steve: Does C win? Mike: Does B win? DEMOREP and everyone else: 1) Using your best understanding of Condorcet's method as discussed on this list, who wins? 2) Who do you think really ought to win (or ought not to win)? Bruce |
Free forum by Nabble | Edit this page |