I'd said: >The strength of a majority pairwise for X over Y is measured by >the number of people who prefer X to Y.
Dave Ketchum replied: Seems like that sentence is missing something: Suppose 10 people prefer X to Y. Shouldn't strength then be affected according to whether 5 or 55 prefer Y to X? I reply: First, let me clarify that, by "majority", I mean a majority of all the voters in that election. If 55 prefer Y to X, and 10 prefer X to Y, then we certainly can't say that X has a majority pairwise preference to Y. I agree with you on that. If a majority of all the voters prefer X to Y, then only a smaller number can prefer Y to X. But say that the number preferring Y to X is smaller than the number preferring X to Y, as it must be in order for X to have a majority preference against Y. You're asking if we should consider that smaller number who prefer Y to X, when evaluating the strength of the majority pairwise preference. But what's the obvious way to judge the strength or size of a majority? By how _big_ a majority it is. And so it's irrelevant how many people prefer Y to X. As soon as we say "majority", we're talking about a majority-size group. The only majority size group, as regards X & Y, is the one that prefers X to Y. We compare 2 majorities by asking which is the larger majority. If 60% prefer X to Y, and 55% prefer Y to Z, then the XY majority is a bigger majority than the YZ majority. That's true without regard to whether a person is a wv advocate or a margins advocate, though I admit that it creates a difficult justification problem for a margins advocate. Mike Ossipoff _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
