You're right about margins being equivalent to winning votes when truncations are not allowed. But when a voter refuses to rank candidates a and b, i.e. the voter truncates above them, then the story changes.
Taking this fact into account changes your first equation to N(a>b) + N(b>a) + N(no preference shown between a and b) = N . On Wed, 5 Jun 2002, [iso-8859-1] Alex Small wrote: > This may be a very naive question, but here goes: > > Mike says that in the wv method the strength of victory is measured by the > number of people who prefer a to b, whereas margins methods use the margin > of victory. > > I know that margins vs. wv was argued at length some time ago, but the > discussion very quickly got beyond me. So, here's my question: > > Say that there are N voters. N(a>b) + N(b>a) = N > > N(a>b) - N(b>a) = N(a>b) - (N - N(a>b)) = 2*N(a>b) - N > > Whether we use N(a>b) to measure the magnitude of a's victory (or b's > defeat) or N(a>b)-N(b>a) seems irrelevant to me, since the two numbers are > connected by a simple linear transformation. > > I can see how a method that looks at victories may have different strategic > considerations than a method that looks at defeats, but I don't see the > difference between margins and wv from my simple understanding of the > definitions. > > Could somebody just give a simple description of each method? > > One thing I can see is how methods emphasizing strength of victory might > have different strategic considerations than methods relying on strenght of > defeat. e.g. say A>B>C>A (simple cyclic ambiguity). If A wins a huge > victory over B but suffers a huge defeat at the hands of C, whereas the B > vs. C contest is close, I can see how the choice of method matters > crucially. > > Alex > > ---- > For more information about this list (subscribe, unsubscribe, FAQ, etc), > please see http://www.eskimo.com/~robla/em > > ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
