_[EM]_unsatisfied_with_implications_of_Condorcet_method

[Forest Simmons]

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
>
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