On May 18, 2010, at 1:30 AM, [email protected] wrote:
There are several common variants to the meaning of “cover”
depending on how ties are treated. For my
purposes, alternative C covers alternative A iff C is not beaten
(pairwise) by any candidate that does not
beat A, AND C beats at least one candidate that A does not beat, or
C ties at least one alternative that
beats A.
In other words C does at least as well as A (with regard to pairwise
win/tie/loss) against each alternative,
and does better on at least one alternative.
Here I assume that A is tied with itself, so if C is tied with A, it
can still cover A, as long as it does as
well as A against the other alternatives and strictly better against
at least one of them.
The first definition seems to allow someone to tie with C and lose to
A. The second definition is simpler and easier to understand if we
consider "do as well" and "do better" to be well defined (and they are
pretty much so).
Juho
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