[EM] Visualizing Covering

[Juho]

On May 18, 2010, at 1:30 AM, fsimmons at pcc.edu 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