[EM] The importance of being uncovered (was C//A)

[fsimmons at pcc.edu]

> From: Kathy Dopp 
>  What does C/A stand for?
> Condorcet/Approval?
> 
Yes, and when the top approval candidate in the Smith set is uncovered, as it is whenever the Smith set 
has fewer than four candidates, the method I described elects the same candidate as Smith//Approval. 

The importance of electing an uncovered alternative when the pairwise defeats are public knowledge (as 
they should be) is shown by the following imaginary conversation between two basket ball coaches after 
a round robin tournament:

A:  How come your team gets the trophy, when my team beat yours?

B:  Well, we could almost beat ourselves, and we did beat team C, which defeated you guys.

A:  I guess you got a point there.

In other words, team B defends its trophy against the claim of team A only by pointing out that A did not 
cover team B.

If A had covered team B, imagine how hard it would be to defend the trophy decision:

B:  Yes, it is true that you beat us, but we beat teams C, D, and E.

A:  So what?  We did too.

B: But we beat team C by twenty points, and you only beat them by five.

A: That's because we sent in our second string players when we saw how weak they were.

In the election context, the corresponding statement would be, "We knew that we were going to beat 
him nationally, so we didn't waste time campaigning in the state where his base supporters live."

In sum, there is no use trying to justify the election of a covered candidate by secondary considerations 
(like defeat strength), since the primary consideration in a pairwise based method is who beats whom 
pairwise, and that by itself is sufficient to eliminate a covered candidate.