[EM] realization on method equivalence

[Russ Paielli]

Folks,

I just realized that two Condorcet-Approval hybrid methods that I had 
thought were distinct are actually equivalent. This may have been 
pointed out already, and it may even be obvious to some, but it was a 
significant realization to me nonetheless. (If it *has* been pointed 
out, please don't hesitate to tell me where.)

Method 1: The winner is the most-approved member of the Smith set.

Method 2: If no CW exists, repeatedly drop the least-approved candidate 
until a CW is found.

Here's why I think they are equivalent:

As you drop candidates, you cannot get a CW until only one member of the 
Smith set remains. Since the candidates are dropped increasing order of 
approval starting with the least-approved, the final remaining member of 
the Smith set must be the most-approved member of that set.

"Method 2" is simpler to explain because the Smith set need not be 
determined or even defined for uninterested members of the general 
public. However, "Method 1" provides the more compelling justification. 
Why *wouldn't* you choose the most-approved member of the Smith set?

--Russ