[EM] simpler proof of "no conflict theorem" now trivial

[Abd ul-Rahman Lomax]

Approval Voting satisfies the Condorcet criterion (as does 
Plurality). The idea that it does not is based on the imputation of 
unexpressed preferences. That is, *if* there were more expressible 
ranks, and the voters used them, the outcome could change.

(But if the Condorcet criterion *requires* that all preferences be 
expressible, i.e., that the number of ranks equals the number of 
candidates, then, of course, any method which does not allow that 
does not satisfy the criterion. I don't know the exact wording. But 
I've never seen anyone objecting that a method which only allows N 
ranks in the presence of more than N candidates does not satisfy the 
Criterion. Obviously, such a method requires equal ranking. Note also 
that a voter might prefer to add more than one write-in candidate. 
Should this too be allowed? If not, why not? -- the answer, ballot 
complexity, would similarly apply to reducing the number of 
expressible ranks when there are many candidates.)

Sometimes we forget that Approval and Plurality are ranked methods 
with only two ranks. The problem with Plurality, of course, is that 
equal ranking is generally prohibited. If overvoting were allowed, 
with one stroke of the deletion pen in the election code, Plurality 
would become Approval, which has got to be the simplest of the 
proposed election reforms.

(But Asset voting, using plurality counting, i.e., no overvoting 
allowed, is just as simple to count and uses the same ballot. If 
overvoting is allowed, the counting gets more complex because in this 
case the votes must become fractional votes, i.e., the method becomes 
Fractional Approval Asset Voting, my current favorite. But what I'll 
now call Standard Asset Voting -- i.e., vote for one only -- is 
really almost as good without the counting complexity. Pick the 
candidate you most trust and vote for him or her, no worry about wasted votes.)