[EM] Range with a hedge

[Kristofer Munsterhjelm]

Here's a method that passes IIA if Range does, and that passes Condorcet 
if Range doesn't pass IIA:

In the first round, voters rate every candidate.[1] The method selects 
the Condorcet winner (or the winner according to some Condorcet method), 
as well as the Range winner, for the second round. If they're the same, 
the method immediately elects that candidate and there is no second round.

Otherwise, the voters rate the two finishers in the second round. The 
candidate with the highest score wins.



Suppose that people vote on an absolute scale. Then the second round is 
a no-operation and the Range winner wins. On the other hand, if voters 
use relative scales and max their favorite and min their least favorite, 
the Condorcet candidate wins whenever there is a CW.

Thus we have Range's performance when voters use absolute scales and 
Condorcet when they don't.

I don't think the absolute scale assumption is very realistic, but this 
should help frame it in another perspective. If it seems obvious that 
voters - even honest ones - would min-max in the second round, well, 
there's your IIA violation right there. Whenever the method picks two 
distinct candidates and the Condorcet candidate wins without the voters 
changing their minds about the candidates, that demonstrates IIA failure 
in practice.

(As an aside, apparently great minds think alike; I thought of this 
yesterday, then saw Abel Stan's top two idea just now.)

-km

[1] Alternatively, the ballot might ask for a rating *and* a ranking. If 
the ranking is consistent with the rating, i.e. the ranking doesn't list 
A>B if the rating gives B a strictly higher score than A, then the 
ranking is used for the Condorcet method. Otherwise the ranking inferred 
from the rating is. This would allow voters to vote Approval-style and 
still provide a proper rank for the Condorcet method to use. The 
consistency requirement reduces strategy.