[EM] Two round Condorcet (or maybe 1.01 round)

[Kristofer Munsterhjelm]

On 9/24/21 12:11 AM, Forest Simmons wrote:
> How about a runoff between the candidate with minimal max pairwise 
> opposition and the candidate with maximal minimum pairwise (inclusive) 
> support.
> 
> With complete rankings they're equivalent. But equal rankings and 
> truncations arising from strategy or indifference can make the runoff 
> more interesting.

That's a good point, because the information concealed by equal-rank 
and/or truncation is information we don't have to begin with.

Suppose that we have two methods that feed into a runoff (as with my 
suggestion). This system takes a strategic ranked ballot for the first 
round and a honest Plurality-style ballot for the second. But by the 
revelation principle, we can replace this by a DSV method that takes a 
honest ballot as input and strategize on behalf of the voter in the 
first round, and then votes according to that ballot on the second.

(This might be a good way to construct strategy-resistant methods. 
Though ensuring properties like monotonicity hold through the DSV 
algorithm is the really difficult part.)

But for a method like the one you're describing, that doesn't work 
because the information that the DSV method would use is hidden behind 
equal-rank. It would only work if the voter always submits a complete 
(no equal rank or truncation) ballot to the DSV method itself.

As such, a runoff might be a good way to clear up ambiguities that come 
from equal rank or truncation. If, in essence, the method says "these 
incomplete ballots can either point to A being a good winner or B being 
a good winner, which one is it?", then the runoff would let the voters 
answer that question.

(Perhaps a manual runoff could also blunt the worst problems of Approval 
by the same logic, i.e. asking "I don't know if X or Y are the best 
candidates or if there's a Burr dilemma going on; could you clarify 
which it is?". But I'm not sure how you'd do that in a cloneproof way.)

-km