[EM] Mutual majority set methods

[Kristofer Munsterhjelm]

Hello,

does anybody know of a summable way of determining the entire mutual 
majority set? The mutual majority set is the set of candidates that are 
ranked above those not in the set by a majority (but not necessarily in 
the same order).

The summable "set method" would take data with space polynomial with 
regards to the number of candidates and return the mutual majority set 
for the ballots from which the data was derived. Does such a method exist?

(In particular, does "take the candidates who get above majority in 
Bucklin at the first round some candidate does" work? I don't think so, 
because of a shadowing problem similar to that which broke the 
proportionality of my semiproportional Bucklin method concept; but I'm 
not sure of that.)

Ideally, the method should return the iterated mutual majority set. Say 
that a majority (and it is the same majority) votes A first, B second, 
but there's no pattern beyond that. Then the iterated set's ordering is 
A > B > C = D = E ... Just returning the mutual majority set itself (A 
in this case) would be good, but getting the iterated set even better.

Perhaps such methods could give some ideas of how to approach DPC while 
still being (strongly) summable. Even if not, they'll still be useful 
for my voting simulation program.

-km