[EM] Mutual majority set methods

[Leon Smith]

How does the mutual majority set differ from either the Smith Set or
the Schwartz Set?  Can't you just sum the "a beats b" half-matrices
and then run a strongly connected component algorithm on the result?
Kosaraju's algorithm produces the SCCs in a topological order,  so
you don't even need serious processing on the output,   just take the
first or last SCC depending on how it's implemented.

But I'm guessing you already know this,  so I'm guessing there is
something I'm missing.

Best,
Leon

On Wed, Feb 2, 2011 at 7:57 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> 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
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