[EM] Interactive Representation

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> Since you are building this on the single-seat district tradition,
> three or four seats and 10 candidates is plenty. I'm used to numbers
> like 6 seats with 108 candidates, and 35 seats with 405 candidates,
> and at least eight parties in the parliament. (In that situation even
> ranking all of the candidates, or even all of the candidates of one's
> favourite party may be too tedious. One may however allow all votes
> (also short ones) to be counted for the party.)
> 
> What would be a good (non-limiting) number of candidates? Maybe
> something like (P * K1) * (S * K2), where P = current number of
> parties with representatives, K1 = 1.5 or 2, S = number of seats, K2
> = 1.

Maybe one can make shortcuts, too. In Kemeny (which is a hard 
single-winner method), you know that the method passes Smith. Therefore, 
only orderings where the winner is in the Smith set needs to be 
considered. (In practice, you can add such a constraint upon the mixed 
integer program; trying every possible ordering would take too much time).

So perhaps there are similar shortcuts one can make for the multiwinner 
method. That would help ward off candidate flooding attacks or simply 
unexpected popularity -- if most of the 405 candidates have no chance of 
winning, one might be able to prune them away and be left with a 
feasible problem even with extreme numbers of candidates.

That would, of course, not help if all 405 candidates are viable, but 
such a situation would be very unlikely to happen in practice, 
particularly if the voters have to rank the candidates manually. If the 
voters don't rank all the candidates manually but instead use some sort 
of party list with overrides hybrid, then that party list structure 
creates a pattern that might itself be used to reduce the scope of the 
problem.