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A Characterization of Approximation Resistance for Even -Partite CSPs
A constraint satisfaction problem (CSP) is said to be \emph{approximation
resistant} if it is hard to approximate better than the trivial algorithm which
picks a uniformly random assignment. Assuming the Unique Games Conjecture, we
give a characterization of approximation resistance for -partite CSPs
defined by an even predicate
Asymptotic bias of some election methods
Consider an election where N seats are distributed among parties with
proportions p_1,...,p_m of the votes. We study, for the common divisor and
quota methods, the asymptotic distribution, and in particular the mean, of the
seat excess of a party, i.e. the difference between the number of seats given
to the party and the (real) number Np_i that yields exact proportionality. Our
approach is to keep p_1,...,p_m fixed and let N tend to infinity, with N random
in a suitable way.
In particular, we give formulas showing the bias favouring large or small
parties for the different election methods.Comment: 54 page
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