We study the formation of a ruling coalition in non-democratic societies where institutions do not enable political commitments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternativ...

Recent advances in voting theory have shed light on the influence of pivotality on voter choices when voters have asymmetric private information, and the implications of this for information aggregation in committees and elections. Of particular interest is the result that voters may optimally choose to vote contrary to their own private information, even in committees or elections where all vo...

The median operator is a nonlinear (morphological) image transformation which has become very popular because it can suppress noise while preserving the edges. I t treats the foreground and background of an image in an identical way, that is, it is a self-dual operator. Unfortunately, the median operator lacks the idempotence property: it is not a morphological filter. This paper gives a comple...

All Boolean variables here range over the two element set {−1, 1}. Given n Boolean variables x1, . . . , xn, a non-monotone MAJORITY gate (in the variables xi) is a Boolean function whose value is the sign of ∑n i=1 ixi, where each i is either 1 or −1. The COMPARISON function is the Boolean function of two n-bits integers X and Y whose value is −1 iff X ≥ Y . We construct an explicit sparse pol...

In this paper, we show that for every constant 0 < ǫ < 1/2 and for every constant d ≥ 2, the minimum size of a depth d Boolean circuit that ǫ-approximates Majority function on n variables is exp(Θ(n)). The lower bound for every d ≥ 2 and the upper bound for d = 2 have been previously shown by O’Donnell and Wimmer [ICALP’07], and the contribution of this paper is to give a matching upper bound f...

A set of voters consults a set of experts before voting over two alternatives. Agents have private biases over which alternative they prefer ex ante, but may be swayed by information about relative values of the alternatives. Experts observe private signals about the relative values of the alternatives and can choose to either reveal that information or conceal it, but they cannot lie. We exami...

Say that f : {0, 1}n → {0, 1} 2-approximates g : {0, 1}n → {0, 1} if the functions disagree on at most an 2 fraction of points. This paper contains two results about approximation by DNF and other small-depth circuits: (1) For every constant 0 < 2 < 1/2 there is a DNF of size 2 √ n) that 2-approximates the Majority function on n bits, and this is optimal up to the constant in the exponent. (2) ...

In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A location of the public facility is a majority rule winner if there is no other location in the network where more than half of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with nice combinatorial struct...

In a previous paper, the authors defined a new class ofmultiple-valued logic functions, called multiple-valued majority func-tions. This correspondence clarifies the distinction of multiple-valuedmajority functions from multiple-valued threshold functions through thedifference between a number function and an inner product of an inputvector and a weight vector. Zndcx Terns-I...

We show that Nechiporuk’s method [26] for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an Ω(n/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [27] states that the majority function does not have a linear–size quantum formula. We also show that quantum formul...