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...

We study in detail the fitness landscape of a difficult cellular automata computational task: the majority problem. Our results show why this problem landscape is so hard to search, and we quantify the large degree of neutrality found in various ways. We show that a particular subspace of the solution space, called the ”Olympus”, is where good solutions concentrate, and give measures to quantit...

Given a set of n coins, some of them weighing H, the others weighing h, h < H, we prove that to determine the set of heavy coins, an optimal algorithm requires an average of 1+ρ 1+ρ+ρ n + O(1) comparisons, using a beam balance, in which ρ denotes the ratio of the probabilities of being light and heavy. A simple quasi-optimal algorithm is described. Similar results are derived for the majority p...

We revisit the range τ -majority problem, which asks us to preprocess an array A[1..n] for a fixed value of τ ∈ (0, 1/2], such that for any query range [i, j] we can return a position in A of each distinct τ majority element. A τ -majority element is one that has relative frequency at least τ in the range [i, j]: i.e., frequency at least τ(j − i + 1). Belazzougui et al. [WADS 2013] presented a ...

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...