Amedian of a sequence π = x1, x2, . . . , xk of elements of a finite metric space (X, d) is an element x for which ∑k i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(π) = {x : x is a median of π} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π)...

We elaborate on the convexity properties of (not necessarily finite) weakly median graphs and their prime constituents in order to establish a number of equations in terms of the weakly median operation. Then the weakly median graphs can be identified with the discrete members of an equational class of ternary algebras satisfying five independent axioms on two to four points. This demonstrates ...

Median voter theory applied to trade policy predicts positive tariffs in capital-abundant countries and negative tariffs in labor-abundant countries. Negative tariffs are rare, and this paper reconciles the median voter theory with observed protectionism across countries. By considering large countries, I show the optimal tariff is a sum of the median voter component and a positive in terms of ...

The concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures. It is found that democratic voting can lead to totalitarianism by keeping in power a small minority. Conditions of this paradox are analyzed and singled out. Indeed majority rule produces critical thresholds to absolute power. Values of these thresholds can vary fro...

A spin wave majority fork-like structure with feature size of 40 nm, is presented and investigated, through micromagnetic simulations. The structure consists of three merging out-of-plane magnetization spin wave buses and four magneto-electric cells serving as three inputs and an output. The information of the logic signals is encoded in the phase of the transmitted spin waves and subsequently ...

We show that Nechiporuk’s method [14] for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an Ω(n2/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [15] states that the majority function does not have a linear–size quantum formula.

Of those eligible, about 40% do not vote in presidential elections. When asked, about a quarter of those nonvoters will lie to the survey takers and claim that they did. Increases in education are associated with higher voting rates and lower rates of lying overall, but with increased rates of lying conditional on not voting. This paper proposes a model of voter turnout in which people who clai...

We prove that the noisy voter model mixes extremely fast – in time of O(logn) on any graph with n vertices – for arbitrarily small values of the ‘noise parameter’. We then explain why, as a result, this is an example of a spin system that is always in the ‘high-temperature regime’.