Related papers: On the Construction of High Dimensional Simple Gam…
Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting…
Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion.…
We study the voting problem with two alternatives where voters' preferences depend on a not-directly-observable state variable. While equilibria in the one-round voting mechanisms lead to a good decision, they are usually hard to compute…
Let $U_{k,N}$ denote the Boolean function which takes as input $k$ strings of $N$ bits each, representing $k$ numbers $a^{(1)},\dots,a^{(k)}$ in $\{0,1,\dots,2^{N}-1\}$, and outputs 1 if and only if $a^{(1)} + \cdots + a^{(k)} \geq 2^N.$…
In this work we are concerned with the design of efficient mechanisms while eliciting limited information from the agents. First, we study the performance of sampling approximations in facility location games. Our key result is to show that…
We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…
Shortlisting of candidates--selecting a group of "best" candidates--is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the perhaps…
In self-assembly, a $k$-counter is a tile set that grows a horizontal ruler from left to right, containing $k$ columns each of which encodes a distinct binary string. Counters have been fundamental objects of study in a wide range of…
We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along three main lines. First, if $d$ represents the doubling dimension of the…
Every simple game is a monotone Boolean function. For the other direction we just have to exclude the two constant functions. The enumeration of monotone Boolean functions with distinguishable variables is also known as the Dedekind's…
A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum,…
For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of…
We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i.e. a special subclass of monotone Boolean functions. Recently,…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
We consider binary group decision-making under a rich model of liquid democracy recently proposed by Colley, Grandi, and Novaro (2022): agents submit ranked delegation options, where each option may be a function of multiple agents' votes;…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
Given a property of Boolean functions, what is the minimum number of queries required to determine with high probability if an input function satisfies this property or is "far" from satisfying it? This is a fundamental question in Property…
Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…