Related papers: Independence of Approximate Clones
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative…
In social choice theory, anonymity (all agents being treated equally) and neutrality (all alternatives being treated equally) are widely regarded as ``minimal demands'' and ``uncontroversial'' axioms of equity and fairness. However, the ANR…
In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our…
We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin and Alon et al. Fisher and Klimm…
Approval-based committee selection is a model of significant interest in social choice theory. In this model, we have a set of voters $\mathcal{V}$, a set of candidates $\mathcal{C}$, and each voter has a set $A_v \subset \mathcal{C}$ of…
Among two-candidate elections that treat the candidates symmetrically and never result in a tie, which voting rules are fair? A natural requirement is that each voter exerts an equal influence over the outcome, i.e., is equally likely to…
We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each…
The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
An assembly of $n$ voters needs to decide on $t$ independent binary issues. Each voter has opinions about the issues, given by a $t$-bit vector. Anscombe's paradox shows that a policy following the majority opinion in each issue may not…
We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score…
In the realizable online setting, a learner is tasked with making predictions for a stream of instances, where the correct answer is revealed after each prediction. A learning rule is online consistent if its mistake rate eventually…
It is common that a jury must grade a set of candidates in a cardinal scale such as {1,2,3,4,5} or an ordinal scale such as {Great, Good, Average, Bad }. When the number of candidates is very large such as hotels (BOOKING), restaurants…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…