相关论文: An impossibility theorem for gerrymandering

Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…

Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…

Impartial selection is the selection of an individual from a group based on nominations by other members of the group, in such a way that individuals cannot influence their own chance of selection. For this problem, we give a deterministic…

We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…

We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$,…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…

The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…

We present the conditions under which probabilistic error-free discrimination of mixed states is possible, and provide upper and lower bounds on the maximum probability of success for the case of two mixed states. We solve certain special…

To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…

We consider the approval-based model of elections, and undertake a computational study of voting rules which select committees whose size is not predetermined. While voting rules that output committees with a predetermined number of winning…

Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have underlying utilities for these options, however, using preference…

We investigate the problem of computing the probability of winning in an election where voter attendance is uncertain. More precisely, we study the setting where, in addition to a total ordering of the candidates, each voter is associated…

Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…

A controversial test for Large Language Models concerns the ability to discern possible from impossible language. While some evidence attests to the models' sensitivity to what crosses the limits of grammatically impossible language, this…

A perfect clone in an ordinal election (i.e., an election where the voters rank the candidates in a strict linear order) is a set of candidates that each voter ranks consecutively. We consider different relaxations of this notion:…

In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…

An impossibility theorem on approximately simulating quantum non-integrable Hamiltonian systems is presented here. This result shows that there is a trade-off between the unitary property and the energy expectation conservation law in…

Complexity of voting manipulation is a prominent topic in computational social choice. In this work, we consider a two-stage voting manipulation scenario. First, a malicious party (an attacker) attempts to manipulate the election outcome in…