arXiv subjects

Patrick Becker

Publications and source records attributed to Patrick Becker.

8 recordsLinked to original sources

arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗

arXiv2026

Efficient and Envy-free Random Assignment Beyond Expected Utility

We consider the random assignment problem with abstract continuous and convex preferences. In particular, we admit preference relations that are not constrained by independence or transitivity. By extending the Hylland--Zeckhauser pseudo-market mechanism, we show that weakly efficient and envy-free random assignments always exist. For preferences that can be represented via skew-symmetric bilinear (SSB) utility functions -- which generalize linear expected utility functions -- we prove the existence of efficient and approximately envy-free random assignments. Efficient and envy-free random assignments exist under a mild additional assumption on preferences. These findings have notable implications for ordinal random assignment, where ordinal preferences are extended to preferences over lotteries via the pairwise comparison (PC) extension. While the probabilistic serial rule and popular random assignments frequently and significantly violate PC-efficiency and PC-envy-freeness, respectively, random assignments that satisfy both conditions do exist.

econ.TH↗

arXiv2026

Fractional Pareto-Optimality in Multiwinner Voting

Efficiency in multiwinner voting is most naturally captured by Pareto-optimality (PO), yet this notion is computationally and structurally difficult to handle. We therefore study fractional Pareto-optimality (fPO), under which a committee may not be dominated even by a fractional committee, i.e., any convex combination of committees. fPO turns out to be a natural refinement of PO as it retains exactly those Pareto-optimal committees whose efficiency is robust under uniform cloning of candidates. Furthermore, fPO committees are guaranteed to exist and have strong structural properties. We present a characterization of fPO in terms of weighted utilitarian welfare maximization, which yields a polynomial-time algorithm for verifying fPO and shows that the set of fPO committees satisfies committee monotonicity and is connected under single-candidate swaps. Analyzing welfarist rules through the lens of fPO, we further uncover an incompatibility between fPO and equality-oriented objectives. Most notably, we show that proportional approval voting (PAV) violates fPO in the approval setting. We close by pinpointing preference domains, including various one-dimensional ones, on which PO and fPO collapse into one notion.

cs.GT↗

arXiv2026

Core Existence in Approval-Based Committee Elections with up to Seven Voter Types

In an approval-based committee election, the task is to select a committee of up to $k$ candidates from a set of $m$ candidates based on the preferences of $n$ voters, each of whom approves a subset of the candidates. A central open question is whether there always exists a committee in the core, a stability notion capturing proportional representation. We prove core non-emptiness for all approval-based committee elections with at most seven voters. The proof is based on affine monoid methods and shows that, for $n\le5$, every fractional committee admits a deterministic rounding to an integral committee that preserves each voter's utility up to floors. This no longer applies for larger $n$. However, for $n \in \{6,7\}$, we show that a Lindahl equilibrium can be adapted and rounded to obtain a core committee. For $n \le 5$, we further provide a polynomial-time algorithm for computing a committee in the core. Our arguments work for the weighted voter setting, which implies core existence for instances with up to seven distinct approval sets. We conclude by providing examples where our methods fail for more general models with additive valuations, non-unit candidate costs, or the related Droop core.

cs.GT↗

arXiv2026

Three Months in the Life of Cloud Quantum Computing

Quantum Computing (QC) has evolved from a few custom quantum computers, which were only accessible to their creators, to an array of commercial quantum computers that can be accessed on the cloud by anyone. Accessing these cloud quantum computers requires a complex chain of tools that facilitate connecting, programming, simulating algorithms, estimating resources, submitting quantum computing jobs, retrieving results, and more. Some steps in the chain are hardware dependent and subject to change as both hardware and software tools, such as available gate sets and optimizing compilers, evolve. Understanding the trade-offs inherent in this process is essential for evaluating the power and utility of quantum computers. ARLIS has been systematically investigating these environments to understand these complexities. The work presented here is a detailed summary of three months of using such quantum programming environments. We show metadata obtained from these environments, including the connection metrics to the different services, the execution of algorithms, the testing of the effects of varying the number of qubits, comparisons to simulations, execution times, and cost. Our objective is to provide concrete data and insights for those who are exploring the potential of quantum computing. It is not our objective to present any new algorithms or optimize performance on any particular machine or cloud platform; rather, this work is focused on providing a consistent view of a single algorithm executed using out-of-the-box settings and tools across machines, cloud platforms, and time. We present insights only available from these carefully curated data.

quant-ph↗

arXiv2025

On Minimal Achievable Quotas in Multiwinner Voting

Justified representation (JR) and extended justified representation (EJR) are well-established proportionality axioms in approval-based multiwinner voting. Both axioms are always satisfiable, but they rely on a fixed quota (typically Hare or Droop), with the Droop quota being the smallest one that guarantees existence across all instances. With this in mind, we take a step beyond the fixed-quota paradigm by studying instance-dependent proportionality notions. More specifically, we minimize the quota requirements for JR and EJR using the parameter $\alpha$. We demonstrate that all commonly studied voting rules can have an additive gap to the optimum of $\frac{k^2}{(k+1)^2}$. Moreover, we examine the computational aspects of our instance-dependent quota and prove that determining the optimal value of $\alpha$ for a given approval profile that allows some committee to satisfy $\alpha$-JR is NP-complete. To address this, we introduce an integer linear programming (ILP) formulation for computing committees that satisfy $\alpha$-JR, and we provide positive computational results in the voter interval (VI) and candidate interval (CI) domains.

cs.GT↗

arXiv2025

Efficiently Computing Equilibria in Budget-Aggregation Games

Budget aggregation deals with the social choice problem of distributing an exogenously given budget among a set of public projects, given agents' preferences. Taking a game-theoretic perspective, we study budget-aggregation games where each agent has virtual decision power over some fraction of the budget. We investigate the structure and show efficient computability of Nash equilibria for various common preference models in this setting. In particular, we show that equilibria for Leontief utilities can be found in polynomial time, solving an open problem from Brandt et al. [2023], and give an explicit polynomial-time algorithm for computing equilibria for $\ell_1$ preferences.

cs.GT↗

arXiv2021

Observation of a prethermal discrete time crystal

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

quant-ph↗