arXiv subjects

Jannik Peters

Publications and source records attributed to Jannik Peters.

At least 19 recordsLinked to original sources

arXiv2026

A Constant Metric Distortion Protocol for Approval Voting Given Plurality Polls

Approval voting is a simple and well-regarded voting rule: voters submit approval ballots (subsets of the candidates) and the candidate receiving the most approvals wins. One major limitation of approval voting is that it is not clear which candidates voters should approve if they have an underlying strict order over the candidates. In this paper, we initiate the study of approval voting under a simple kind of information: plurality polls. That is, we assume that for each candidate we know the share of voters who rank this candidate as their top choice. Using these plurality polls, we suggest a simple protocol parameterized by a fraction $k \in (0,1)$: every voter should approve the smallest prefix of their preference list containing the first choices of at least a fraction $k$ of the voters. We evaluate this protocol via the framework of metric distortion and show that for the optimal choice of $k$, this rule achieves a metric distortion of $2 + \sqrt{5} \simeq 4.236$. The proof techniques we use for this statement also show that the Bucklin voting rule has a metric distortion of at most $5$. Finally, we evaluate the robustness of our protocol to noise and show that the upper bounds obtained for our protocol are tight.

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arXiv2026

A Polynomial-Time Rule Satisfying Full Justified Representation

In approval-based multiwinner voting, voters submit an approval ballot on which basis a committee of fixed size $k$ has to be selected. Compared to single-winner voting this makes it possible to represent minorities in the selection of the committee as well. Thus, one of the most desirable goals of multiwinner voting is to satisfy proportional representation. In this paper we propose a variant of the Greedy Justified Candidate rule that satisfy the notion of Full Justified Representation (FJR). This variant can be computed in polynomial time answering the open question of whether an FJR committee can always be computed efficiently. Additionally, we answer an open question whether committees returned by MES can always be extended in a way to satisfy FJR negatively.

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arXiv2026

Individual Fairness in Budget Aggregation

We consider the problem of aggregating $n$ individual distributions over $m$ alternatives into a collective distribution, also known as budget aggregation. Existing fairness notions in this literature typically do not guarantee fairness to individual agents. To address this, we define two versions of individual fair share guarantees. We show that when agents' utilities are derived from $\ell_t$ metrics for any $t\geq 1$, both these guarantees can be satisfied along with Pareto efficiency, and the corresponding distributions can be computed in polynomial time. On the other hand, for $\ell_1$ utilities, we prove that Pareto efficiency, strategyproofness, and a very weak fairness notion called single-minded positive share are not always compatible for $n,m \ge 3$. For smaller parameters, we provide rules that satisfy these three axioms. We also establish similar impossibility results for $\ell_2$ utilities.

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arXiv2026

Beyond Lower Quota: Avoiding Overrepresentation in Multi-Winner Voting

Recently, in the social choice literature, much attention has been given to the question of avoiding underrepresentation in approval-based multi-winner voting. In this paper, we explore the largely overlooked complementary question of avoiding overrepresentation. This has not been explored systematically, despite being a desirable property with concrete applications. Intuitively, overrepresentation happens when a group determines a disproportionately large part of the committee, thereby exceeding the group's quota. We formulate a strong and appealing axiom for avoiding overrepresentation, called justifiable upper quota (JUQ). We introduce a generalization of Thiele rules, composite Thiele rules, and characterize the unique rule in this class satisfying our axiom. This rule, Adams-AV, which naturally extends Adams' apportionment method, has not been studied before. Additionally, we introduce a polynomial-time rule that satisfies JUQ. Furthermore, we introduce justified near quota, an axiom that balances avoiding under- and overrepresentation. It characterizes the unique Thiele rule extending the Sainte-Lagu\"e apportionment method. Finally, we analyze the compatibility of our axioms with established proportionality notions such as EJR+.

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arXiv2026

Two Observations on Metric Distortion and Condorcet Winning Sets

In this research note we briefly connect two well-studied topics in computational social choice: metric distortion and the selection of undominated committees. In particular, we show that undominated committees are (in some sense) both necessary and sufficient to achieve bi-criteria metric distortion below $3$ (Banishashem et al., 2026). First, we show that any $\alpha$-undominated committee with $\alpha \le 0.5 - \Omega(1)$ has a bi-criteria metric distortion strictly of $3 - \Omega(1)$. In particular, this implies that a committee of size $5$ with distortion at most $2.7384$ exists. Secondly, we show that if a committee has a bi-criteria metric distortion strictly of $3 - \Omega(1)$, then it must also be $1 - \Omega(1)$-undominated.

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arXiv2026

An Axiomatic Analysis of Proportionality Notions in Approval-Based Multiwinner Voting

Even though proportional representation is a fundamental goal in multiwinner voting and a plethora of proportionality notions has been introduced, the normative justifications for choosing one notion over another remain poorly understood. We address this by introducing the axiomatic study of proportionality notions in the approval-based multiwinner voting setting. That is, we define axioms (or desirable properties) that ``good'' proportionality notions should possess. Using these axioms, we then provide axiomatic characterizations of two prominent recently introduced notions: PJR+ and EJR+ [Brill and Peters 2023]. Our characterization proceeds in two parts. Firstly, we provide a characterization of refinements of PJR+ and EJR+. That is, we define axioms such that any notion satisfying these axioms must imply PJR+ (or EJR+, respectively). In particular, the fundamental axiom distinguishing PJR+ and EJR+ from their predecessors PJR and EJR is the classical axiom of monotonicity. Secondly, we introduce our framework of witness-based proportionality notions, that is, proportionality notions that certify ``misrepresentation'' via a witness set of misrepresented voters. In this class, we provide characterizations of PJR+ and EJR+ as the strongest (assuming certain axioms). Thus, by putting both directions together we obtain exact characterizations of both notions. Among our results, it may be worth highlighting that any notion satisfying mild conditions (monotonicity, independence of losers, robustness to fully satisfied voters, and lower quota) refines PJR+. In this sense, PJR+ turns out to be the canonical minimal requirement that one may impose on proportionality.

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arXiv2026

Explanation Systems for Approval-Based Multiwinner Voting

In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work has focused on the study of binary proportionality axioms that certify whether a given committee is proportionally representative or not. We take a more fine-grained perspective and initiate the study of explanation systems that quantify how a committee represents the electorate, i.e., how much influence each voter exerts, how this influence is allocated across selected candidates, how each candidate is backed by the voters, and why certain candidates were not chosen. Building on the notion of priceability, we propose price systems as a framework for such explanations. A price system assigns each voter an individual budget, which they can spend on selected candidates they approve, and each candidate needs to be purchased at a unit price. Since many price systems can exist for a given outcome, selecting among them requires care. We initiate an axiomatic study of price systems and propose several axioms capturing structural coherence, faithful attribution of influence, and alignment with proportionality. On the algorithmic side, we introduce a polynomial-time computable rule in which voters continuously gain and exercise influence and show that it satisfies all jointly satisfiable axioms. Experiments on synthetic and real-world instances indicate that our explanations correlate with established proportionality notions and can recover unequal influence when it is present.

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arXiv2025

Candidate Monotonicity and Proportionality for Lotteries and Non-Resolute Rules

We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone. We further show that Phragmén's Ordered Rule can be turned into a candidate monotone probabilistic rule which randomizes over committees satisfying proportionality for solid coalitions.

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arXiv2025

Utilitarian Guarantees for the Method of Equal Shares

In recent years, research in Participatory Budgeting (PB) has put a greater emphasis on rules satisfying notions of fairness and proportionality, with the Method of Equal Shares (MES) being a prominent example. However, proportionality can come at a cost to the total utilitarian welfare. Our work formalizes this relationship, by deriving minimum utilitarian welfare guarantees for MES for a subclass of satisfaction functions called DNS functions, which includes two of the most popular ways of measuring a voter's utility in the PB setting: considering (1) the total cost of approved projects or (2) the total number of those projects. Our results are parameterized in terms of minimum and maximum project costs, which allows us to improve on the mostly negative results found in prior studies, and reduce to the existing multiwinner guarantee when project costs are equal. We show that our guarantees are asymptotically tight for rules satisfying Extended Justified Representation up to one project, showing that no proportional rule can achieve a better utilitarian guarantee than MES.

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arXiv2025

The Core in Max-Loss Non-Centroid Clustering Can Be Empty

We study core stability in non-centroid clustering under the max-loss objective, where each agent's loss is the maximum distance to other members of their cluster. We prove that for all $k\geq 3$ there exist metric instances with $n\ge 9$ agents, with $n$ divisible by $k$, for which no clustering lies in the $α$-core for any $α<2^{\frac{1}{5}}\sim 1.148$. The bound is tight for our construction. Using a computer-aided proof, we also identify a two-dimensional Euclidean point set whose associated lower bound is slightly smaller than that of our general construction. This is, to our knowledge, the first impossibility result showing that the core can be empty in non-centroid clustering under the max-loss objective.

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arXiv2025

Understanding the Impact of Proportionality in Approval-Based Multiwinner Elections

Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the computational complexity of several natural problems related to the behavior of proportionality axioms, and (ii) conducting an extensive experimental study on both real-world and synthetic elections. Our findings reveal substantial variation in the restrictiveness of proportionality across instances, including previously unobserved high levels of restrictiveness in some real-world cases. We also introduce and evaluate new measures for quantifying a candidate's importance for achieving proportional outcomes, which differ clearly from assessing candidate strength by approval score.

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arXiv2025

Online Fair Division with Additional Information

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.

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arXiv2025

Proportionality in Practice: Quantifying Proportionality in Ordinal Elections

Proportional representation plays a crucial role in electoral systems. In ordinal elections, where voters rank candidates based on their preferences, the Single Transferable Vote (STV) is the most widely used proportional voting method. STV is considered proportional because it satisfies an axiom requiring that large enough solid coalitions of voters are adequately represented. Using real-world data from local Scottish elections, we observe that solid coalitions of the required size rarely occur in practice. This observation challenges the importance of proportionality axioms and raises the question of how the proportionality of voting methods can be assessed beyond their axiomatic performance. We address these concerns by developing quantitative measures of proportionality. We apply these measures to evaluate the proportionality of voting rules on real-world election data. Besides STV, we consider SNTV, the Expanding Approvals Rule, and Sequential Ranked-Choice Voting. We also study the effects of ballot truncation by artificially completing truncated ballots and comparing the proportionality of outcomes under complete and truncated ballots.

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arXiv2025

Reconfiguring Proportional Committees

An important desideratum in approval-based multiwinner voting is proportionality. We study the problem of reconfiguring proportional committees: given two proportional committees, is there a transition path that consists only of proportional committees, where each transition involves replacing one candidate with another candidate? We show that the set of committees satisfying the proportionality axiom of justified representation (JR) is not always connected, and it is PSPACE-complete to decide whether two such committees are connected. On the other hand, we prove that any two JR committees can be connected by committees satisfying a $2$-approximation of JR. We also obtain similar results for the stronger axiom of extended justified representation (EJR). In addition, we demonstrate that the committees produced by several well-known voting rules are connected or at least not isolated, and investigate the reconfiguration problem in restricted preference domains.

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arXiv2025

Committee Monotonicity and Proportional Representation for Ranked Preferences

We study committee voting rules under ranked preferences, which map the voters' preference relations to a subset of the alternatives of predefined size. In this setting, the compatibility between proportional representation and committee monotonicity is a fundamental open problem that has been mentioned in several works. We address this research question by designing a new committee voting rule called the Solid Coalition Refinement (SCR) rule that simultaneously satisfies committee monotonicity and Dummett's Proportionality for Solid Coalitions (PSC) property as well as one of its variants called inclusion PSC. This is the first rule known to satisfy both of these properties. Moreover, we show that this is effectively the best that we can hope for as other fairness notions adapted from approval voting are incompatible with committee monotonicity. For truncated preferences, we prove that the SCR rule still satisfies PSC and a property called independence of losing voter blocs, thereby refuting a conjecture of Graham-Squire et al. (2024). Finally, we discuss the consequences of our results in the context of rank aggregation.

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arXiv2025

Emergent Language: A Survey and Taxonomy

The field of emergent language represents a novel area of research within the domain of artificial intelligence, particularly within the context of multi-agent reinforcement learning. Although the concept of studying language emergence is not new, early approaches were primarily concerned with explaining human language formation, with little consideration given to its potential utility for artificial agents. In contrast, studies based on reinforcement learning aim to develop communicative capabilities in agents that are comparable to or even superior to human language. Thus, they extend beyond the learned statistical representations that are common in natural language processing research. This gives rise to a number of fundamental questions, from the prerequisites for language emergence to the criteria for measuring its success. This paper addresses these questions by providing a comprehensive review of 181 scientific publications on emergent language in artificial intelligence. Its objective is to serve as a reference for researchers interested in or proficient in the field. Consequently, the main contributions are the definition and overview of the prevailing terminology, the analysis of existing evaluation methods and metrics, and the description of the identified research gaps.

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arXiv2025

Proportional Clustering, the $β$-Plurality Problem, and Metric Distortion

We show that the proportional clustering problem using the Droop quota for $k = 1$ is equivalent to the $β$-plurality problem. We also show that the Plurality Veto rule can be used to select ($\sqrt{5} - 2$)-plurality points using only ordinal information about the metric space and resolve an open question of Kalayci et al. (AAAI 2024) by proving that $(2+\sqrt{5})$-proportionally fair clusterings can be found using purely ordinal information.

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arXiv2025

Verifying Proportionality in Temporal Voting

We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of justified representation as well as voting rules that provide strong representation guarantees from the multiwinner election setting to this model. In our work, we focus on the complexity of verifying whether a given outcome offers proportional representation. We show that in the temporal setting verification is strictly harder than in multiwinner voting, but identify natural special cases that enable efficient algorithms.

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