arXiv subjects

Sonja Kraiczy

Publications and source records attributed to Sonja Kraiczy.

10 recordsLinked to original sources

arXiv2026

Social Choice Foundations for Simulation-Augmented Generation

Simulation-augmented generation (SAGE) is a recent technical proposal in which models simulate individuals' viewpoints at inference time in order to provide more representative answers to contentious user queries. A core challenge for SAGE is making inference-time simulation efficient without sacrificing representation quality. We introduce the first formalization of this problem, based upon an axiom from proportional clustering known as metric proportional justified representation+ (mPJR+) which is the strongest proportionality axiom known to always be satisfiable by centroid-based clustering. We prove that to proportionally represent the viewpoints of a population of $n_H$ humans on a given prompt, we need only create simulations of $n \ll n_H$ individuals, and at inference time, need only dynamically route to $k \ll n$ of those simulations based upon the prompt. This twofold reduction still yields approximate proportional representation guarantees for the entire population. Empirically, across two domains-political questions and personal advice-our proposed routing algorithm achieves higher mPJR+ satisfaction rates than $k$-means-based or random selection baselines.

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arXiv2026

Where Should Society Draw the Line? A Social Choice Approach to Collective Consent

Society constantly has to determine the boundaries of what it deems acceptable, from legislative decisions to the guardrails governing autonomous systems. We initiate the axiomatic study of collective consent: given individuals' attitudes toward options, which options should receive societal consent? We organize our analysis around three principles: sufficient support, minority protection, and dominance by decisively better options. Each captures a distinct reason for withholding societal consent from an option. For each principle, we develop a corresponding solution concept that transparently implements the principle and is canonical in a mathematically precise sense. For example, for minority protection, the resulting concept is a consent-adapted version of Moulin's Proportional Veto Core. Balancing multiple principles simultaneously is more challenging. To address this, we develop a game-theoretic characterization of our veto core that naturally gives rise to a family of related concepts. From this family, we identify the Approval-Weighted Veto Core as particularly desirable. By making minorities' blocking power depend on the approval support of the options being challenged, it smoothly interpolates between proportional minority protection and majority support. Experiments on five datasets spanning high-stakes decision-making (such as political elections, ethical AI evaluations, and moral decision-making) show that solution concepts violating a principle in theory also violate it empirically.

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arXiv2026

Proportional Committee Elections with Positive and Negative Votes

In the classic committee election setting each voter approves a subset of candidates and the goal is to select $k$ winners based on these preferences. A central focus of recent research in the area has been to achieve proportional representation. In this work, we explore notions of proportionality in a more expressive setting that allows voters to vote against candidates---a common feature on online polling platforms and beyond. We propose two conceptually distinct interpretations of negative votes, resulting in different perspectives of proportionality. In the first, preventing the election of disapproved candidates is as important to voters as electing approved ones. In the second, approvals and disapprovals are treated separately, with each receiving its own fairness guarantees. For each approach, we introduce suitable axioms capturing proportionality and examine their satisfiability by appropriate variants of Phragmén's rule, Proportional Approval Voting rule (PAV), and the Method of Equal Shares (MES).

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arXiv2025

Streamlining Equal Shares

Participatory budgeting (PB) is a form of citizen participation that allows citizens to decide how public funds are spent. Through an election, citizens express their preferences on various projects (spending proposals). A voting mechanism then determines which projects will be approved. The Method of Equal Shares (MES) is the state of the art algorithm for a proportional, voting based approach to participatory budgeting and has been implemented in cities across Poland and Switzerland. A significant drawback of MES is that it is not \textit{exhaustive} meaning that it often leaves a portion of the budget unspent that could be used to fund additional projects. To address this, in practice the algorithm is combined with a completion heuristic - most often the ``add-one" heuristic which artificially increases the budget until a heuristically chosen threshold. This heuristic is computationally inefficient and will become computationally impractical if PB is employed on a larger scale. We propose the more efficient \textsc{add-opt} heuristic for Exact Equal Shares (EES), a variation of MES that is known to retain many of its desirable properties. We solve the problem of identifying the next budget for which the outcome for EES changes in $O(mn)$ time for cardinal utilities and $O(m^2n)$ time for uniform utilities, where $m$ is the number of projects and $n$ is the number of voters. Our solution to this problem inspires the efficient \textsc{add-opt} heuristic which bypasses the need to search through each intermediary budget. We perform comprehensive experiments on real-word PB instances from Pabulib and show that completed EES outcomes usually match the proportion of budget spent by completed MES outcomes. Furthermore, the \textsc{add-opt} heuristic matches the proportion of budget spend by add-one for EES.

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arXiv2024

A Lower Bound for Local Search Proportional Approval Voting

Selecting $k$ out of $m$ items based on the preferences of $n$ heterogeneous agents is a widely studied problem in algorithmic game theory. If agents have approval preferences over individual items and harmonic utility functions over bundles -- an agent receives $\sum_{j=1}^t\frac{1}{j}$ utility if $t$ of her approved items are selected -- then welfare optimisation is captured by a voting rule known as Proportional Approval Voting (PAV). PAV also satisfies demanding fairness axioms. However, finding a winning set of items under PAV is NP-hard. In search of a tractable method with strong fairness guarantees, a bounded local search version of PAV was proposed by Aziz et al. It proceeds by starting with an arbitrary size-$k$ set $W$ and, at each step, checking if there is a pair of candidates $a\in W$, $b\not\in W$ such that swapping $a$ and $b$ increases the total welfare by at least $\varepsilon$; if yes, it performs the swap. Aziz et al.~show that setting $\varepsilon=\frac{n}{k^2}$ ensures both the desired fairness guarantees and polynomial running time. However, they leave it open whether the algorithm converges in polynomial time if $\varepsilon$ is very small (in particular, if we do not stop until there are no welfare-improving swaps). We resolve this open question, by showing that if $\varepsilon$ can be arbitrarily small, the running time of this algorithm may be super-polynomial. Specifically, we prove a lower bound of~$Ω(k^{\log k})$ if improvements are chosen lexicographically. To complement our lower bound, we provide an empirical comparison of two variants of local search -- better-response and best-response -- on several real-life data sets and a variety of synthetic data sets. Our experiments indicate that, empirically, better response exhibits faster running time than best response.

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arXiv2024

Stability in Random Hedonic Games

Partitioning a large group of employees into teams can prove difficult because unsatisfied employees may want to transfer to other teams. In this case, the team (coalition) formation is unstable and incentivizes deviation from the proposed structure. Such a coalition formation scenario can be modeled in the framework of hedonic games and a significant amount of research has been devoted to the study of stability in such games. Unfortunately, stable coalition structures are not guaranteed to exist in general and their practicality is further hindered by computational hardness barriers. We offer a new perspective on this matter by studying a random model of hedonic games. For three prominent stability concepts based on single-agent deviations, we provide a high probability analysis of stability in the large agent limit. Our first main result is an efficient algorithm that outputs an individually and contractually Nash-stable partition with high probability. Our second main result is that the probability that a random game admits a Nash-stable partition tends to zero. Our approach resolves the two major downsides associated with individual stability and contractual Nash stability and reveals agents acting single-handedly are usually to blame for instabilities.

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arXiv2024

Properties of the Mallows Model Depending on the Number of Alternatives: A Warning for an Experimentalist

The Mallows model is a popular distribution for ranked data. We empirically and theoretically analyze how the properties of rankings sampled from the Mallows model change when increasing the number of alternatives. We find that real-world data behaves differently than the Mallows model, yet is in line with its recent variant proposed by Boehmer et al. [2021]. As part of our study, we issue several warnings about using the model.

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arXiv2023

An Adaptive and Verifiably Proportional Method for Participatory Budgeting

Participatory Budgeting (PB) is a form of participatory democracy in which citizens select a set of projects to be implemented, subject to a budget constraint. The Method of Equal Shares (MES), introduced in [18], is a simple iterative method for this task, which runs in polynomial time and satisfies a demanding proportionality axiom (Extended Justified Representation) in the setting of approval utilities. However, a downside of MES is that it is non-exhaustive: given an MES outcome, it may be possible to expand it by adding new projects without violating the budget constraint. To complete the outcome, the approach currently used in practice is as follows: given an instance with budget $b$, one searches for a budget $b'\ge b$ such that when MES is executed with budget $b'$, it produces a maximal feasible solution for $b$. The search is greedy, i.e., one has to execute MES from scratch for each value of $b'$. To avoid redundant computation, we introduce a variant of MES, which we call Adaptive Method of Equal Shares (AMES). Our method is budget-adaptive, in the sense that, given an outcome $W$ for a budget $b$ and a new budget $b'>b$, it can compute the outcome $W'$ for budget $b'$ by leveraging similarities between $W$ and $W'$. This eliminates the need to recompute solutions from scratch when increasing virtual budgets. Furthermore, AMES satisfies EJR in a certifiable way: given the output of our method, one can check in time $O(n\log n+mn)$ that it provides EJR (here, $n$ is the number of voters and $m$ is the number of projects). We evaluate the potential of AMES on real-world PB data, showing that small increases in budget typically require only minor modifications of the outcome.

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arXiv2023

On weakly and strongly popular rankings

Van Zuylen et al. [35] introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking of all candidates. A popular ranking $π$ of the candidates is at least as good as any other ranking $σ$ in the following sense: if we compare $π$ to $σ$, at least half of all voters will always weakly prefer $π$. Whether a voter prefers one ranking to another is calculated based on the Kendall distance. A more traditional definition of popularity -- as applied to popular matchings, a well-established topic in computational social choice -- is stricter, because it requires at least half of the voters who are not indifferent between $π$ and $σ$ to prefer $π$. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results in [35]. We also point out connections to the famous open problem of finding a Kemeny consensus with three voters.

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arXiv2022

Explaining Preferences by Multiple Patterns in Voters' Behavior

In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree (so that voters' preferences are group-separable). However, sometimes a single axis or a decision tree is insufficient to capture the voters' preferences; rather, there is a small number $k$ of axes or decision trees such that each vote in the profile is consistent with one of these axes (resp., trees). In this work, we study the complexity of deciding whether voters' preferences can be explained in this manner. For $k=2$, we use the technique developed by Yang~[2020] in the context of single-peaked preferences to obtain a polynomial-time algorithm for several domains: value-restricted preferences, group-separable preferences, and a natural subdomain of group-separable preferences, namely, caterpillar group-separable preferences. For $k\ge 3$, the problem is known to be hard for single-peaked preferences; we show that this is also the case for value-restricted and group-separable preferences. Our positive results for $k=2$ make use of forbidden minor characterizations of the respective domains; in particular, we establish that the domain of caterpillar group-separable preferences admits a forbidden minor characterization.

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