arXiv subjects

Daniel Halpern

Publications and source records attributed to Daniel Halpern.

At least 19 recordsLinked to original sources

arXiv2026

AI Alignment From Social Choice Perspectives

Alignment from human feedback uses human judgments about model outputs to steer the behavior of language models after pretraining. When those judgments reflect conflicting views of desirable behavior, the learned objective becomes an aggregate determination of what the model should prefer. We survey recent work that has studied this aggregation problem through the lens of social choice theory. We illustrate how the social choice perspective helps identify failure modes in the feedback aggregation layer and reveals a broader design space for handling disagreement in explicit and principled ways.

cs.AI↗

arXiv2026

Linear Social Choice with Few Queries: A Moment-Based Approach

Most social choice rules assume access to full rankings, while current alignment practice -- despite aiming for diversity -- typically treats voters as anonymous and comparisons as independent, effectively extracting only about one bit per voter. Motivated by this gap, we study social choice under an extreme communication budget in the linear social choice model, where each voter's utility is the inner product between a latent voter type and the embedding of the context and candidate. The candidate and voter spaces may be very large or even infinite. Our core idea is to model the electorate as an unknown distribution over voter types and to recover its moments as informative summary statistics for candidate selection. We show that one pairwise comparison per voter already suffices to select a candidate that maximizes social welfare, but this elicitation cannot identify the second moment and therefore cannot support objectives that account for inequality. We prove that two pairwise comparisons per voter, or alternatively a single graded comparison, identify the second moment; moreover, these richer queries suffice to identify all moments, and hence the entire voter-type distribution. These results enable principled solutions to a range of social choice objectives including inequality-aware welfare criteria such as taking into account the spread of voter utilities and choosing a representative subset.

cs.GT↗

arXiv2026

Fair Division Under Inaccurate Preferences

The fair allocation of scarce resources is a central problem in mathematics, computer science, operations research, and economics. While much of the fair-division literature assumes that individuals have underlying cardinal preferences, eliciting exact numerical values is often cognitively burdensome and prone to inaccuracies. A growing body of work in fair division addresses this challenge by assuming access only to ordinal preferences. However, the restricted expressiveness of ordinal preferences makes it challenging to quantify and optimize cardinal fairness objectives such as envy. In this paper, we explore the broad landscape of fair division of indivisible items given inaccurate cardinal preferences, with a focus on minimizing envy. We consider various settings based on whether the true preferences of the agents are stochastic or worst-case, and whether the inaccuracies, modeled as additive noise, are stochastic or worst-case. When the true preferences are stochastic, we show that envy-free allocations can be computed with high probability; this is achieved both in the setting with stochastic and worst-case noise. This generalizes a notable result in stochastic fair division, which establishes a similar guarantee, albeit in the absence of any noise. When the true preferences are worst-case, and the noise is bounded, we analyze the maximum envy achieved by the Round-Robin algorithm. This bound is shown to be tight for deterministic algorithms, and applications of this bound are provided. Lastly, we consider a setting with worst-case preferences and noise, where the true preferences for each item are revealed upon its allocation. Here, we give an efficient online algorithm that guarantees logarithmic maximum envy with high probability. This result generalizes a known result from algorithmic discrepancy to a setting with noisy input data.

cs.GT↗

arXiv2026

Robust AI Evaluation through Maximal Lotteries

The standard way to evaluate language models on subjective tasks is through pairwise comparisons: an annotator chooses the "better" of two responses to a prompt. Leaderboards aggregate these comparisons into a single Bradley-Terry (BT) ranking, forcing heterogeneous preferences into a total order and violating basic social-choice desiderata. In contrast, social choice theory provides an alternative approach called maximal lotteries, which aggregates pairwise preferences without imposing any assumptions on their structure. However, we show that maximal lotteries are highly sensitive to preference heterogeneity and can favor models that severely underperform on specific tasks or user subpopulations. We introduce robust lotteries that optimize worst-case performance under plausible shifts in the preference data. On large-scale preference datasets, robust lotteries provide more reliable win rate guarantees across the annotator distribution and recover a stable set of top-performing models. By moving from rankings to pluralistic sets of winners, robust lotteries offer a principled step toward an ecosystem of complementary AI systems that serve the full spectrum of human preferences.

cs.LG↗

arXiv2026

Truthful Fair Division under Stochastic Valuations

We study no-money mechanisms for allocating indivisible items to strategic agents with additive preferences under a stochastic model. In this model, items' values are drawn from an underlying distribution and mechanisms are evaluated with respect to this draw (e.g., in expectation, or with high probability). Motivated by worst-case impossibilities which show that truthfulness severely restricts fairness and efficiency, we ask whether truthful mechanisms continue to perform poorly on random instances. We first focus on dominant-strategy incentive compatible (DSIC) mechanisms. For two agents, we obtain a tight picture. Specifically, we show that there exists a distribution under which no DSIC mechanism achieves an expected welfare approximation better than $\frac{2+\sqrt{2}}{4}\approx 0.854$, and we give a DSIC mechanism that matches this bound for all distributions simultaneously. We further show that, for every distribution, there exists a DSIC mechanism that is envy-free with high probability and obtains the same welfare. A key ingredient is a new, tight connection between welfare guarantees of a family of DSIC, no-money mechanisms and i.i.d.\ prophet inequalities. This connection allows us to generalize to $n$ agents; in particular, we obtain a DSIC mechanism that achieves a $\approx 0.745$ approximation to welfare, and another DSIC mechanism achieving a $1/2$-approximation welfare that is envy-free with high probability. We then turn to Bayesian incentive compatibility (BIC). Under i.i.d.\ valuations, we show that BIC comes at essentially no cost: we design a prior-independent BIC mechanism that achieves a $(1-\varepsilon)$-approximation to the optimal welfare, while being envy-free with high probability. Under independent but non-identical priors, we obtain BIC mechanisms that are $(1-\varepsilon)$-approximately Pareto efficient and envy-free with high probability.

cs.GT↗

arXiv2025

Pairwise Calibrated Rewards for Pluralistic Alignment

Current alignment pipelines presume a single, universal notion of desirable behavior. However, human preferences often diverge across users, contexts, and cultures. As a result, disagreement collapses into the majority signal and minority perspectives are discounted. To address this, we propose reflecting diverse human preferences through a distribution over multiple reward functions, each inducing a distinct aligned policy. The distribution is learned directly from pairwise preference without annotator identifiers or predefined groups. Instead, annotator disagreements are treated as informative soft labels. Our central criterion is pairwise calibration: for every pair of candidate responses, the proportion of reward functions preferring one response matches the fraction of annotators with that preference. We prove that even a small outlier-free ensemble can accurately represent diverse preference distributions. Empirically, we introduce and validate a practical training heuristic to learn such ensembles, and demonstrate its effectiveness through improved calibration, implying a more faithful representation of pluralistic values.

cs.LG↗

arXiv2025

The Proportional Veto Principle for Approval Ballots

The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for approval ballots, which we call flexible-voter representation (FVR). We show that while the approval voting rule and other natural scoring rules provide the optimal FVR guarantee only for some flexibility threshold, there exists a scoring rule that is FVR-optimal for all thresholds simultaneously. We also extend our results to multi-winner voting.

cs.GT↗

arXiv2025

Online Envy Minimization and Multicolor Discrepancy: Equivalences and Separations

We consider the fundamental problem of allocating $T$ indivisible items that arrive over time to $n$ agents with additive preferences, with the goal of minimizing envy. This problem is tightly connected to online multicolor discrepancy: vectors $v_1, \dots, v_T \in \mathbb{R}^d$ with $\| v_i \|_2 \leq 1$ arrive over time and must be, immediately and irrevocably, assigned to one of $n$ colors to minimize $\max_{i,j \in [n]} \| \sum_{v \in S_i} v - \sum_{v \in S_j} v \|_{\infty}$ at each step, where $S_\ell$ is the set of vectors that are assigned color $\ell$. The special case of $n = 2$ is called online vector balancing. Any bound for multicolor discrepancy implies the same bound for envy minimization. Against an adaptive adversary, both problems have the same optimal bound, $\Theta(\sqrt{T})$, but whether this holds for weaker adversaries is unknown. Against an oblivious adversary, Alweiss et al. give a $O(\log T)$ bound, with high probability, for multicolor discrepancy. Kulkarni et al. improve this to $O(\sqrt{\log T})$ for vector balancing and give a matching lower bound. Whether a $O(\sqrt{\log T})$ bound holds for multicolor discrepancy remains open. These results imply the best-known upper bounds for envy minimization (for an oblivious adversary) for $n$ and two agents, respectively; whether better bounds exist is open. In this paper, we resolve all aforementioned open problems. We prove that online envy minimization and multicolor discrepancy are equivalent against an oblivious adversary: we give a $O(\sqrt{\log T})$ upper bound for multicolor discrepancy, and a $\Omega(\sqrt{\log T})$ lower bound for envy minimization. For a weaker, i.i.d. adversary, we prove a separation: For online vector balancing, we give a $\Omega\left(\sqrt{\frac{\log T}{\log \log T}}\right)$ lower bound, while for envy minimization, we give an algorithm that guarantees a constant upper bound.

cs.GT↗

arXiv2024

Federated Assemblies

A citizens' assembly is a group of people who are randomly selected to represent a larger population in a deliberation. While this approach has successfully strengthened democracy, it has certain limitations that suggest the need for assemblies to form and associate more organically. In response, we propose federated assemblies, where assemblies are interconnected, and each parent assembly is selected from members of its child assemblies. The main technical challenge is to develop random selection algorithms that meet new representation constraints inherent in this hierarchical structure. We design and analyze several algorithms that provide different representation guarantees under various assumptions on the structure of the underlying graph.

cs.GT↗

arXiv2024

Axioms for AI Alignment from Human Feedback

In the context of reinforcement learning from human feedback (RLHF), the reward function is generally derived from maximum likelihood estimation of a random utility model based on pairwise comparisons made by humans. The problem of learning a reward function is one of preference aggregation that, we argue, largely falls within the scope of social choice theory. From this perspective, we can evaluate different aggregation methods via established axioms, examining whether these methods meet or fail well-known standards. We demonstrate that both the Bradley-Terry-Luce Model and its broad generalizations fail to meet basic axioms. In response, we develop novel rules for learning reward functions with strong axiomatic guarantees. A key innovation from the standpoint of social choice is that our problem has a linear structure, which greatly restricts the space of feasible rules and leads to a new paradigm that we call linear social choice.

cs.GT↗

arXiv2024

Computing Voting Rules with Elicited Incomplete Votes

Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on specific instances of this problem, our paper fully characterizes the set of positional scoring rules that can be computed for any $1 \leq t < m$, which, notably, does not include plurality. We then extend this to show a similar impossibility result for single transferable vote (elimination voting). These negative results are information-theoretic and agnostic to the number of queries. Finally, for scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries a deterministic or randomized algorithm must make to determine the score-maximizing candidate. While there is no gap between our bounds for deterministic algorithms, identifying the exact query complexity for randomized algorithms is a challenging open problem, of which we solve one special case.

cs.GT↗

arXiv2023

On the Existence of Envy-Free Allocations Beyond Additive Valuations

We study the problem of fairly allocating $m$ indivisible items among $n$ agents. Envy-free allocations, in which each agent prefers her bundle to the bundle of every other agent, need not exist in the worst case. However, when agents have additive preferences and the value $v_{i,j}$ of agent $i$ for item $j$ is drawn independently from a distribution $D_i$, envy-free allocations exist with high probability when $m \in \Omega( n \log n / \log \log n )$. In this paper, we study the existence of envy-free allocations under stochastic valuations far beyond the additive setting. We introduce a new stochastic model in which each agent's valuation is sampled by first fixing a worst-case function, and then drawing a uniformly random renaming of the items, independently for each agent. This strictly generalizes known settings; for example, $v_{i,j} \sim D_i$ may be seen as picking a random (instead of a worst-case) additive function before renaming. We prove that random renaming is sufficient to ensure that envy-free allocations exist with high probability in very general settings. When valuations are non-negative and ``order-consistent,'' a valuation class that generalizes additive, budget-additive, unit-demand, and single-minded agents, SD-envy-free allocations (a stronger notion of fairness than envy-freeness) exist for $m \in \omega(n^2)$ when $n$ divides $m$, and SD-EFX allocations exist for all $m \in \omega(n^2)$. The dependence on $n$ is tight, that is, for $m \in O(n^2)$ envy-free allocations don't exist with constant probability. For the case of arbitrary valuations (allowing non-monotone, negative, or mixed-manna valuations) and $n=2$ agents, we prove envy-free allocations exist with probability $1 - \Theta(1/m)$ (and this is tight).

cs.GT↗

arXiv2023

Optimal Engagement-Diversity Tradeoffs in Social Media

Social media platforms are known to optimize user engagement with the help of algorithms. It is widely understood that this practice gives rise to echo chambers\emdash users are mainly exposed to opinions that are similar to their own. In this paper, we ask whether echo chambers are an inevitable result of high engagement; we address this question in a novel model. Our main theoretical results establish bounds on the maximum engagement achievable under a diversity constraint, for suitable measures of engagement and diversity; we can therefore quantify the worst-case tradeoff between these two objectives. Our empirical results, based on real data from Twitter, chart the Pareto frontier of the engagement-diversity tradeoff.

cs.SI↗

arXiv2022

Representation with Incomplete Votes

Platforms for online civic participation rely heavily on methods for condensing thousands of comments into a relevant handful, based on whether participants agree or disagree with them. These methods should guarantee fair representation of the participants, as their outcomes may affect the health of the conversation and inform impactful downstream decisions. To that end, we draw on the literature on approval-based committee elections. Our setting is novel in that the approval votes are incomplete since participants will typically not vote on all comments. We prove that this complication renders non-adaptive algorithms impractical in terms of the amount of information they must gather. Therefore, we develop an adaptive algorithm that uses information more efficiently by presenting incoming participants with statements that appear promising based on votes by previous participants. We prove that this method satisfies commonly used notions of fair representation, even when participants only vote on a small fraction of comments. Finally, an empirical evaluation using real data shows that the proposed algorithm provides representative outcomes in practice.

cs.GT↗

arXiv2022

Smoothed Analysis of Social Choice, Revisited

A canonical problem in social choice is how to aggregate ranked votes: given $n$ voters' rankings over $m$ candidates, what voting rule $f$ should we use to aggregate these votes into a single winner? One standard method for comparing voting rules is by their satisfaction of axioms - properties that we want a "reasonable" rule to satisfy. Unfortunately, this approach leads to several impossibilities: no voting rule can simultaneously satisfy all the properties we want, at least in the worst case over all possible inputs. Motivated by this, we consider a relaxation of these worst case requirements. We do so using a "smoothed" model of social choice, where votes are perturbed with small amounts of noise. If, no matter which input profile we start with, the probability (post-noise) of an axiom being satisfied is large, we will consider the axiom as good as satisfied - called "smoothed-satisfied" - even if it may be violated in the worst case. Our model is a mild restriction of Lirong Xia's, and corresponds closely to that in Spielman and Teng's original work on smoothed analysis. Much work has been done so far in several papers by Xia on axiom satisfaction under such noise. In our paper, we aim to give a more cohesive overview on when smoothed analysis of social choice is useful. Within our model, we give simple sufficient conditions for smoothed-satisfaction or smoothed-violation of several previously-unstudied axioms and paradoxes, plus many of those studied by Xia. We then observe that, in a practically important subclass of noise models, although convergence eventually occurs, known rates may require an extremely large number of voters. Motivated by this, we prove bounds specifically within a canonical noise model from this subclass - the Mallows model. Here, we present a more nuanced picture on exactly when smoothed analysis can help.

cs.GT↗

arXiv2021

Tracking Truth with Liquid Democracy

The dynamics of random transitive delegations on a graph are of particular interest when viewed through the lens of an emerging voting paradigm, liquid democracy. This paradigm allows voters to choose between directly voting and transitively delegating their votes to other voters, so that those selected cast a vote weighted by the number of delegations they received. In the epistemic setting, where voters decide on a binary issue for which there is a ground truth, previous work showed that a few voters may amass such a large amount of influence that liquid democracy is less likely to identify the ground truth than direct voting. We quantify the amount of permissible concentration of power and examine more realistic delegation models, showing they behave well by ensuring that (with high probability) there is a permissible limit on the maximum number of delegations received. Our theoretical results demonstrate that the delegation process is similar to well-known processes on random graphs that are sufficiently bounded for our purposes. Along the way, we prove new bounds on the size of the largest component in an infinite P\'olya urn process, which may be of independent interest. In addition, we empirically validate the theoretical results, running six experiments (for a total of $N=168$ participants, $62$ delegation graphs and over $11k$ votes collected). We find that empirical delegation behaviors meet the conditions for our positive theoretical guarantees. Overall, our work alleviates concerns raised about liquid democracy and bolsters the case for the applicability of this emerging paradigm.

cs.DM↗

arXiv2021

The Optimal Size of an Epistemic Congress

We analyze the optimal size of a congress in a representative democracy. We take an epistemic view where voters decide on a binary issue with one ground truth outcome, and each voter votes correctly according to their competence levels in $[0, 1]$. Assuming that we can sample the best experts to form an epistemic congress, we find that the optimal congress size should be linear in the population size. This result is striking because it holds even when allowing the top representatives to be accurate with arbitrarily high probabilities. We then analyze real world data, finding that the actual sizes of congresses are much smaller than the optimal size our theoretical results suggest. We conclude by analyzing under what conditions congresses of sub-optimal sizes would still outperform direct democracy, in which all voters vote.

cs.AI↗

arXiv2021

Can Buyers Reveal for a Better Deal?

We study market interactions in which buyers are allowed to credibly reveal partial information about their types to the seller. Previous recent work has studied the special case of one buyer and one good, showing that such communication can simultaneously improve social welfare and ex ante buyer utility. However, with multiple buyers, we find that the buyer-optimal signalling schemes from the one-buyer case are actually harmful to buyer welfare. Moreover, we prove several impossibility results showing that, with either multiple i.i.d. buyers or multiple i.i.d. goods, maximizing buyer utility can be at odds with social efficiency, which is surprising in contrast with the one-buyer, one-good case. Finally, we investigate the computational tractability of implementing desirable equilibrium outcomes. We find that, even with one buyer and one good, optimizing buyer utility is generally NP-hard but tractable in a practical restricted setting.

cs.GT↗