Bailey Flanigan

Chris Hays, Rachel Li, Bailey Flanigan et al.

AI arenas, which rank generative models from pairwise preferences of users, are a popular method for measuring the relative performance of models in the course of their organic use. Because rankings are computed from noisy preferences, there is a concern that model producers can exploit this randomness by submitting many models (e.g., multiple variants of essentially the same model) and thereby artificially improve the rank of their top models. This can lead to degradations in the quality, and therefore the usefulness, of the ranking. In this paper, we begin by establishing, both theoretically and in simulations calibrated to data from the platform Arena (formerly LMArena, Chatbot Arena), conditions under which producers can benefit from submitting clones when their goal is to be ranked highly. We then propose a new mechanism for ranking models from pairwise comparisons, called You-Rank-We-Rank (YRWR). It requires that producers submit rankings over their own models and uses these rankings to correct statistical estimates of model quality. We prove that this mechanism is approximately clone-robust, in the sense that a producer cannot improve their rank much by doing anything other than submitting each of their unique models exactly once. Moreover, to the extent that model producers are able to correctly rank their own models, YRWR improves overall ranking accuracy. In further simulations, we show that indeed the mechanism is approximately clone-robust and quantify improvements to ranking accuracy, even under producer misranking.

Angelos Assos, Carmel Baharav, Bailey Flanigan et al.

Citizens' assemblies are an increasingly influential form of deliberative democracy, where randomly selected people discuss policy questions. The legitimacy of these assemblies hinges on their representation of the broader population, but participant dropout often leads to an unbalanced composition. In practice, dropouts are replaced by preselected alternates, but existing methods do not address how to choose these alternates. To address this gap, we introduce an optimization framework for alternate selection. Our algorithmic approach, which leverages learning-theoretic machinery, estimates dropout probabilities using historical data and selects alternates to minimize expected misrepresentation. Our theoretical bounds provide guarantees on sample complexity (with implications for computational efficiency) and on loss due to dropout probability mis-estimation. Empirical evaluation using real-world data demonstrates that, compared to the status quo, our method significantly improves representation while requiring fewer alternates.

Carmel Baharav, Bailey Flanigan

Sortition, the random selection of political representatives, is increasingly being used around the world to choose participants of deliberative processes like Citizens' Assemblies. Motivated by sortition's practical importance, there has been a recent flurry of research on sortition algorithms, whose task it is to select a panel from among a pool of volunteers. This panel must satisfy quotas enforcing representation of key population subgroups. Past work has contributed an algorithmic approach for fulfilling this task while ensuring that volunteers' chances of selection are maximally equal, as measured by any convex equality objective. The question, then, is: which equality objective is the right one? Past work has mainly studied the objectives Minimax and Leximin, which respectively minimize the maximum and maximize the minimum chance of selection given to any volunteer. Recent work showed that both of these objectives have key weaknesses: Minimax is highly robust to manipulation but is arbitrarily unfair; oppositely, Leximin is highly fair but arbitrarily manipulable. In light of this gap, we propose a new equality objective, Goldilocks, that aims to achieve these ideals simultaneously by ensuring that no volunteer receives too little or too much chance of selection. We theoretically bound the extent to which Goldilocks achieves these ideals, finding that in an important sense, Goldilocks recovers among the best available solutions in a given instance. We then extend our bounds to the case where the output of Goldilocks is transformed to achieve a third goal, Transparency. Our empirical analysis of Goldilocks in real data is even more promising: we find that this objective achieves nearly instance-optimal minimum and maximum selection probabilities simultaneously in most real instances -- an outcome not even guaranteed to be possible for any algorithm.