Recent research on instant runoff voting (IRV) shows that it exhibits a striking property over unimodal one-dimensional preferences: there is an exclusion zone around the median voter such that the winner must come from the exclusion zone, unless no such candidate exists. Thus, IRV cannot elect an extreme candidate in this setting as long as a sufficiently moderate candidate runs. In this work, we examine the mathematical structure of exclusion zones as a broad phenomenon in more general preference spaces. We prove that with voters uniformly distributed over any d-dimensional hyperrectangle (for d > 1), IRV has no such exclusion zone. However, we also show that IRV exclusion zones are not solely a one-dimensional phenomenon. For irregular higher-dimensional preference spaces with fewer symmetries than hyperrectangles, IRV can have nontrivial exclusion zones. As a further exploration, we study IRV exclusion zones with graph-based preferences, where nodes represent voters who prefer candidates closer to them in the graph. Here, we show that IRV exclusion zones present a surprising computational challenge: even checking whether a given set of positions is an IRV exclusion zone is NP-hard. We develop an efficient randomized approximation algorithm for checking and finding exclusion zones in graphs. Finally, we report on computational experiments with exclusion zones: (i) performing an exhaustive computer search of small graphs and trees, we find nontrivial IRV exclusion zones in most small graphs; and (ii) applying our approximation algorithm to a collection of larger real-world school friendship networks, we find that about 60% of these networks have probable nontrivial IRV exclusion zones. While our focus is on IRV, the properties of exclusion zones we establish provide new methods for analyzing voting systems in metric spaces more generally.

Academic publishing requires solving a collective coordination problem: among thousands of possible publication venues, which deserve a community's attention? A clear consensus helps scholars allocate attention, match submissions to appropriate outlets, and evaluate scholars for hiring and promotion. Yet preferences are not centrally coordinated--they emerge within each field over time. Here we ask whether all fields have arrived at similar solutions to this coordination problem, and whether preferences vary systematically with individual characteristics. Using an adaptive survey of 3,510 US tenure-track faculty yielding 163,002 pairwise comparisons across 8,044 venues, we show that fields occupy a wide spectrum of coordination. Economics, Chemistry, and Physics exhibit strong consensus, with respondents agreeing on elite venues and accurately predicting one another's choices. Computer Science and Engineering show fragmented preferences distributed across hundreds of outlets with minimal overlap. Within fields, preferences correlate with institutional prestige--faculty at elite institutions prefer higher-ranked venues--and with gender, as men prefer higher-ranked venues than women even after accounting for prestige and career stage. Scholars realize their personal preferences more successfully than their respective fields' consensus preferences, indicating that heterogeneity, not just selective hierarchy, shapes publishing outcomes. Journal Impact Factors explain only 64% of preference choices, systematically undervaluing what fields actually prefer. These results quantify how publication preferences vary across the structural diversity of academic fields.

A wide range of graph embedding objectives decompose into two components: one that enforces similarity, attracting the embeddings of nodes that are perceived as similar, and another that enforces dissimilarity, repelling the embeddings of nodes that are perceived as dissimilar. Without repulsion, the embeddings would collapse into trivial solutions. Skip-Gram Negative Sampling (SGNS) is a popular and efficient repulsion approach that prevents collapse by repelling each node from a sample of dissimilar nodes. In this work, we show that when repulsion is most needed and the embeddings approach collapse, SGNS node-wise repulsion is, in the aggregate, an approximate re-centering of the node embedding dimensions. Such dimension operations are more scalable than node operations and produce a simpler geometric interpretation of the repulsion. Our theoretical result establishes dimension regularization as an effective and more efficient, compared to skip-gram node contrast, approach to enforcing dissimilarity among embeddings of nodes. We use this result to propose a flexible algorithm augmentation framework that improves the scalability of any existing algorithm using SGNS. The framework prioritizes node attraction and replaces SGNS with dimension regularization. We instantiate this generic framework for LINE and node2vec and show that the augmented algorithms preserve downstream link-prediction performance while reducing GPU memory usage by up to 33.3% and training time by 23.4%. Moreover, we show that completely removing repulsion (a special case of our augmentation framework) in LINE reduces training time by 70.9% on average, while increasing link prediction performance, especially for graphs that are globally sparse but locally dense. Global sparsity slows down dimensional collapse, while local density ensures that node attraction brings the nodes near their neighbors. In general, however, repulsion is needed, and dimension regularization provides an efficient alternative to SGNS.

A popular method for variance reduction in observational causal inference is propensity-based trimming, the practice of removing units with extreme propensities from the sample. This practice has theoretical grounding when the data are homoscedastic and the propensity model is parametric (Yang and Ding, 2018; Crump et al. 2009), but in modern settings where heteroscedastic data are analyzed with non-parametric models, existing theory fails to support current practice. In this work, we address this challenge by developing new methods and theory for sample trimming. Our contributions are three-fold: first, we describe novel procedures for selecting which units to trim. Our procedures differ from previous work in that we trim not only units with small propensities, but also units with extreme conditional variances. Second, we give new theoretical guarantees for inference after trimming. In particular, we show how to perform inference on the trimmed subpopulation without requiring that our regressions converge at parametric rates. Instead, we make only fourth-root rate assumptions like those in the double machine learning literature. This result applies to conventional propensity-based trimming as well and thus may be of independent interest. Finally, we propose a bootstrap-based method for constructing simultaneously valid confidence intervals for multiple trimmed sub-populations, which are valuable for navigating the trade-off between sample size and variance reduction inherent in trimming. We validate our methods in simulation, on the 2007-2008 National Health and Nutrition Examination Survey, and on a semi-synthetic Medicare dataset and find promising results in all settings.

Data recording connections between people in communities and villages are collected and analyzed in various ways, most often as either networks of individuals or as networks of households. These two networks can differ in substantial ways. The methodological choice of which network to study, therefore, is an important aspect in both study design and data analysis. In this work, we consider various key differences between household and individual social network structure, and ways in which the networks cannot be used interchangeably. In addition to formalizing the choices for representing each network, we explore the consequences of how the results of social network analysis change depending on the choice between studying the individual and household network – from determining whether networks are assortative or disassortative to the ranking of influence-maximizing nodes. As our main contribution, we draw upon related work to propose a set of systematic recommendations for determining the relevant network representation to study. Our recommendations include assessing a series of entitativity criteria and relating these criteria to theories and observations about patterns and norms in social dynamics at the household level: notably, how information spreads within households and how power structures and gender roles affect this spread. We draw upon the definition of an illusion of entitativity to identify cases wherein grouping people into households does not satisfy these criteria or adequately represent given cultural or experimental contexts. Given the widespread use of social network data for studying communities, there is broad impact in understanding which network to study and the consequences of that decision. We hope that this work gives guidance to practitioners and researchers collecting and studying social network data.

A core tension in the study of plurality elections is the clash between the classic Hotelling-Downs model, which predicts that two office-seeking candidates should cater to the median voter, and the empirical observation that democracies often have two major parties with divergent policies. Motivated in part by this tension, we introduce a dynamic model of candidate positioning based on a simple bounded rationality heuristic: candidates imitate the policy of previous winners. The resulting model is closely connected to evolutionary replicator dynamics. For uniformly-distributed voters, we prove in our model that with k = 2, 3, or 4 candidates per election, any symmetric candidate distribution converges over time to the center. With k ≥ 5 candidates per election, however, we prove that the candidate distribution does not converge to the center and provide an even stronger non-convergence result in a special case with no extreme candidates. Our conclusions are qualitatively unchanged if a small fraction of candidates are not winner-copiers and are instead positioned uniformly at random in each election. Beyond our theoretical analysis, we illustrate our results in extensive simulations; for five or more candidates, we find a tendency towards the emergence of two clusters, a mechanism suggestive of Duverger's Law, the empirical finding that plurality leads to two-party systems. Our simulations also explore several variations of the model, where we find the same general pattern: convergence to the center with four or fewer candidates, but not with five or more. Finally, we discuss the relationship between our replicator dynamics model and prior work on strategic equilibria of candidate positioning games.

On Sinkhorn’s Algorithm and Choice Modeling Choice modeling is an important topic that underlies a wide range of applications involving human decision making, and it traces its roots to the 1920s. Matrix balancing has an equally long history and wide applicability (e.g., in transportation and mobility networks). Recently, its celebrated Sinkhorn’s algorithm has been instrumental in the efficient approximation of optimal transport distances. However, the two topics have largely developed independently. In “On Sinkhorn’s Algorithm and Choice Modeling,” Qu, Galichon, Gao, and Ugander establish extensive connections between a class of Luce choice models and a common matrix-balancing problem. They leverage these connections to resolve open problems on the convergence of Sinkhorn’s algorithm for nonnegative matrices, characterizing its global linear convergence rate in terms of the algebraic connectivity and deriving the sharp asymptotic rate. The connections established in this paper between two seemingly unrelated topics help the transmission of ideas and lead to further interesting results.

The value alignment of sociotechnical systems has become a central debate, but progress depends on how human values are perceived in the content these systems surface and how such perceptions can be measured at scale. Social media platforms are a prominent class of sociotechnical systems where algorithmic curation shapes exposure to value-laden content at scale. Large-language models offer new opportunities for measuring expressions of human values (e.g., humility or equality) in social media data, but value expressions can be subjective: different people will annotate the same post with different values. In this paper, we draw on the Schwartz value system as a broadly encompassing and theoretically grounded set of basic human values, and introduce a framework to personalize the measurement of expressions of Schwartz values in social media posts at scale. We collect 32,370 ground truth value expression annotations from N=1,079 people on 5,211 social media posts representative of real users' feeds. Due to the subjectivity of the task, we observe low levels of inter-rater agreement between people, and low agreement between human raters and LLM-based methods. In response, we construct a personalization architecture for classifying value expressions by learning from a small number of highly informative calibration annotations per user. In evaluation, we find that modeling these differences successfully yields value expression predictions that people agree with more than they agree with other people. These results contribute new methods and understanding for the measurement of human values in social media data.

Social networks scaffold the diffusion of information on social media. Much attention has been given to the spread of true vs. false content on online social platforms, including the structural differences between their diffusion patterns. However, much less is known about how platform interventions on false content alter the engagement with and diffusion of such content. In this work, we estimate the causal effects of Community Notes, a novel fact-checking feature adopted by X (formerly Twitter) to solicit and vet crowd-sourced fact-checking notes for false content. We gather detailed time series data for 40,078 posts for which notes have been proposed and use synthetic control methods to estimate a range of counterfactual outcomes. We find that attaching fact-checking notes significantly reduces the engagement with and diffusion of false content. We estimate that, on average, the notes resulted in reductions of 46.1% in reposts, 44.1% in likes, 21.9% in replies, and 13.5% in views after being attached. Over the posts' entire lifespans, these reductions amount to 11.6% fewer reposts, 13.3% fewer likes, 6.9% fewer replies, and 5.5% fewer views on average. In reducing reposts, we observe that diffusion cascades for fact-checked content are less deep and less "viral," but not less broad, than synthetic control estimates for non-fact-checked content with similar reach. This structural difference contrasts notably with differences between false vs. true content diffusion itself, where false information diffuses farther, but with structural patterns that are otherwise indistinguishable from those of true information, conditional on reach.

In many contexts involving ranked preferences, agents submit partial orders over available alternatives. Statistical models often treat these as marginal in the space of total orders, but this approach overlooks information contained in the list length itself. In this work, we introduce and taxonomize approaches for jointly modeling distributions over top-k partial orders and list lengths k, considering two classes of approaches: composite models that view a partial order as a truncation of a total order, and augmented ranking models that model the construction of the list as a sequence of choice decisions, including the decision to stop. For composite models, we consider three dependency structures for joint modeling of order and truncation length. For augmented ranking models, we consider different assumptions on how the stop-token choice is modeled. Using data consisting of partial rankings from San Francisco school choice and San Francisco ranked choice elections, we evaluate how well the models predict observed data and generate realistic synthetic datasets. We find that composite models, explicitly modeling length as a categorical variable, produce synthetic datasets with accurate length distributions, and an augmented model with position-dependent item utilities jointly models length and preferences in the training data best, as measured by negative log loss. Methods from this work have significant implications on the simulation and evaluation of real-world social systems that solicit ranked preferences.

When people are asked to recall their social networks, theoretical and empirical work tells us that they rely on shortcuts, or heuristics. Cognitive social structures (CSSs) are multilayer social networks where each layer corresponds to an individual's perception of the network. With multiple perceptions of the same network, CSSs contain rich information about how these heuristics manifest, motivating the question, Can we identify people who share the same heuristics? In this work, we propose a method for identifying cognitive structure across multiple network perceptions, analogous to how community detection aims to identify social structure in a network. To simultaneously model the joint latent social and cognitive structure, we study CSSs as three-dimensional tensors, employing low-rank nonnegative Tucker decompositions (NNTuck) to approximate the CSS-a procedure closely related to estimating a multilayer stochastic block model (SBM) from such data. We propose the resulting latent cognitive space as an operationalization of the sociological theory of social cognition by identifying individuals who share relational schema. In addition to modeling cognitively independent, dependent, and redundant networks, we propose a specific model instance and related statistical test for testing when there is social-cognitive agreement in a network: when the social and cognitive structures are equivalent. We use our approach to analyze four different CSSs and give insights into the latent cognitive structures of those networks.

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn’s algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF’s parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.

Multilayer networks describe the rich ways in which nodes are related by accounting for different relationships in separate layers. These multiple relationships are naturally represented by an adjacency tensor. In this work we study the use of the nonnegative Tucker decomposition (NNTuck) of such tensors under a KL loss as an expressive factor model that naturally generalizes existing stochastic block models of multilayer networks. Quantifying interdependencies between layers can identify redundancies in the structure of a network, indicate relationships between disparate layers, and potentially inform survey instruments for collecting social network data. We propose definitions of layer independence, dependence, and redundancy based on likelihood ratio tests between nested nonnegative Tucker decompositions. Using both synthetic and real-world data, we evaluate the use and interpretation of the NNTuck as a model of multilayer networks. Algorithmically, we show that using expectation maximization (EM) to maximize the log-likelihood under the NNTuck is step-by-step equivalent to tensorial multiplicative updates for the NNTuck under a KL loss, extending a previously known equivalence from nonnegative matrices to nonnegative tensors.

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

Off-policy evaluation (OPE) is the problem of estimating the value of a target policy using historical data collected under a different logging policy. OPE methods typically assume overlap between the target and logging policy, enabling solutions based on importance weighting and/or imputation. In this work, we approach OPE without assuming either overlap or a well-specified model by considering a strategy based on partial identification under non-parametric assumptions on the conditional mean function, focusing especially on Lipschitz smoothness. Under such smoothness assumptions, we formulate a pair of linear programs whose optimal values upper and lower bound the contributions of the no-overlap region to the off-policy value. We show that these linear programs have a concise closed form solution that can be computed efficiently and that their solutions converge, under the Lipschitz assumption, to the sharp partial identification bounds on the off-policy value. Furthermore, we show that the rate of convergence is minimax optimal, up to log factors. We deploy our methods on two semi-synthetic examples, and obtain informative and valid bounds that are tighter than those possible without smoothness assumptions.

Variance reduction for causal inference in the presence of network interference is often achieved through either outcome modeling, typically analyzed under unit-randomized Bernoulli designs, or clustered experimental designs, typically analyzed without strong parametric assumptions. In this work, we study the intersection of these two approaches and make the following threefold contributions. First, we present an estimator of the total treatment effect (or global average treatment effect) in low-order outcome models when the data are collected under general experimental designs, generalizing previous results for Bernoulli designs. We refer to this estimator as the pseudoinverse estimator and give bounds on its bias and variance in terms of properties of the experimental design. Second, we evaluate these bounds for the case of Bernoulli graph cluster randomized (GCR) designs. Its variance scales like the smaller of the variance obtained by the estimator derived under a low-order assumption, and the variance obtained from cluster randomization, showing that combining these variance reduction strategies is preferable to using either individually. When the order of the potential outcomes model is correctly specified, our estimator is always unbiased, and under a misspecified model, we upper bound the bias by the closeness of the ground truth model to a low-order model. Third, we give empirical evidence that our variance bounds can be used to select a good clustering that minimizes the worst-case variance under a cluster randomized design from a set of candidate clusterings. Across a range of graphs and clustering algorithms, our method consistently selects clusterings that perform well on a range of response models, suggesting the practical use of our bounds.

Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than single votes. In practice, elections using IRV often restrict the ballot length , the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k — 1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide a construction matching the lower bound for unrestricted voter preferences. Additionally, we characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. We also examine how classic preference restrictions influence our results—for instance, single-peakedness makes k — 1 different winners impossible but still allows at least ω(√ k ). Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

School choice mechanism designers use discrete choice models to understand and predict families' preferences. The most widely-used choice model, the multinomial logit (MNL), is linear in school and/or household attributes. While the model is simple and interpretable, it assumes the ranked preference lists arise from a choice process that is uniform throughout the ranking, from top to bottom. In this work, we introduce two strategies for rank-heterogeneous choice modeling tailored for school choice. First, we adapt a context-dependent random utility model (CDM), considering down-rank choices as occurring in the context of earlier up-rank choices. Second, we consider stratifying the choice modeling by rank, regularizing rank-adjacent models towards one another when appropriate. Using data on household preferences from the San Francisco Unified School District (SFUSD) across multiple years, we show that the contextual models considerably improve our out-of-sample evaluation metrics across all rank positions over the non-contextual models in the literature. Meanwhile, stratifying the model by rank can yield more accurate first-choice predictions while down-rank predictions are relatively unimproved. These models provide performance upgrades that school choice researchers can adopt to improve predictions and counterfactual analyses.

Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used in both Horvitz–Thompson estimators, which normalize by the sample size, and Hájek/self-normalized estimators, which normalize by the sum of the inverse probability weights. In this work, we study a family of IPW estimators, first proposed by Trotter and Tukey in the context of Monte Carlo problems, that are normalized by an affine combination of the sample size and a sum of inverse weights. We show how selecting an estimator from this family in a data-dependent way to minimize asymptotic variance leads to an iterative procedure that converges to an estimator with connections to regression control methods. We refer to such estimators as adaptively normalized estimators. For mean estimation in survey sampling, the adaptively normalized estimator has asymptotic variance that is never worse than the Horvitz–Thompson and Hájek estimators. Going further, we show that adaptive normalization can be used to propose improvements of the augmented IPW (AIPW) estimator, average treatment effect (ATE) estimators, and policy learning objectives. Appealingly, these proposals preserve both the asymptotic efficiency of AIPW and the regret bounds for policy learning with IPW objectives, and deliver consistent finite sample improvements in simulations for all three of mean estimation, ATE estimation, and policy learning.

Many policies in the US are determined locally, e.g., at the county-level. Local policy regimes provide flexibility between regions, but may become less effective in the presence of geographic spillovers, where populations circumvent local restrictions by traveling to less restricted regions nearby. Due to the endogenous nature of policymaking, there have been few opportunities to reliably estimate causal spillover effects or evaluate their impact on local policies. In this work, we identify a novel setting and develop a suitable methodology that allow us to make unconfounded estimates of spillover effects of local policies. Focusing on California’s Blueprint for a Safer Economy, we leverage how county-level mobility restrictions were deterministically set by public COVID-19 severity statistics, enabling a regression discontinuity design framework to estimate spillovers between counties. We estimate these effects using a mobility network with billions of timestamped edges and find significant spillover movement, with larger effects in retail, eating places, and gyms. Contrasting local and global policy regimes, our spillover estimates suggest that county-level restrictions are only 54% as effective as statewide restrictions at reducing mobility. However, an intermediate strategy of macro-county restrictions---where we optimize county partitions by solving a minimum k-cut problem on a graph weighted by our spillover estimates---can recover over 90% of statewide mobility reductions, while maintaining substantial flexibility between counties.