We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. We model aggregate count data as arising from the Poisson binomial, the distribution of the sum of independent but not identically distributed Bernoulli random variables. We relate individual-level probabilities to individual covariates using both a logistic regression and a neural network. A normal approximation is derived via the Lyapunov Central Limit Theorem, allowing us to efficiently fit these models on large datasets. We apply this technique to the problem of revealing voter preferences in the 2016 presidential election, fitting a model to a sample of over four million voters from the highly contested swing state of Pennsylvania. We validate the model at the precinct level via a holdout set, and at the individual level using weak labels, finding that the model is predictive and it learns intuitively reasonable associations.
There is a richer body of literature on modeling voter preferences. Most of this research separates into two primary methodologies. In the first, researchers are interested in the relationship between voter characteristics and ballot preferences. To obtain labeled datasets, researchers use voter surveys @cite_16 and exit polls @cite_12 . They then fit models via simple GLMs, like the multinomial probit or multinomial logit model, which represent voter choice as a decision among unordered alternatives (parties, candidates) as a function of chooser (voter) attributes" @cite_17 .
@cite_16 @cite_12 @cite_17
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Abstract Several recent studies of voter choice in multiparty elections point to the advantages of multinomial probit (MNP) relative to multinomial conditional logit (MNL). We compare the MNP and MNL models and argue that the simpler logit is often preferable to the more complex probit for the study of voter choice in multi-party elections. Our argument rests on three areas of comparison between MNP and MNL. First, within the limits of typical data—a small sample of revealed voter choices among a few candidates or parties—neither model will clearly appear to have generated the observed data. Second, MNP is susceptible to a number of estimation problems, the most serious of which is that the MNP is often weakly identified in application. Weak identification is difficult to diagnose and may lead to plausible, yet arbitrary or misleading inferences. Finally, the logit model is criticized because it imposes the independence of irrelevant alternatives (IIA) property on voter choice. For most applications the IIA property is neither relevant nor particularly restrictive. We illustrate our arguments using data from recent US and French presidential elections. Opinion mining and demographic attribute inference have many applications in social science. In this paper, we propose models to infer daily joint probabilities of multiple latent attributes from Twitter data, such as political sentiment and demographic attributes. Since it is costly and time-consuming to annotate data for traditional supervised classification, we instead propose scalable Learning from Label Proportions (LLP) models for demographic and opinion inference using U.S. Census, national and state political polls, and Cook partisan voting index as population level data. In LLP classification settings, the training data is divided into a set of unlabeled bags, where only the label distribution in of each bag is known, removing the requirement of instance-level annotations. Our proposed LLP model, Weighted Label Regularization (WLR), provides a scalable generalization of prior work on label regularization to support weights for samples inside bags, which is applicable in this setting where bags are arranged hierarchically (e.g., county-level bags are nested inside of state-level bags). We apply our model to Twitter data collected in the year leading up to the 2016 U.S. presidential election, producing estimates of the relationships among political sentiment and demographics over time and place. We find that our approach closely tracks traditional polling data stratified by demographic category, resulting in error reductions of 28-44 over baseline approaches. We also provide descriptive evaluations showing how the model may be used to estimate interactions among many variables and to identify linguistic temporal variation, capabilities which are typically not feasible using traditional polling methods. To help their users to discover important items at a particular time, major websites like Twitter, Yelp, TripAdvisor or NYTimes provide Top-K recommendations (e.g., 10 Trending Topics, Top 5 Hotels in Paris or 10 Most Viewed News Stories), which rely on crowdsourced popularity signals to select the items. However, different sections of a crowd may have different preferences, and there is a large silent majority who do not explicitly express their opinion. Also, the crowd often consists of actors like bots, spammers, or people running orchestrated campaigns. Recommendation algorithms today largely do not consider such nuances, hence are vulnerable to strategic manipulation by small but hyper-active user groups. To fairly aggregate the preferences of all users while recommending top-K items, we borrow ideas from prior research on social choice theory, and identify a voting mechanism called Single Transferable Vote (STV) as having many of the fairness properties we desire in top-K item (s)elections. We develop an innovative mechanism to attribute preferences of silent majority which also make STV completely operational. We show the generalizability of our approach by implementing it on two different real-world datasets. Through extensive experimentation and comparison with state-of-the-art techniques, we show that our proposed approach provides maximum user satisfaction, and cuts down drastically on items disliked by most but hyper-actively promoted by a few users. We present a systematic study of Plurality elections with strategic voters who, in addition to having preferences over election winners, also have secondary preferences, governing their behavior when their vote cannot affect the election outcome. Specifically, we study two models that have been recently considered in the literature: lazy voters, who prefer to abstain when they are not pivotal, and truth-biased voters, who prefer to vote truthfully when they are not pivotal. For both lazy and truth-biased voters, we are interested in their behavior under different tie-breaking rules (lexicographic rule, random voter rule, random candidate rule). Two of these six combinations of secondary preferences and tie-breaking rules have been studied in prior work; for the remaining four, we characterize pure Nash equilibria (PNE) of the resulting strategic games and study the complexity of related computational problems. We then use these results to analyze the impact of different secondary preferences and tie-breaking rules on the election outcomes. Our results extend to settings where some of the voters are non-strategic.