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Growing disparities of income and wealth have prompted extensive survey research to measure the effects on public beliefs about the causes and fairness of economic inequality. However, observational data confound responses to unequal outcomes with highly correlated inequality of opportunity. This study uses a novel experiment to disentangle the effects of unequal outcomes and unequal opportunities on cognitive, normative, and affective responses. Participants were randomly assigned to positions with unequal opportunities for success. Results showed that both winners and losers were less likely to view the outcomes as fair or attributable to skill as the level of redistribution increased, but this effect of redistribution was stronger for winners. Moreover, winners were generally more likely to believe that the game was fair, even when the playing field was most heavily tilted in their favor. In short, it’s not just how the game is played, it’s also whether you win or lose.

Log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association not covered by model candidates. In this article, we propose an application of Lasso regularization that addresses the aforementioned limitations. We evaluate our method through a Monte Carlo experiment and an empirical study of educational assortative mating in Chile, 1990–2015. Results demonstrate that our approach has the virtue, relative to ad hoc specification searches, of offering a principled statistical criterion to inductively select a model. Importantly, we show that in situations where conventional fit statistics provide conflicting diagnostics, our Lasso-based approach is consistent in its model choice, yielding solutions that are both predictive and parsimonious.

Log-linear models offer a detailed characterization of the association between categorical variables, but the breadth of their outputs is difficult to grasp because of the large number of parameters these models entail. Revisiting seminal findings and data from sociological work on social mobility, the author illustrates the use of heatmaps as a visualization technique to convey the complex patterns of association captured by log-linear models. In particular, turning log odds ratios derived from a model’s predicted counts into heatmaps makes it possible to summarize large amounts of information and facilitates comparison across models’ outcomes.