Condorcet’s Jury Theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter’s independent probability of voting for that outcome is greater than 1/2. Previous research has found that switching to a hierarchical system always leads to an inferior result. Yet, in many situations direct voting is infeasible (e.g., due to high implementation or infrastructure costs), and hierarchical voting may provide a reasonable alternative. This paper examines differences in accuracy rates of hierarchical and direct voting systems for varying group sizes, abstention rates, and voter competences. We derive three main results. First, we prove that indirect two-tier systems differ most from their direct counterparts when group size and number are equal (i.e., when each equals [Formula: see text], where N d is the total number of voters in the direct system). In multitier systems, we prove that this difference is maximized when group size equals [Formula: see text], where n is the number of hierarchical levels. Second, we show that while direct majority rule always outperforms indirect voting for homogeneous electorates, hierarchical voting gains in accuracy when either the number of groups or the number of individuals within each group increases. Third, we prove that when voter abstention and competency are correlated within groups, hierarchical systems can outperform direct voting. The results have implications beyond voting, including information processing in the brain, collective cognition in animal groups, and information aggregation in machine learning.
This article argues that the common practice of using presidential vote shares to measure congressional district ideology is logically flawed. I propose two alternative methods - a classical and Bayesian model - that employ multiple election returns to estimate voters' ideological distributions within districts. Simulations and empirical applications demonstrate that the proposed models outperform direct vote shares, and they externally validate estimates of district ideology. Moreover, by generating estimates of districts' variances, these models also provide information on constituency heterogeneity, a quality that is perhaps equally valuable for understanding representatives' strategic behavior.
Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate. We explain this apparent contradiction by developing a dynamical model that predicts ideological positions of political parties. Our approach tackles the challenge of incorporating bounded rationality into mathematical models and integrates the empirical finding of satisficing decision making---voters settle for candidates who are “good enough" when deciding for whom to vote. We test the model using data from the U.S. Congress over the past 150 years and find that our predictions are consistent with the two major political parties' historical trajectories. In particular, the model explains how polarization between the Democrats and Republicans since the 1960s could be a consequence of increasing ideological homogeneity within the parties.
This paper develops and tests arguments about how national-level social and institutional factors shape the propensity of individuals to form attachments to political parties. Our tests employ a two-step estimation procedure that has attractive properties when there is a binary dependent variable in the first stage and when the number of second-level units is relatively small. We find that voters are most likely to form party attachments when group identities are salient and complimentary. We also find that institutions that assist voters in retrospectively evaluating parties—specifically, strong party discipline and few parties in government—increase partisanship. These institutions matter most for those individuals with the fewest cognitive resources, measured here by education. Supplementary data available here
