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Bayesian Polarization

Tuval Danenberg

Abstract

Discussions of political disagreement emphasize two patterns: polarization, where beliefs diverge toward opposite extremes on each issue dimension; and issue alignment, where individuals' views across issues become more internally consistent. We show that both can simultaneously arise under Bayesian learning from public information. We characterize the public signals that can induce persistent polarization on all dimensions and find that evidence of issue alignment can polarize Bayesian agents. However, we show that even stronger notions of polarization, requiring divergence beyond marginal beliefs, are inconsistent with Bayesian rationality. Whether multidimensional belief polarization translates into divergent aggregate positions depends on cross-issue separability.

Bayesian Polarization

Abstract

Discussions of political disagreement emphasize two patterns: polarization, where beliefs diverge toward opposite extremes on each issue dimension; and issue alignment, where individuals' views across issues become more internally consistent. We show that both can simultaneously arise under Bayesian learning from public information. We characterize the public signals that can induce persistent polarization on all dimensions and find that evidence of issue alignment can polarize Bayesian agents. However, we show that even stronger notions of polarization, requiring divergence beyond marginal beliefs, are inconsistent with Bayesian rationality. Whether multidimensional belief polarization translates into divergent aggregate positions depends on cross-issue separability.

Paper Structure

This paper contains 19 sections, 15 theorems, 39 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Preliminaries
  4. One-shot and Limit Polarization
  5. Limit Beliefs and Partitional Signals
  6. Coordinatewise Polarization
  7. Definition
  8. Possibility of Coordinatewise Polarization
  9. Which Signals Lead to Limit Coordinatewise Polarization
  10. Constraints on Bayesian Polarization
  11. Robust Polarization in Aggregate Positions
  12. Conclusion
  13. Proofs
  14. Impossibility of limit $\succeq_{uo}$-polarization:
  15. Possibility of one-shot $\succeq_{uo}$-polarization:
  16. ...and 4 more sections

Key Result

Lemma 1

For every $\theta\in\Theta$, $Q(t)(\theta)\rightarrow Q^*(\theta)$ almost surely.

Figures (10)

  • Figure 1: Priors for Example \ref{['example:coordinatewise']}.
  • Figure 2: Posteriors for Example \ref{['example:coordinatewise']}.
  • Figure 3: Spanning conditions.
  • Figure 4: Violations of the balance condition.
  • Figure 5: Compensatory and non-compensatory sets.
  • ...and 5 more figures

Theorems & Definitions (29)

  • Example 1
  • Definition 1: One-shot polarization
  • Definition 2: Limit polarization
  • Lemma 1
  • Definition 3: Coordinatewise dominance
  • Theorem 1
  • Definition 4: Spanning
  • Definition 5: Biased and balanced
  • Definition 6: Compensatory
  • Theorem 2
  • ...and 19 more