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Divide and Diverge

Giampaolo Bonomi

TL;DR

The paper addresses why political polarization emerges when electoral competition features office-marshalling parties with decreasing marginal utility from political power. It develops a probabilistic voting model with aggregate shocks and a concave power payoff, showing that platform differentiation functions as insurance, generating divergence even in a symmetric, ideologically neutral setting. The analysis derives unidimensional and multidimensional polarization results: equilibrium platforms diverge endogenously, voters on opposite sides become more extreme raise payoffs, and ideological coherence across dimensions further enhances separation. These findings imply a trade-off between representation and policy stability, with institutional design such as the majority premium offering a potential lever to attenuate polarization by altering incentives to appeal to pivotal voters.

Abstract

Political polarization can be beneficial to competing political parties. I study how electoral competition itself generates incentives to polarize voters, even when parties are ex ante identical and motivated purely by political power, interpreted as office rents or influence. I develop a probabilistic voting model with aggregate popularity shocks in which parties have decreasing marginal utility from political power. Equilibrium policy convergence fails. Platform differentiation provides insurance against electoral volatility by securing loyal voter bases and stabilizing political power. In a unidimensional policy space, parties' equilibrium payoffs rise as voters on opposite sides of the median become more extreme, including when polarization is driven by changes in the opponent's supporters. In a multidimensional setting, parties benefit from ideological coherence, the alignment of disagreements across issues. The results have implications for polarizing political communication, party identity, and electoral institutions.

Divide and Diverge

TL;DR

The paper addresses why political polarization emerges when electoral competition features office-marshalling parties with decreasing marginal utility from political power. It develops a probabilistic voting model with aggregate shocks and a concave power payoff, showing that platform differentiation functions as insurance, generating divergence even in a symmetric, ideologically neutral setting. The analysis derives unidimensional and multidimensional polarization results: equilibrium platforms diverge endogenously, voters on opposite sides become more extreme raise payoffs, and ideological coherence across dimensions further enhances separation. These findings imply a trade-off between representation and policy stability, with institutional design such as the majority premium offering a potential lever to attenuate polarization by altering incentives to appeal to pivotal voters.

Abstract

Political polarization can be beneficial to competing political parties. I study how electoral competition itself generates incentives to polarize voters, even when parties are ex ante identical and motivated purely by political power, interpreted as office rents or influence. I develop a probabilistic voting model with aggregate popularity shocks in which parties have decreasing marginal utility from political power. Equilibrium policy convergence fails. Platform differentiation provides insurance against electoral volatility by securing loyal voter bases and stabilizing political power. In a unidimensional policy space, parties' equilibrium payoffs rise as voters on opposite sides of the median become more extreme, including when polarization is driven by changes in the opponent's supporters. In a multidimensional setting, parties benefit from ideological coherence, the alignment of disagreements across issues. The results have implications for polarizing political communication, party identity, and electoral institutions.
Paper Structure (43 sections, 15 theorems, 122 equations, 1 figure)

This paper contains 43 sections, 15 theorems, 122 equations, 1 figure.

Key Result

Proposition 3.1

If a pure-strategy equilibrium exists, the two candidates offer different policy platforms.

Figures (1)

  • Figure 1: Increase in ideological coherence holding marginal distributions fixed. Greater alignment of voter preferences across dimensions generates more cohesive ideological factions and allows parties to diverge further in equilibrium. Panel (b) is obtained from panel (a) by applying a $d$-spread, where $d$ is the equilibrium ideological direction in panel (a). Party-preferred equilibrium platforms are represented by dark x markers, and are identified using the method of Appendix \ref{['appendixA2']}

Theorems & Definitions (32)

  • Remark 1
  • Proposition 3.1: Party Divergence
  • Proposition 4.1: Equilibrium
  • Remark 2
  • Definition 1
  • Proposition 4.2
  • Remark 3
  • Definition 2
  • Proposition 4.3
  • Definition 3: Local Equilibrium
  • ...and 22 more