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Bounding the Effect of Persuasion with Monotonicity Assumptions: Reassessing the Impact of TV Debates

Sung Jae Jun, Sokbae Lee

TL;DR

This paper challenges the view that televised debates dramatically alter electoral outcomes by developing a monotonicity-based partial identification framework. It leverages Monotone Treatment Response and Monotone Treatment Selection to bound the persuasion rate $\theta$ and its reverse $\theta^{(r)}$ without relying on exogenous treatments or credible instruments, yielding sharp upper bounds that remain small. The framework also translates to Pearl's probabilities of causation (PS, PN, PNS), preserving robustness across identifying assumptions. Empirically, reanalyzing LP’s data with a local event window finds an average treatment effect upper bound of about $0.68$ percentage points and a persuasion rate upper bound around $3.4\%$, with about 80% of the population classified as Already-Persuaded or Never-Persuadable. Overall, the results reinforce the conclusion that TV debates exert only modest influence on voting behavior, while providing a practical, assumption-light pathway for empirical bounding in persuasion research.

Abstract

Televised debates between presidential candidates are often regarded as the exemplar of persuasive communication. Yet, recent evidence from Le Pennec and Pons (2023) indicates that they may not sway voters as strongly as popular belief suggests. We revisit their findings through the lens of the persuasion rate and introduce a robust framework that does not require exogenous treatment, parallel trends, or credible instruments. Instead, we leverage plausible monotonicity assumptions to partially identify the persuasion rate and related parameters. Our results reaffirm that the sharp upper bounds on the persuasive effects of TV debates remain modest.

Bounding the Effect of Persuasion with Monotonicity Assumptions: Reassessing the Impact of TV Debates

TL;DR

This paper challenges the view that televised debates dramatically alter electoral outcomes by developing a monotonicity-based partial identification framework. It leverages Monotone Treatment Response and Monotone Treatment Selection to bound the persuasion rate and its reverse without relying on exogenous treatments or credible instruments, yielding sharp upper bounds that remain small. The framework also translates to Pearl's probabilities of causation (PS, PN, PNS), preserving robustness across identifying assumptions. Empirically, reanalyzing LP’s data with a local event window finds an average treatment effect upper bound of about percentage points and a persuasion rate upper bound around , with about 80% of the population classified as Already-Persuaded or Never-Persuadable. Overall, the results reinforce the conclusion that TV debates exert only modest influence on voting behavior, while providing a practical, assumption-light pathway for empirical bounding in persuasion research.

Abstract

Televised debates between presidential candidates are often regarded as the exemplar of persuasive communication. Yet, recent evidence from Le Pennec and Pons (2023) indicates that they may not sway voters as strongly as popular belief suggests. We revisit their findings through the lens of the persuasion rate and introduce a robust framework that does not require exogenous treatment, parallel trends, or credible instruments. Instead, we leverage plausible monotonicity assumptions to partially identify the persuasion rate and related parameters. Our results reaffirm that the sharp upper bounds on the persuasive effects of TV debates remain modest.

Paper Structure

This paper contains 15 sections, 5 theorems, 101 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Identification
  4. Estimation and Inference
  5. Persuasion Rates
  6. Specification Testing
  7. Shares of Already-Persuaded and Never-Persuadable Types
  8. Bounding the Probabilities of Causation
  9. Bounds under Alternative Assumptions
  10. Empirical Example
  11. Conclusions
  12. The Empirical Framework of TVdebate:23
  13. Proof of \ref{['thm:alternative_bounds']}
  14. Proof of \ref{['thm:alternative_bounds_pearl_tian']}
  15. Comments on Confidence Intervals

Key Result

Lemma 1

Under ass:overlapass:unconfass:mtr, we have In particular, $\theta$ and $\theta^{(r)}$ are point-identified by $\theta_U$ and $\theta^{(r)}_U$, respectively.

Figures (2)

  • Figure 1: Data Construction. Panel A illustrates the coding rules for the outcome variable $Y$. Panel B illustrates the sample restriction and treatment assignment relative to the debate timing.
  • Figure 2: Decision Rule for Estimating Persuasion Rates

Theorems & Definitions (7)

  • Lemma 1: Benchmark
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • proof
  • Theorem 4
  • proof