[Paper Review] Information Revelation in Constant-Sum Games: Elections and Beyond

Navin Kartik, Francesco Squintani+1 more|arXiv (Cornell University)|Jun 24, 2024

Social Media and Politics12 citations

TL;DR

The paper shows that in a two-candidate Downsian election with private information, voter welfare cannot exceed what is obtained by using just one candidate’s information, and it identifies anti-pandering (overreacting) as a natural equilibrium outcome; it also argues under certain conditions that some pandering can improve welfare.

ABSTRACT

We study two-player constant-sum Bayesian games with type-independent payoffs. Under a "completeness" statistical condition, any "identifiable'" equilibrium is an ex-post equilibrium. We apply this result to a Downsian election in which office-motivated candidates possess private information about policy consequences. The ex-post property implies a sharp bound on information aggregation: equilibrium voter welfare is at best equal to the efficient use of a single candidate's information. In canonical specifications, politicians may "anti-pander" (overreact to their information), whereas some degree of pandering would be socially beneficial. We discuss other applications of the ex-post result.

Motivation & Objective

• Assess whether elections efficiently aggregate politicians’ policy-relevant private information.
• Characterize how office motivation and constant-sum incentives affect information revelation in a Downsian framework.
• Identify equilibria with pandering and anti-pandering and their welfare implications.
• Specialize to a normal-quadratic setting to illustrate strategic overreaction (anti-pandering) and potential welfare gains from pandering.

Proposed method

• Extend the canonical Downsian model to include two candidates with private information about policy consequences.
• Allow each candidate to observe a private signal and choose a policy platform to maximize winning probability.
• Model the voter's posterior updating after observing platforms and compute ex-ante welfare.
• Prove Theorem 1: under Condition 1, equilibrium welfare equals the maximum of the welfare when either candidate is always elected using his own information.
• Provide a normal-normal (one-dimensional) specialization to derive unbiased strategies, anti-pandering, and conditions under which pandering can improve welfare.
• Discuss robustness to mixing and broader information structures.

Experimental results

Research questions

• RQ1 Can elections aggregate more than one candidate’s private, policy-relevant information in a standard Downsian framework?
• RQ2 What is the welfare implication of office-motivated candidates who engage in information revelation under constant-sum incentives?
• RQ3 Do equilibria exhibit pandering or anti-pandering, and under what conditions can pandering improve voter welfare?
• RQ4 How does a normal-quadratic specification illustrate the allocation of information and strategic behavior?
• RQ5 Is the main welfare bound robust to strategic mixing or variations in information structures?

Key findings

• Voter ex-ante welfare in any equilibrium is the same as if the better of the two candidates were elected deterministically using his information, implying welfare cannot exceed using a single candidate’s information.
• The model induces a constant-sum game structure, making candidates’ probability of winning independent of their exact platforms on the equilibrium path (ex-postness).
• In the normal-quadratic specialization, there is a symmetric anti-pandering equilibrium where both candidates overreact to their private signals, causing more extreme platforms but equal election probabilities.
• Fully-revealing equilibria with anti-pandering are shown to exist and are unique among continuous symmetric equilibria under certain conditions.
• A welfare-improving pandering strategy is identified, where candidates condition on relative signal strength to underreact, potentially beating unbiased strategies.
• Panderying that discounts extreme signals (underreacting to private information) can, in some setups, raise voter welfare compared to equilibria with unbiased strategies.