Persuading part of an audience

TL;DR

This paper introduces a cheap-talk model where a sender persuades only a subset of an audience, showing that partial persuasion can be credible and effective, especially when the target subset is small, with implications for political and strategic communication.

Contribution

It develops a model allowing for credible partial persuasion through private messages, extending existing cheap-talk frameworks to scenarios with selective audience targeting and analyzing equilibrium outcomes.

Findings

Senders can gain credibility by truthful communication to some receivers.

Partial persuasion enables the sender to approximate preferred outcomes when targeting a small audience.

The model's results are robust to various extensions, including non-transparent motives and full commitment.

Abstract

I propose a cheap-talk model in which the sender can use private messages and only cares about persuading a subset of her audience. For example, a candidate only needs to persuade a majority of the electorate in order to win an election. I find that senders can gain credibility by speaking truthfully to some receivers while lying to others. In general settings, the model admits information transmission in equilibrium for some prior beliefs. The sender can approximate her preferred outcome when the fraction of the audience she needs to persuade is sufficiently small. I characterize the sender-optimal equilibrium and the benefit of not having to persuade your whole audience in separable environments. I also analyze different applications and verify that the results are robust to some perturbations of the model, including non-transparent motives as in Crawford and Sobel (1982), and full commitment as in Kamenica and Gentzkow (2011).