Bayesian explanations for persuasion
| Published date | 01 July 2023 |
| DOI | http://doi.org/10.1177/09516298231185060 |
| Author | Andrew T Little |
| Date | 01 July 2023 |
| Subject Matter | Articles |
Bayesian explanations for
persuasion
Andrew T Little
Department of Political Science, UC Berkeley, CA, USA
Abstract
The central puzzle of persuasion is why a receiver would listen to a sender who they know is try-
ing to change their beliefs or behavior. This article summarizes five approaches to solving this puz-
zle: (1) some messages are easier to send for those with favorable information (costly signaling), (2)
the sender and receiver have common interest, (3) the sender messages are verifiable information, (4)
the sender cares about their reputation for competence/honesty, and (5) the sender can commit to
a messaging strategy (often called ‘Bayesian Persuasion’). After reviewing these approaches with
common notation, I discuss which provide insight into prominent empirical findings on campaigns,
partisan media, and lobbying. While models focusing on commitment have rapidly become prom-
inent (if not dominant) in the recent theoretical literature on persuasion in political science and
economics, the insights they provide are primarily technical, and are not particularly well-suited
to explaining most of these phenomena.
Keywords
Cheap talk; costly signaling; persuasion; reputation
Communication and persuasion are central to much if not most of politics. Democratic
politicians try to persuade donors to donate and voters to vote for them. For autocrats,
relatively free of institutional constraints, persuading others that they are strong leaders
who should not be challenged may be even more central. Pundits aim to persuade an audi-
ence to adopt their views, or at least persuade an audience to continue paying attention to
what they say. Ordinary citizens frequently talk to each other about politics—though cer-
tainly far less than political scientists—either to persuade or just for entertainment.
Corresponding author:
Andrew T Little, Department of Political Science, UC Berkeley, 210 SSB, Berkeley, CA 94720, USA.
Email: andrew.little@berkeley.edu
Article
Journal of Theoretical Politics
2023, Vol. 35(3) 147–181
© The Author(s) 2023
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/ 09516298231185060
journals.sagepub.com/home/jtp
This article overviews formal approaches to persuasion, with as much common nota-
tion as possible. A more specificdefinition will come in the context of the formalization,
but in general I use persuasion to mean any attempt by a sender to change the beliefs or
behavior of a receiver to be ‘more favorable’. The formal analysis restricts attention to
models where the target of persuasion is fully rational, or Bayesian. That is, they under-
stand the speaker’s strategy and update their beliefs by Bayes’rule, in addition to stand-
ard sequential rationality requirements for decisions.
Given the constraint of rational updating, under some conditions persuasion is impos-
sible.
1
Intuitively, if the speaker (or sender) always wants the listener (or receiver) to take
certain actions, and faces no constraints on what they say, they would always say what-
ever makes the listener do what they want. Knowing this, the receiver has no reason to
pay attention.
Of course, persuasion does sometimes occur both in theories and reality. The bulk of
the analysis shows how modifying the assumptions in this benchmark makes persuasion
possible. While inevitably nonexhaustive, much applied theoretical work uses at least one
of five modifications. First, some kinds of messages are costly, and cheaper to send for
those with favorable information (costly signaling). Second, the sender and receiver
can have partially aligned goals (common interest). Third, the sender messages can be
checked (verifiable information). Fourth, the sender may care about perceptions of
their competence/honesty (reputation concerns). Finally, senders may be able to
commit to a strategy where they don’t lie so much that their messages still affect the
receiver behavior (often called ‘Bayesian persuasion’, though this isn’t ideal). I then
informally discuss ‘non-Bayesian’models of persuasion which are driven by receivers
being less than fully rational in how they process information.
After describing the differences and commonalities of these models, I overview how
they have been applied to three empirical literatures on campaigns, partisan and state-
controlled media, and lobbying. In each case I discuss when the assumptions and predic-
tions of different models seem in line (or not) with empirical results.
1. Insights and trends
The first four explanations contain fundamental insights about communication which can
be explained without going into any technical detail.
•Costly signaling models tell us that people may engage in seemingly wasteful,
inefficient, or harmful behavior if it shows off that they are a ‘type’who is
willing to do this.
•Common interest models tell us that communication is easier when the sender and
receiver have more closely aligned goals, and so doing what the sender wants can
be good for the receiver, or at least better than ignoring him.
•Verifiable information models give a simple explanation for communication:
when favorable information can’t be faked, messages claiming good news
should be believed. More subtly, an important insight from these models is that
people may reveal mediocre or even somewhat unfavorable information (from
148 Journal of Theoretical Politics 35(3)
their own perspective) as well if keeping quiet would make things look even
worse.
•Reputation models teach us that when speakers care about a reputation for com-
petence, they may tell the truth in order to seem smart. However, these incentives
may also cause senders to cater to the prior belief of their audience or make stron-
ger claims than are warranted by their information.
A valuable feature of these classes of models is that their central forces are straightfor-
ward to apply to specific examples of political communication and persuasion. This is
useful for applied theorists; for example, when we see people taking seemingly inefficient
actions to try and induce others to do what they want, it is natural to develop a costly sig-
naling model to explain this. It is also useful for empirical scholars who want to motivate
their analysis or interpret results without having to write an original formal model.
The key insights from models with commitment are harder to boil down. But this has
not hindered their popularity. In fact, part of the motivation for writing this is a sense that,
following Kamenica and Gentzkow (2011), the number of papers on communication and
persuasion in political science (and economics) that focus on persuasion via commitment
has been dramatically rising, perhaps becoming the modal approach in applied theory
papers (see Kamenica, 2019: for a recent review).
Figure 1 provides some suggestive evidence. The left panel shows the number of
Google Scholar search hits for the phrases ‘Cheap talk’,‘Costly signaling’, and
‘Bayesian persuasion’from 2012 to 2021. ‘Cheap talk’can loosely describe any
approach where messages are not costly, though it is often associated with the second
explanation (common interests).
The first two increase steadily—perhaps explained by more papers being indexed in
general—while the latter goes from almost no hits to nearly as many as costly signaling.
As discussed further in Section 7, informal perusing indicates that results for costly sig-
naling and cheap talk include many empirical papers while Bayesian persuasion returns
Figure 1. Google scholar search hits for kinds of model (left panel) and citations to influential
papers (right panel).
Little 149
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