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Skepticism and Credulity: A Model and Applications to Political Spin, Belief Formation, and Decision Weights

James David Campbell ORCID logo

Abstract

In this paper I model a decision maker who forms beliefs and opinions using a dialectic heuristic that depends on their degree of skepticism or credulity. In an application to political spin, two competing parties choose how to frame commonly observed evidence. If the receiver is sufficiently credulous, equilibrium spin is maximally extreme and generates short, superficial news cycles. When receivers vary in their skepticism, there is partisan sorting by skepticism parameter: the more credulous group systematically favors one party and displays hostility to evidence and a media they see as biased. In behavioral applications in which the frames arise from the decision maker’s internal deliberation, a decision maker with the same credulous nature would display known behavioral anomalies in forming beliefs and forming decision weights from stated probabilities. The dialectic model therefore captures a simple psychological mechanism and matches closely some stylized facts across these three disparate applications.

JEL codes: D72; D81; D83; D91

Corresponding author: James David Campbell, Providence College, 02918-7000Providence, RI, USA; and University of California Berkeley, Berkeley, CA, USA, E-mail:

A Result 1

Let us call the upper and lower bounds chosen by sender LL and L respectively, and similarly the upper and lower bounds chosen by sender RR and R respectively. The receiver’s assessment of the frames is given by:

(A.1)μˆ=wHswLs+wHsμL+wLswLs+wHsμH
(A.2)=12(L+L)[(HH)s(LL)s+(HH)s]+12(H+H)[(LL)s(LL)s+(HH)s] .

Recall that each sender must use a frame with strictly positive width (this is by assumption, but it is equivalent to saying that the distribution of the evidence itself is not degenerate). Consider the perspective of sender R deciding where to set the upper bound of their frame. The derivative of the receiver’s assessment with respect to H is

(A.3)0.5(LL)s((LL)s+(HH)s1(s(L+LHH)+HH))((LL)s+(HH)s)2

The denominator here is certainly positive, as is the first term, 0.5(LL)s, in the numerator. We may therefore say that the whole expression is positive if

(A.4)((LL)s+(HH)s1(s(L+LHH)+HH))>0 .

When evaluated at the s = 0, this expression is certainly positive for any values of the bounds on the two frames. When evaluated at s = 1, this expression is equivalent to

(A.5)L2LLLH+LH
(A.6)=LL+(LL)HH

which is certainly larger than zero since L>L and L<1.

This means that sender R can always increase the receiver’s assessment μˆ in their preferred direction (toward the endpoint 1 of the spectrum) by increasing H so long as s is sufficiently small. Since the problem for sender L is symmetric, for both senders to extend their frames as much as possible toward their preferred endpoint forms a Nash equilibrium pair.

B Results 2 and 3

These results follow directly from the characteristics of Result 1 and the properties of the uniform distribution.

C Result 4

dμˆdL>0, so that the marginal value to a party of releasing evidence that forces their opponent to expand their frame is always positive. In the case in which the parties use maximally extreme frames, d2μˆdL2<0, so that the marginal value of these actions is higher when their opponent’s existing frame is narrower in scope.

Consider the sender who prefers the receiver to make a high assessment, who we may call the high type sender for convenience. Let us consider the marginal effect of raising L on the receiver’s assessment μˆ. This captures the effect of the high type sender releasing evidence unfavorable to their opponent.

From Eq. (A.2), the derivative of μˆ with respect to L is

(C.1)(HH)s((LL)(HH)s+(LL)s(s(H+HLL)+LL))(LL)((HH)s+(LL)s)2 .

This expression is always positive, since L>L, H>H, and H+H>L+L. This means that the receiver’s assessment μˆ always moves in the direction favorable to the high type sender when they are able to force L to be higher.

Next consider the case in which the senders use maximally extreme frames, so that H=1 and L=0. The second derivative d2μˆdL2 is given by

(C.2)0.5s(1H)sLs(H(s1)s(L1)L1)L2s(H(s+1)s(L1)+L+1)L2((1H)s+Ls)3 .

The denominator and the first term 0.5s(1H)sLs in the numerator are certainly positive, since L and H are between 0 and 1. This leaves the term

(C.3)(H(s1)s(L1)L1)L2s(H(s+1)s(L1)+L+1) .

The first part of this expression is certainly negative, and the second part being subtracted is certainly positive. This means that the second derivative as a whole is negative. This means that an increase in L has a smaller positive effect on μˆ when L is higher. The largest positive effect comes when the upper bound of the existing evidence is least favorable to the high type sender.

Acknowledgments

I am grateful to Bernhard Ganglmair and Stephanie Tilden for extremely helpful discussions and to two anonymous referees and the editor, Burkhard Schipper, for their excellent comments. Thanks also to seminar participants at Providence College and the 2020 Eastern Economic Association Meetings and to the invaluable Berkeley Teach-Net community for their advice and feedback.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/bejte-2019-0184).

Received: 2019-12-17
Accepted: 2021-03-02
Published Online: 2021-03-19

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