A Bayesian solution to Hallsson’s puzzle

ABSTRACT

Politics is rife with motivated cognition. People do not dispassionately engage with the evidence when they form political beliefs; they interpret it selectively, generating justifications for their desired conclusions and reasons why contrary evidence should be ignored. Moreover, research shows that epistemic ability (e.g. intelligence and familiarity with evidence) is correlated with motivated cognition. Bjørn Hallsson has pointed out that this raises a puzzle for the epistemology of disagreement. On the one hand, we typically think that epistemic ability in an interlocutor gives us reason to downgrade our belief upon learning that we disagree. On the other hand, if our interlocutor is under the sway of motivated cognition, then we have reason to discount his opinion. In this paper, I argue that Hallsson's puzzle is solved by adopting a Bayesian approach to disagreement. If an interlocutor is under the sway of motivated cognition, his disagreement should not affect our beliefs – no matter his ability. Because we implicitly and to high accuracy know his beliefs before he reveals them to us, disagreement provides us with no new information on which to conditionalize. I advance a model which accommodates the motivated cognition dynamic and other key epistemic features of disagreement.

KEYWORDS:

• Epistemology of disagreement
• Bayesian inference
• political disagreement
• motivated cognition
• Bjørn Hallsson

Acknowledgement

I thank Bjørn Hallsson and Kirun Sankaran for helpful comments on this paper. I am also grateful to Desmos, Inc., for its kind permission to use Figure 1, which was generated with its graphing calculator (URL = <https://www.desmos.com/calculator>, retrieved 14 July 2019).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 On these two notions, see, respectively, Kelly 2005 and Elga 2007.

2 This is the justification for BP’s having low ACCURACY which Hallsson finally settles on (2019, 2194). He considers other possibilities earlier in the section.

3 See Easwaran et al. 2016; Isaacs 2019; Jehle and Fitelson 2009; Lasonen-Aarnio 2013; Levinstein 2015; Mulligan Forthcoming; Shogenji Manuscript.

4 The Bayesian approach, in its full generality, allows for p to take on three, four, or more discrete values (rather than just true and false), or even be treated as continuous.

5 For example, in Christensen’s (2007) ‘Restaurant Tip’ case, two friends go out to dinner and calculate their shares of the bill. They are epistemic peers (i.e. equally good at math, they both took a careful look at the check, etc.), but they come to different conclusions about what their shares are. Suppose that EP1 is right and EP2 is wrong. The traditionalist surely holds that EP1 should lose confidence in his belief, despite, ex hypothesi, being right. (And I agree that he should.) It is the (internalist) possibility of error that demands epistemic compromise.

6 I am going to abuse notation a little from here on out, using q to refer to both a random variable and its realization.

7 These considerations are related to Hallsson’s discussion of ‘clustering’ on pp. 2197–2198 (see also Elga 2007). But here we are not denying that political disagreements are epistemically significant. Nor are we begging the question by claiming that because some interlocutor is wrong about related disagreements, she is wrong about this one, too. What matters is the predictive nature of political partisanship – what an interlocutor’s opinions about related issues suggest for her opinion about this one.

8 Summaries of these models may be found in Clemen and Winkler 1990 and 1999; and in French 1985.

9 Because the support of this distribution is (0, 1), is no longer technically Normal. Therefore, its mean is no longer (generally) equal to its mode. Figure 1 is, rather, a Truncated Normal  distribution, with parent parameters μ = 0.1 and σ = 0.1. Its mean is $\mu +\sigma {\displaystyle \frac{\varphi \left({\displaystyle \frac{0-\mu }{\sigma }}\right)-\varphi \left({\displaystyle \frac{1-\mu }{\sigma }}\right)}{\mathrm{\Phi }\left({\displaystyle \frac{1-\mu }{\sigma }}\right)-\mathrm{\Phi }\left({\displaystyle \frac{0-\mu }{\sigma }}\right)}=0.13}$, where ϕ(x) is the probability density function of the Standard Normal distribution, and Φ(x) its cumulative distribution function.

10 Here is how I selected this value. Observe that we can use equation (2.4) to work backwards, computing λ by specifying a posterior probability for some given value of q. I might think, thus, that my posterior probability of p ought to be 0.9 in the event that my interlocutor ends up agreeing with me, Pr(p) = q = 0.8. That yields λ = 0.15. In many cases, it may be easiest to compute λ by choosing a value for q very close to 0 or 1.

11 A possibility discussed in Gardiner 2014 and Mulligan 2015. For n interlocutors, equation (2.4) becomes $Pr\left(p|q\right)=Pr\left(p\right)+\sum _{i=1}^n{\lambda }_i\left(q_i-{\mu }_i\right)$. The consistency conditions change accordingly.