The Bayesian fallacy: Distinguishing internal motivations and religious beliefs from other beliefs

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Abstract

This paper advances the two-axis of information hypothesis. One axis concerns whether one's belief is about the environment as opposed to one's own action (the self). The other axis of information concerns whether the information is about content as opposed to context. Given the two axes, we have four kinds of beliefs: convictions, conceptions, perception, and confidence. The Bayesian fallacy is the failure to observe the differences among the four kinds of beliefs. For instance, convictions are about internal motivations, such as “I can climb this mountain”, which cannot be updated via Bayes's rule as the case with the other three beliefs.

Introduction

James Heckman has stumbled onto a puzzle. While the expected return on investment in education has risen in the US in the last few decades, people have reduced their investment in education (Heckman, 2007, Heckman and Krueger, 2003, Heckman and Rubinstein, 2001). To explain this phenomenon, Heckman has proposed that investment in education, “cognitive skills,” is not only a function of expected returns, but also a function of “non-cognitive” skills, where non-cognitive skills consist of perseverance, tenacity, morale, and internal motivations. Heckman explains the decline in education investment by arguing that internal motivations to invest in education must have declined at a steeper rate than the rise in expected returns (which, in turn, can be regarded as the external motivations or stimuli). He has advocated a policy of focusing on early child development to stave off any further decline in morale, given that such non-cognitive skills are nurtured mostly in the first seven years of life.

The term “non-cognitive,” however, is problematic. First, in the cognitive psychology literature (Garnham, 1994, p. 167; Lycan, 1999, Reber, 2003, Still and Costall, 1991), “non-cognition” denotes the emotions, while “cognition” denotes the faculty of knowing, or mental processes undertaken to solve a problem, i.e., to decide on the proper response to a stimulus. But all beliefs, including morale and internal motivations, involve both cognitive and non-cognitive elements. Second, in the same literature, the two terms are opposed, invoking the famous Cartesian dichotomy between the emotions and reason (Greene, 2005). The emotion/reason opposition begs, at a deeper level, bigger questions. Although it is outside the scope of this paper, one such question is how could reason be independent of the emotions, when both are related to the striving of the organism to enhance its wellbeing or fitness? (Khalil, 2010a).

Instead of the term “non-cognitive,” this paper employs the term “convictions” to denote beliefs concerning morale or internal motivations. Convictions are beliefs about one's ability with respect to goal commitment such as running in a race, starting an enterprise, managing a business, or persevering through a storm. Convictions can be defined as self-beliefs in relation to the capability of the organism to produce: “I can paint this wall,” “I can finish this project,” or “I rely on God's support in opening my business”. In this proposed usage, convictions include religious beliefs insofar as they sustain the agent's inner motivation or morale.

This paper draws a radical distinction between convictions and three other beliefs, called here “confidence,” “perception”, and “conception”. Confidence is also a self-belief—but it is about the assertion of rights of the self vis-à-vis the rights of others and, in the case of temptations, vis-à-vis the rights of the future self: “I will not overeat”. Perception, on the other hand, is a belief about the environment that is empirical: “the storm will incur about $2 billion in damages”. Conception is also an environment-related belief that involves empirical date—but it also involves framing, meaning, or context, which is non-empirical: “the storm will incur about $2 billion in an area that has $15 trillion worth of real estate”.

What is the payoff of the proposed four-way distinction of beliefs? The main payoff is the ability to differentiate convictions from the other kinds of beliefs. Convictions include the set of religious beliefs related to one's internal motivation and ability to undertake tasks. Beliefs about internal motivation, as the case with religious convictions, cannot be empirically updated—unlike the case of scientific beliefs such as perceptions that can be empirically updated. The fact that agents cannot use Bayes's rule to update a class of beliefs, viz., convictions, does not mean they are irrational. This payoff should shed light on the findings of behavioral economics: many of the supposed behavioral anomalies, i.e., behavior that seems to deviate from the predictions of standard rationality theory, are not anomalies because they are based on beliefs (convictions) that cannot be updated via Bayes's rule to start with.

The four-way distinction of beliefs is grounded on a hypothesis called here the “two-axis information hypothesis”. One axis identifies whether the object of the belief is the agent or his or her environment; the other axis identifies whether the information is about content or context. Using the two axes, convictions concern the self and are about context; while conceptions concern the environment and are about content. And it is shown, corollary, why convictions are non-correctable with regard to truth and, further, are non-warrantable because the object of the belief is not a fixed reality; while conceptions are likewise non-correctable with regard to truth but are warrantable because the object of the belief is a fixed reality.

This will become clearer below. But to define the Bayesian fallacy, it is sufficient to clarify that convictions and conceptions are non-correctable in the sense that they cannot be judged, via Bayes's rule, as being true or false because both involve meaning (context), which is non-empirical. Thus, when one asserts “I can paint” or when one conjures the help of God to finish a project, one creates an aspiration that acts as a context and is, hence, non-empirical. On the other hand, warrantability is a weaker criterion of empirical corroboration than correctability. Convictions are non-warrantable because they involve the development of potentiality or capability: as one pursues a goal, the supposed evidence that supports one's belief in achieving the goal, the perceived self-ability, develops, which means that one cannot use self-ability as such evidence. The same cannot be said about conceptions because the evidence, i.e., the environment, is a fixed reality—it does not develop.

In this light, we can define the “Bayesian fallacy”:

The Bayesian fallacy: One commits the Bayesian fallacy when one treats convictions, which cannot be the subject of Bayes's rule, as no different from other beliefs which are, although in different ways, the subject of Bayes's rule.1

This paper argues that there are, in fact, two degrees of the Bayesian fallacy. To do this, Section 1 explicates the proposed two-axis information hypothesis. Section 2 stresses the importance of convictions. Sections 3 Why convictions?, 4 Why are convictions non-evidential?, 4.1 The issue of meaning (context): some philosophy of science, 4.2 Non-evidential beliefs, 4.3 Evidential beliefs, 5 Why are convictions internal? then advance the core thesis: convictions are non-Bayesian beliefs because, following the two-axis information hypothesis, they involve meaning as well as development.

Section snippets

The two-axis information hypothesis

The proposed two-axis information hypothesis affords a taxonomy of beliefs. If the proposed differences among beliefs are granted, the conclusion that Bayes's rule is problematic is readily clear.

The first axis categorizes beliefs as either about the internal world (self) or external world (environment). We will call this axis the “Domain of Information”, because what matters here is the subject matter of the belief. The term “internal” is employed to denote beliefs about the self. Beliefs

Why convictions?

Psychologists have focused on desire, morale and aspirations, which are all related to convictions. Economists have, at least until recently, ignored morale—which is strange given the role of morale in explaining creativity, productivity, the division of labor, entrepreneurship, the development of capability and economic growth (Khalil, 1997a, Khalil, 2008). In particular, morale is important for the functioning of organizations and, hence, has ramifications for the theory of the firm (

The issue of meaning (context): some philosophy of science

The question of “meaning” has been the focal point of many debates about the distinctive methodology in the social sciences that sets the social sciences apart from natural sciences. Many philosophers of social science, such as Winch (1958), have argued that only human action has meaning that can be understood by fellow beings. Thus, the social sciences differ from the biological sciences, in which the behavior of non-human animals does not – supposedly – involve meaning that can be understood

The issue of development of capability

The issue of meaning sets evidential beliefs, i.e., confidence and perceptions, apart from non-evidential beliefs, i.e., convictions and conceptions. However, the issue of meaning; is not sufficient to set convictions apart from conceptions. The pertinent issue that separates convictions from conceptions is the domain of information. Conceptions, involved in the interpretation of Rubin's Vase or the Asian disease remedy, are about the environment, and are called here external. Convictions,

First- and second-degree Bayesian fallacy

So, convictions are characterized according to the type and domain of information axes as providing context/meaning (non-evidential) and self-development (internal). As a result, we can identify two degrees of the Bayesian fallacy:

First-degree Bayesian fallacy: One commits the first-degree Bayesian fallacy when one treats convictions (non-Bayesian beliefs) as no different from confidence or perceptions (Bayesian beliefs).

For example, one commits the first-degree Bayesian fallacy when one

Conclusion

Not all beliefs are born equal. The proposed four-way distinction of beliefs would, foremost, help us to avoid the Bayesian fallacy. One commits the Bayesian fallacy by treating beliefs as if they are all equally updatable via Bayes's rule. The four-way distinction allows us to identify one kind of beliefs, “convictions,” which proves to be of particular importance. Convictions are about internal motivations, which differ from external motivations or what economists call “incentives” and

Acknowledgments

The paper benefited from the support of the Konrad Lorenz Institute for Evolution and Cognition Research (Altenberg, Austria) and Monash University's Faculty Research Grants 2006 and 2007. Early drafts benefited from the comments of Alex Viskovatof, Daniel Palmer, John Shook, Adam Gifford, Young Back Choi, Pekka Mäkelä, John Nye, Jonathan Baron, Jack Vromen, Sean Flynn, Frank Ryan, Richard Posner, Ian McDonald, participants of seminars at the University of Helsinki and the Washington University

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