Abstract
This essay answers the “Bayesian Challenge,” which is an argument offered by Bayesians that concludes that belief is not relevant to rational action. Patrick Maher and Mark Kaplan argued that this is so because there is no satisfactory way of making sense of how it would matter. The two ways considered so far, acting as if a belief is true and acting as if a belief has a probability over a threshold, do not work. Contrary to Maher and Kaplan, Keith Frankish argued that there is a way to make sense of how belief matters by introducing a dual process theory of mind in which decisions are made at the conscious level using premising policies. I argue that Bayesian decision theory alone shows that it is sometimes rational to base decisions on beliefs; we do not need a dual process theory of mind to solve the Bayesian Challenge. This point is made clearer when we consider decision levels: acting as if a belief is true is sometimes rational at higher decision levels.
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Notes
Maher (1986) agreed that these are the only ways of identification so far considered, however, he did not rule out the possibility of other ways, though he seemed to place the burden of producing one on those who reject the Bayesian Challenge.
I am not considering here the cost of belief acquisition, as I am assuming that the agent already has the belief—he acquired it before the need for a decision arose. I think this is the best way to frame the problem, as cost of belief acquisition has already been paid, regardless of what the agent does next. However it may seem strange to think that the agent actually has a belief that it will rain with the probability of it raining being merely 0.5. However, I don’t think this is a deep problem for the example, for there are examples of people holding beliefs on far less probability. And even if belief in a proposition with this probability is problematic, other examples could easily be constructed in which the probability of the believed proposition is higher. I use this one for the sake of continuity with Maher’s argument.
One might argue that decision making methods like Maximin would be less costly than calculating expected utility. Thus it should be considered in the above umbrella example. As my point in the example wasn’t to show that acting as a belief is true can be more rational than any decision making method, only that it can be more rational than calculating expected utility, I don’t see this as a problem. However, one might reply that Maximin is very likely a better decision making method than acting as if a belief is true, given the acquisition cost of the belief, so much so that the Bayesian Challenge could easily be replaced with an equally potent “Maximin Challenge” to acting on beliefs. I think this argument needs to assume that the decision costs regarding acting on a belief include those of belief acquisition, which I argued in an earlier note need not be considered. Given the fact that acting on beliefs that one already holds is very fast and involves a minimal amount of effort, its calculation cost is significantly lower than methods like Maximin. Sometimes Maximin’s advantage in producing better decisions outweighs this greater cost, but often it won’t. As my claim here is the minimal one that it is sometimes, perhaps often, rational to act on beliefs (not the stronger one that it is always rational to act on beliefs), I think it is adequately supported by the examples given.
Maher’s reply was in the context of considering an objection to his Bayesian theory of rational acceptance. However, his reply applies to all decision problems.
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Acknowledgements
I would like to thank Patrick Maher, Gary Ebbs, and Kevin Heinrich for their useful comments and suggestions.
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Sargent, M. Answering the Bayesian Challenge. Erkenn 70, 237–252 (2009). https://doi.org/10.1007/s10670-008-9142-x
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DOI: https://doi.org/10.1007/s10670-008-9142-x