Decision Theory

I present a new argument for the repugnant conclusion. The core of the argument is a risky, intrapersonal analogue of the mere addition paradox. The argument is important for three reasons. First, some solutions to Parfit’s original puzzle do not obviously generalize to the intrapersonal puzzle in a plausible way. Second, it raises independently important questions about how to make decisions under uncertainty for the sake of people whose existence might depend on what we do. And, third, it suggests various (...) difficulties for leading views about the value of a person’s life compared to her nonexistence. (shrink)

The Precautionary Principle (PP) is an influential principle of risk management. It has been widely introduced into environmental legislation, and it plays an important role in most international environmental agreements. Yet, there is little consensus on precisely how to understand and formulate the principle. In this paper I prove some impossibility results for two plausible formulations of the PP as a decision-rule. These results illustrate the difficulty in making the PP consistent with the acceptance of any trade-offs between catastrophic risks (...) and more ordinary goods. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Can an agent deliberating about an action A hold a meaningful credence that she will do A? 'No', say some authors, for 'Deliberation Crowds Out Prediction' (DCOP). Others disagree, but we argue here that such disagreements are often terminological. We explain why DCOP holds in a Ramseyian operationalist model of credence, but show that it is trivial to extend this model so that DCOP fails. We then discuss a model due to Joyce, and show that Joyce's rejection of DCOP rests (...) on terminological choices about terms such as 'intention', 'prediction', and 'belief'. Once these choices are in view, they reveal underlying agreement between Joyce and the DCOP-favouring tradition that descends from Ramsey. Joyce's Evidential Autonomy Thesis (EAT) is effectively DCOP, in different terminological clothing. Both principles rest on the so-called 'transparency' of first-person present-tensed reflection on one's own mental states. (shrink)

There is a puzzle about the very possibility of foreseen but unintended side effects, and solving this puzzle requires us to revise our basic picture of the structure of practical deliberation. The puzzle is that, while it seems that we can rationally foresee, but not intend, bringing about foreseen side effects, it also seems that we rationally must decide to bring about foreseen side effects and that we intend to do whatever we decide to do. I propose solving this puzzle (...) by rejecting the idea that we intend to do whatever we decide to do. My solution involves taking account of the underappreciated role that qualified intentions play in deliberation. I also argue that this solution fares better than those that instead reject the idea that we rationally must decide to bring about foreseen side effects, for these solutions are committed to rejecting the even more compelling idea that decisions rationally serve as the conclusions of practical deliberation. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

There is a long-standing disagreement in the philosophy of probability and Bayesian decision theory about whether an agent can hold a meaningful credence about an upcoming action, while she deliberates about what to do. Can she believe that it is, say, 70% probable that she will do A, while she chooses whether to do A? No, say some philosophers, for Deliberation Crowds Out Prediction (DCOP), but others disagree. In this paper, we propose a valid core for DCOP, and identify terminological (...) causes for some of the apparent disputes. (shrink)

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

In the recent literature on episodic memory, there has been increasing recognition of the need to provide an account of its adaptive function. In this context, it is sometimes argued that episodic memory is critical for certain forms of decision making about the future. We criticize existing accounts that try to give episodic memory a role in decision making, before giving a novel such account of our own. This turns on the thought of a link between episodic memory and the (...) emotion of regret. We discuss how both experienced and anticipated regret can have a distinctive influence on decision making, and argue that the ability to recollect past events in episodic memory underpins the capacity to engage in the sophisticated types of mental time travel recruited in experiencing and anticipating regret. (shrink)

I analyze a recent exchange between Adam Elga and Julian Jonker concerning unsharp (or imprecise) credences and decision-making over them. Elga holds that unsharp credences are necessarily irrational; I agree with Jonker's reply that they can be rational as long as the agent switches to a nonlinear valuation. Through the lens of computational complexity theory, I then argue that even though nonlinear valuations can be rational, they come in general at the price of computational intractability, and that this problematizes their (...) use in defining rationality. I conclude that the meaning of "rationality" may be philosophically vague. (shrink)

Behaviourism is the view that preferences, beliefs, and other mental states in social-scientific theories are nothing but constructs re-describing people's behaviour. Mentalism is the view that they capture real phenomena, on a par with the unobservables in science, such as electrons and electromagnetic fields. While behaviourism has gone out of fashion in psychology, it remains influential in economics, especially in ‘revealed preference’ theory. We defend mentalism in economics, construed as a positive science, and show that it fits best scientific practice. (...) We distinguish mentalism from, and reject, the radical neuroeconomic view that behaviour should be explained in terms of brain processes, as distinct from mental states. (shrink)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

review of McLennen's *Rationality and Dynamic Choice*. The topic is important and the discussion is powerful. Some connection with modelling and simulation would be valuable.

This article argues that Lara Buchak’s risk-weighted expected utility theory fails to offer a true alternative to expected utility theory. Under commonly held assumptions about dynamic choice and the framing of decision problems, rational agents are guided by their attitudes to temporally extended courses of action. If so, REU theory makes approximately the same recommendations as expected utility theory. Being more permissive about dynamic choice or framing, however, undermines the theory’s claim to capturing a steady choice disposition in the face (...) of risk. I argue that this poses a challenge to alternatives to expected utility theory more generally. (shrink)

This paper argues that instrumental rationality is more permissive than expected utility theory. The most compelling instrumentalist argument in favour of separability, its core requirement, is that agents with non-separable preferences end up badly off by their own lights in some dynamic choice problems. I argue that once we focus on the question of whether agents' attitudes to uncertain prospects help define their ends in their own right, or instead only assign instrumental value in virtue of the outcomes they may (...) lead to, we see that the argument must fail. Either attitudes to prospects assign non-instrumental value in their own right, in which case we cannot establish the irrationality of the dynamic choice behaviour of agents with non-separable preferences. Or they don't, in which case agents with non-separable preferences can avoid the problematic choice behaviour without adopting separable preferences. (shrink)

Standard decision theory, or rational choice theory, is often interpreted to be a theory of instrumental rationality. This dissertation argues, however, that the core requirements of orthodox decision theory cannot be defended as general requirements of instrumental rationality. Instead, I argue that these requirements can only be instrumentally justified to agents who have a desire to have choice dispositions that are stable over time and across different choice contexts. Past attempts at making instrumentalist arguments for the core requirements of decision (...) theory fail due to a pervasive assumption in decision theory, namely the assumption that the agent’s preferences over the objects of choice – be it outcomes or uncertain prospects – form the standard of instrumental rationality against which the agent’s actions are evaluated. I argue that we should instead take more basic desires to be the standard of instrumental rationality. But unless agents have a desire to have stable choice dispositions, according to this standard, instrumental rationality turns out to be more permissive than orthodox decision theory. (shrink)

This article reviews Herbert Simon's theory of bounded rationality, with a view of deemphasizing his "satisficing" model, and by contrast, of emphasizing his distinction between "procedural" and "substantive" rationality. The article also discusses a possible move from neo-classical economists to respond to Simon's criticisms, i.e., a reduction of bounded rationality to a special case of second-optimization, using Stigler's search theory. This move is eventually dismissed.

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires that revised beliefs (...) incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

In a widely discussed forthcoming article, “What you can't expect when you're expecting,” L. A. Paul challenges culturally and philosophically traditional views about how to rationally make major life-decisions, most specifically the decision of whether to have children. The present paper argues that because major life-decisions are transformative, the only rational way to approach them is to become resilient people: people who do not “over-plan” their lives or expect their lives to play out “according to plan”—people who understand that beyond (...) a certain limit, life cannot be rationally planned and must be accepted as it comes. I show that this focus on resilience—on self-mastery—stands in direct opposition to culturally dominant attitudes toward decision-making, which focus not on the self-mastery but on control and mastery over one's surroundings. In short, I argue that if Paul's general point about transformative experiences is correct, it follows that we rationally ought to adopt a very different approach to life choices, self-development, and the moral education of our children than currently-dominant cultural norms and practices suggest. (shrink)

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational (...) and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the individuals. While (...) the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (shrink)