Decision-Theoretic Frameworks

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult (...) to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: as we argue, continuity for easy cases gives rise to a sorites. (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)

A method for forcing norms onto individual agents in a multi-agent system is presented. The agents under study are supersoft agents: autonomous artificial agents programmed to represent and evaluate vague and imprecise information. Agents are further assumed to act in accordance with advice obtained from a normative decision module, with which they can communicate. Norms act as global constraints on the evaluations performed in the decision module and hence no action that violates a norm will be suggested to any agent. (...) Further constraints on action may then be added locally. The method strives to characterise real-time decision making in agents, in the presence of risk and uncertainty. (shrink)

We suscribe to an account of framing-effects in decision theory in terms of an inference to a background informationa by the hearer when a speaker uses a certain frame while other equivalent frames were also available. This account was sketched by Craig McKenzie. We embed it in Bolker-Jeffrey decision model - one main reason of this is that this latter model makes preferences bear on propositions. We can deduce a given anomaly or cognitive bias in a formal decision theory. This (...) leads to some philosophical considerations on the relationship between the rationality of preferences and the sensitivity to descriptions or labels of states of affairs in decision-making. (shrink)

This dissertation interprets the lack of uniqueness in probability representations of agents' degrees of belief in the decision theory of Richard Jeffrey as a formal statement of an important epistemological problem: the underdetermination of our attributions of belief and desire to agents by the evidence of their observed behaviour. A solution is pursued through investigation of agents' attitudes to information of a conditional nature. ;As a first step, Jeffrey's theory is extended to agents' conditional attitudes of belief and desire by (...) introduction of a definition of conditional desirability. The second step is an analysis of agents' attitudes to conditionals. Following Adams it is argued that the probability of a conditional is the conditional probability of its consequent given the antecedent. Since numerous 'trivialization' results show that no proposition could be such that this were the case, it is proposed that conditionals express a variable proposition as a function of the context in which they are asserted. The consequent technical treatment of conditionals as proposition-valued functions of sets of possible worlds delivers Adams' thesis as a natural consequence without fear of trivialization. ;Conditionals are the underlying objects of the decision theory that is presented in the final chapter. A representation theorem is proven for preferences defined over sets of such conditionals satisfying certain closure conditions, where an agent is understood to prefer one conditional over another just in case she prefers that the former by true rather than the latter. The theorem establishes that a rational preference ranking of conditionals implies the existence of a unique probability function and a desirability function unique up to choice of scale, that agree with the preference ranking, and that these functions satisfy both the axioms of Jeffrey's decision calculus and Adams' thesis. The theorem is interpreted as saying that elicitation of an agent's choices amongst conditional options suffices to determine our attributions of belief and desire to them. (shrink)

Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision (...) rule is based not only on a profile in the standard sense, but in addition on a profile of judged-right procedures. To justify this decision rule, I present a set of simple axioms leading to it as the only solution. (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)

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)

Dreier shows how the formal apparatus of decision theory is connected to some abstract issues in moral theory. He begins by explaining how to think about utility and the advice that decision theory gives us, in particular, decision theory does not assume or insist that all rational agents act in their own self-interest. Next he examines decision theory’s contributions to social contract theory, with emphasis on David Gauthier’s rationalist contractualism. Dreier’s third section considers a reinterpretation of the formal theory that (...) decision theorists use: utility might represent goodness rather than preference. His last section discusses Harsanyi’s Theorem. (shrink)

This paper presents a decision theory which allows subjects to account for the uncertainties of their probability estimates. This is accomplished by modelling beliefs about states of nature by means of a class of probability measures. In order to represent uncertainties of those beliefs a measure of epistemic reliability is introduced. The suggested decision theory is evaluated in the light of empirical evidence on ambiguity and uncertainty in decision making. The theory is also compared to Tversky & Kahneman's prospect theory.

In this commentary, after first summarizing the three major theses of Jeffrey's paper Probability and Falsification: Critique of the Popper Program, and sketching out what I take to be his central argument, I criticize Jeffrey on two grounds. The first is that he has failed to explain why his version of Bayesianism provides us with better theories upon which to make decisions; the second is that he has offered a theory about decision-making that by-passes the important question: How can we (...) make more rational decisions? (shrink)

I explore the prospects for modelling epistemic rationality (in the probabilist setting) via an epistemic decision theory, in a consequentialist spirit. Previous work has focused on cases in which the truth-values of the propositions in which the agent is selecting credences do not depend, either causally or merely evidentially, on the agent’s choice of credences. Relaxing that restriction leads to a proliferation of puzzle cases and theories to deal with them, including epistemic analogues of evidential and causal decision theory, and (...) of the Newcomb Problem and ‘Psychopath Button’ Problem. A variant of causal epistemic decision theory deals well with most cases. However, there is a recalcitrant class of problem cases for which no epistemic decision theory seems able to match our intuitive judgements of epistemic rationality. This lends both precision and credence to the view that there is a fundamental mismatch between epistemic consequentialism and the intuitive notion of epistemic rationality; the implications for understanding the latter are briefly discussed. (shrink)

This paper revisits the Pasadena game (Nover and Háyek 2004), a St Petersburg-like game whose expectation is undefined. We discuss serveral respects in which the Pasadena game is even more troublesome for decision theory than the St Petersburg game. Colyvan (2006) argues that the decision problem of whether or not to play the Pasadena game is ‘ill-posed’. He goes on to advocate a ‘pluralism’ regarding decision rules, which embraces dominance reasoning as well as maximizing expected utility. We rebut Colyvan’s argument, (...) offering several considerations in favour of the Pasadena decision problem being well posed. To be sure, current decision theory, which is underpinned by various preference axioms, leaves indeterminate how one should value the Pasadena game. But we suggest that determinacy might be achieved by adding further preference axioms. We conclude by opening the door to a far greater plurality of decision rules. We suggest how the goal of unifying these rules might guide future research. (shrink)

Bayesian decision theorists argue that rational agents should always perform acts that maximize subjective expected utility. To justify this claim, they prove representation theorems which are designed to show that any decision maker whose beliefs and desires satisfy reasonable axiomatic constraints will necessarily behave like an expected utility maximizer. The existence of such a representation result is a prerequisite for any adequate account of rational choice because one is only able to determine what a decision theory says about beliefs and (...) desires by looking at the axioms used in the proof of its representation result. ;I examine a number of versions of decision theory and their representation theorems. Particular attention is paid to so-called causal and evidential decision theories. It is argued that only the latter has an adequate representation which is found in a theorem due to Ethan Bolker which was adapted to the decision theoretic context by R. Jeffrey. I remove the single outstanding problem with Bolker's theorem by reformulating it in a way which yields a unique probability and utility representation. This is possible because, unlike Bolker, I make use of axioms which govern not only preference but comparative probability. ;I show how this reformulated version of Bolker's result can be further generalized to a representation theorem for a generic theory of conditional expected utility whose basic term is a function which measures the strength of an agent's desires when he supposes that various hypotheses are true. Evidential and causal decision theories are show to be special cases of this generic theory. They differ only in the interpretation they give to the notion of supposition. The evidential account interprets it indicatively, while the causal account views it subjunctively. ;Finally, I show how my generic representation theorem for conditional decision theory can serve as a foundation for both causal and evidential decision theories. This provides the first fully adequate representation result for causal decision theory, thereby removing its most serious defect. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

The existence of a transitive, complete, and weakly independent relation on the full set of gambles implies the existence of a non-Ramsey set. Therefore, each transitive and weakly independent relation on the set of gambles either is incomplete or does not have an explicit description. Whatever tools decision theory makes available, there will always be decision problems where these tools fail us. In this sense, decision theory remains incomplete.

An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure $\langle\mathbf{R}, \leq, +\rangle$ this gives a decision procedure for the ∃ x∀ y-part of the theory of all substructures, yet we show that the ∃ x 1x 2 ∀ y-part, and the entire theory, is Π 1 1 -complete. The theory of all ordered subsemigroups (...) of $\langle\mathbf{R}, \leq, +\rangle$ is also shown Π 1 1 -complete. Applications in the philosophy of science are mentioned. (shrink)

The simple heuristics that may indeed usually make us smart–or at least smart enough–in contexts of individual choice will sometimes make us dumb, especially in contexts of social choice. Here each individual choice (or vote) has little impact on the overall choice, although the overall choice is compounded out of the individual choices. I use an example (risk aversion) to illustrate the point.

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.

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)

This French paper is a preliminary version of P. Mongin, "Does Optimization Imply Rationality?", Synthese, 124, 2000, p. 73-111, to which readers are referred to.