Decision Theory

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.

“Radical The paper provides a survey of arguments for claims that rational agents should have transitive preferences and argues that they are not valid. The presentation is based on a chapter for the forthcoming Oxford Handbook of Rational and Social Choice.

There is, however, an important subjective difference; the purpose of the essay is to exploit it. A purely logical analysis cannot adjudicate the following dispute: an agent, wishing to preserve an air of ignorance and innocence, may claim merely to have selected P, while an analyst, wishing to prove knowledge and guilt, may claim that the agent 'really' discounted Q, as a relevant reason for action. Such a dispute about basicness of actions is meaningful, if not resolvable. Thus, if the (...) incontinent agent's second-order choice were a mere event, i.e. if its very description did not depend on the agent's or analyst's own interests, we could scientifically describe the place of that choice in some causal chain of events. But just this claim of neutral or independent description cannot be granted to the causal theorist. To act 'by choice' is not to have one's behavior caused by some event; it is just to act freely. Moreover, because we may not even know the objective effects of some choice, I use the above distinction between 'selecting' and 'discounting' as the basis for distinguishing two types of moral dilemmas: one choice rule will presuppose a correspondence, and the other a consistency, notion of truth. Choice must agree either with the facts or with other choices in order for it to be a datum for attributions of identity. ; S. All pleasant things are to be pursued. ; U. All painful things are to be avoided. ; P. Object x will produce pleasure . ;but Q. Object x will produce unhappiness . ;The word 'but' is just one way of ordering P and Q, as different reasons or motivations for action; more generally, P and Q are comparable. The preference R is a characteristic first-order choice only of the profligate; although the incontinent agent believes R, s/he simplifies that preference to P, in order to pursue x. There is nothing deductively irrational about incontinence. Similarly, the 'impetuous' agent simplifies preference R, as a description of the context of action, before perceiving x, and is thus 'unconscious' of 'acting against choice'. There is no objective difference between the second-order choices of the weak and impetuous incontinent agents. ;Because Aristotle offers an analysis of incontinent action with the epithet that the incontinent agent 'acts against choice', with the cognate claim that to exercise choice is to prefer one thing to another, I address this analysis to a more general dilemma between decisionistic and causal accounts of action. I argue that 'choice' can be explicated as the preference of long- to short-term interest, where 'incontinent' action is the pursuit of the short-term despite an agent's belief in consequent negative long-term effects. Thus, the original or general preference of long-term interest is only a first-order choice; the contextual or particular use of that preference ordering is a second-order choice. In order to pose the incompatibility of causal and decisionistic models of action, I adapt two Socratic/hedonistic premises. (shrink)

In (Hertwig et al. , 2003) Hertwig et al. draw a distinction between decisions from experience and decisions from description. In a decision from experience an agent does not have a summary description of the possible outcomes or their likelihoods. A career choice, deciding whether to back up a computer hard drive, cross a busy street, etc., are typical examples of decisions from experience. In such decisions agents can rely only of their encounters with the corresponding prospects. By contrast, an (...) agent furnished with information sources such as drug-package inserts or mutual-fund brochures—all of which describe risky prospects—will often make decisions from description. In (Hertwig et al. , 2003) it is shown (empirically) that decisions from experience and decisions from description can lead to dramatically different choice behavior. Most of these results (summarized and analyzed in (Hertwig, 2009)) are concerned with the role of risk in decision making. This article presents some preliminary results concerning the role of uncertainty in decision-making. We focus on Ellsberg’s two-color problem and consider a chance setup based on double sampling. We report empirical results which indicate that decisions from description where subjects select between a clear urn, the chance setup based on double sampling and Ellsberg’s vague urn, are such that subjects perceive the chance setup at least as an intermediate option between clear and vague choices (and there is evidence indicating that the double sampling chance setup is seen as operationally indistinguishable from the vague urn). We then suggest how the iterated chance setup can be used in order to study decisions from experience in the case of uncertainty. (shrink)

The disjunction effect (Tversky and Shafir in Psychol Sci 3:305–309, 1992) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage’s (Cognition 57:31–95, 1954) sure-thing principle, one of the basic axioms of the rational theory of decision-making. The phenomenon was attributed to a lack of (...) clear reasons for accepting an option (x) when the subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction into the text-problem of a non-relevant goal. (shrink)

Frank Knight (1921) famously distinguished the epistemic modes of certainty, risk, and uncertainty in order to characterize situations where deterministic, probabilistic or possibilistic foreknowledge is available. Because our probabilistic knowledge is limited, i.e. because many systems, e.g. the global climate, cannot be described and predicted probabilistically in a reliable way, Knight's third category, possibilistic foreknowledge, is not simply swept by the probabilistic mode. This raises the question how to justify possibilistic predictionsincluding the identication of the worst case. The development of (...) such a modal methodology is particularly vital with respect to predictions of climate change. I show that a methodological dilemma emerges when possibilistic predictions are framed in traditional terms and argue that a more nuanced conceptual framework, distinguishing dierent types of possibility, should be used in order to convey our uncertain knowledge about the future. The new conceptual scheme, however, questions the applicability of standard rules of rational decision-making, thus generating new challenges. (shrink)

The classical theory of rational choice is built on several important internal consistency conditions. In recent years, the reasonableness of those internal consistency conditions has been questioned and criticized, and several responses to accommodate such criticisms have been proposed in the literature. This paper develops a general framework to accommodate the issues raised by the criticisms of classical rational choice theory, and examines the broad impact of these criticisms from both normative and positive points of view.

El artículo se propone mostrar la originalidad de la libertad kierkegaardiana, concentrada en una decisión absoluta que determina por entero la realidad del sujeto singular existente. La decisión produce la síntesis de la existencia personal, unificando todos los elementos y dimensiones que configuran la vida humana, y armonizando las fuerzas del yo hacia la confluencia en un mismo fin, a saber, en el Ser absoluto. La unidad interior producida por la decisión es posible gracias al “salto” trascendente de la libertad, (...) por el cual la existencia humana se afirma en el fundamento uno y simple del cual ella procede. --- This paper attempts to show the originality of Kierkegaard’s notion of freedom, that brings into focus an absolute decision that wholly determines the reality of the singular existing subject. Such decision brings forth the synthesis of personal existence, unifying all the elements and dimensions that constitute human life, and harmonizing the strengths of the self toward their confluence in one final end, which is absolute Being. Immanent unity brought about by the decision is possible due to a transcendental “leap” of freedom, whereby human existence affirms itself on the One and Simple Foundation out of which it proceeds. (shrink)

SummaryA critical outline, primarily for non‐professionals, of some leading ideas and normative implications of “Bayesian Decision Theory”.Violations of the postulated transitivity of the chooser's preference relation are not necessarily symptoms of irrationality. Indeed, the overall normative constraint of “consistency” is too restrictive a guide for many real‐life choices. Rational choice might perhaps be more usefully conceived as an informal art, rather than as the pursuit, in Bayesian style, of maximal expected utility.RésuméUne description critique, destinée avant tout aux non‐professionnels, de quelques (...) idées directrices et implications normatives de la «theorie bayésienne de la décision».Le fait que la transitivité qu'on exige de la relation de préférence du décideur soit violée ne doit pas ětre nécessairement interprétée comme un signe d'irrationnalité. En effet, la contrainte normative universelle de «consistence» est un guide trop restrictif pour maint choix de la vie réelle. Le choix rationnel pourrait ětre plus utilement conçu comme un art, et non comme une recherche à la Bayes de L'utilité maximale attendue.ZusammenfassungEs wird eine kritische Darstellung einiger Hauptgedanken und normativen Implikationen der Bayesschen Entscheidungstheorie vorgelegt, die sich vor allem an Nichtprofessionelle richtet.Verletzungen der postulierten Transitivität der Relation, die das Vorziehen des Wählers ausgedrückt, sind nicht notwendigerweise Symptome für Irrationalität. Die normative Forderung der durchgängigen Konsistenz ist in der Tat als Führer in manchen aus dem Leben gegriffenen Wahlsituationen zu restriktiv. Rationale Entscheidungen sollten vielleicht in nützlicherer Weise als eine Kunst und nicht als das Verfolgen maximaler, erwarteter Nützlichkeit im Sinne Bayes' betrachtet werden. (shrink)

We consider a special set of risky prospects in which the outcomes are either life or death. There are various alternatives to the utilitarian objective of minimizing the expected loss of lives in such prospects. We start off with the two-person case with independent risks and construct taxonomies of ex ante and ex post evaluations for such prospects. We examine the relationship between the ex ante and the ex post in this restrictive framework: There are more possibilities to respect ex (...) ante and ex post objectives simultaneously than in the general framework, i.e. without the restriction to binary utilities. We extend our results to n persons and to dependent risks. We study optimal strategies for allocating risk reductions given different objectives. We place our results against the backdrop of various pro-poorly off value functions for the evaluation of risky prospects. (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.

The feedback arrow extending from the response to the distal state in the lens model, together with Brunswik's dictum that the organism is a stabiliser of systems, implies a dynamic view of behaviour. This paper describes the main problems in the study of dynamic decision making: feedback delays and the feedback structure of the tasks. It also describes microworlds, a methodology for studying dynamic decision making in the laboratory. The results from experiments with microworlds show that subjects have problems compensating (...) for feedback delays and side effects. These results are discussed in terms of Brunswik's distinction between perception and thinking. (shrink)

This paper combines Alfred Shultz and Herbert Simon's theories of action in order to understand the grey area between dynamic and completely unstructured decision making better. As a result I have put together a specific scheme of how choice elements are represented from an agent's personal experience, so as to create a bridge between the phenomenological and cognitive-procedural approaches of decision making. I first look at the key points of their original models relating Alfred Schutz's “provinces of meaning” and Herbert (...) Simon's “satisficing” mechanism. I then consider the particular concept of intentionality and reasoning by analogy for different choice settings. Finally I have suggested a perspective based on creative behaviour and sense-making for ill-structured conditions. (shrink)

Decision theory aims to provide mathematical analysis of which choice one should rationally make in a given situation. Our current decision theory norms have been very successful, however, several problems have proven vexing for standard decision theory. In this paper, I show that these problems all share a similar structure and identify a class of problems which decision theory overvalues. I demonstrate that agents who follow current standard decision theory can be exploited and have their preferences reordered if offered decision (...) problems of this class. I show that preference reordering is a serious problem, which motivates my search for a decision theory which is immune to exploitation. I find Dr. Nick Smith’s theory of Rationally Negligible Probabilities cannot be exploited in this way and discuss why agents should adopt it. (shrink)

It is claimed in the structural realism in philosophy of science that scientists aim to preserve the true structure, represented by the equations in their models. We reinterpret structural realism as a doctrine involving representation. Proving the existence of a representation theorem secures the problem of lacking independent criteria for identification between structure and non?structure. This paper argues that a similar realist view of structure can be found in the theory of consumption in which the Fisherian framework of intertemporal choices (...) is regarded as the true structure of the consumption function. Unlike the passive strategy of inducing the structure contained in structural realism, economists define structure in terms of invariance under intervention. Such a definition serves as a crucial device to examine and develop models for the adequacy of representing the structure of the consumption functions. JEL Classification: B22, B41, C50, E21. (shrink)