We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition (...) of rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Utility maximization is a key element of a number of theoretical approaches to explaining human behavior. Among these approaches are rational analysis, ideal observer theory, and signal detection theory. While some examples of these approaches define the utility maximization problem with little reference to the bounds imposed by the organism, others start with, and emphasize approaches in which bounds imposed by the information processing architecture are considered as an explicit part of the utility maximization problem. These latter (...) approaches are the topic of this issue of the journal. (shrink)

The rational price of the Pasadena and Altadena games, introduced by Nover and Hájek (2004 ), has been the subject of considerable discussion. Easwaran (2008 ) has suggested that weak expectations — the value to which the average payoffs converge in probability — can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders (...) the problem more realistic and accounts for the role of weak expectations. In particular, we demonstrate that in a bounded utility framework, all agents, even if they have different value functions and disagree on the price of an individual game, will finally agree on the rational price of a repeated, averaged game. Thus, we explain the intuitive appeal of weak expectations, while avoiding both trivialization of the original paradox and the drawbacks of previous approaches. (shrink)

Econometric analysis of discrete choice has made considerable use of random utility models to interpret observed choice behavior. Much empirical research concerns choice problems in which persons act with partial knowledge of the utilities of the feasible actions. Economists use random expected utility models to analyze such choice problems. A common practice is to specify fully the expectations that persons hold, in which case choice analysis reduces to inference on preferences alone. However, the expectations assumptions made in empirical (...) research rarely have much foundation. To enable more credible research, this paper considers inference when one specifies a set of expectations that decision makers may plausibly hold. I first pose the idea in abstraction and then specialize to binary response with linear utilities, where the analysis is particularly straightforward. I initially assume that decision makers possess unique subjective probability distributions on the states of nature and make choices that maximize expected utility. I later consider the possibility that persons place only partial probabilistic structure on the states of nature and make undominated choices. (shrink)

Game theory is a branch of economics that uses powerful mathematical models to predict what agents ought to do when interacting with other agents strategically. Bounded rationality is a sub-field of game theory that sets out to explain why, in some interesting cases, people don't act according their utility maximizing strategies, as described by game theory. Interactive Epistemology is formal tool used by Game Theorists and computer scientists to model interactive cases of knowledge. This interesting and useful tool (...) has been previously ignored by philosophers. I'd like to introduce philosophers to interactive epistemology. After doing so, I'll go on to describe the way I've used this powerful formal tool in my own research, by giving some arguments about Bounded Epistemology, which is an analogue of Bounded Rationality, and, if I'm right, is explainable according to many, but not all, of the same models. Doing so, however, requires first setting out and explaining many of these concepts more fully. (shrink)

The bounded rationality theory has been perceived by social scientists as a more flexible version of the rational choice theory, also called expected utility theory. The former has the avantage of taking into consideration the fact that information is generally costly. It corrects the RCT on an important point. For the social sciences, the RCT is very useful, but far from representing a general theory which could explain the various kinds of behaviour the social sciences are confronted to, (...) even in its more flexible BRT version. The article makes the postulates underlying the RCT and the BRT explicit and shows that, when some of the postulates are eliminated, a genuinely general model is obtained: the model which is actually used in convincing sociological analyses.La Théorie de la rationalité limitée a été perçue par les sciences sociales comme une version assouplie de la théorie du choix rationnel, aussi appelée Modèle de l’utilité espérée. La TRL a l’avantage de tenir compte notamment du fait que l’information est généralement coûteuse, corrigeant ainsi l’irréalisme de la TCR sur un point essentiel. Du point de vue des sciences sociales, la TCR est fort utile, mais elle est loin de proposer une théorie générale de la rationalité permettant de rendre compte des divers types de comportement dont les sciences sociales ont à connaître, même dans sa version assouplie de la TRL. On identifie ici les postulats de la TCR et de la TRL et l’on montre qu’en abandonnant certains de ces postulats, l’on définit un modèle, le MRG qui, lui, peut prétendre à la généralité. C’est celui qui est utilisé naturellement par les analyses sociologiques qui ses sont imposées. (shrink)

With the discovery of voluminous discordant empirical evidence, maximizing expected utility is rapidly disappearing as the core of the theory of human rationality, and a theory of bounded rationality, embracing both the processes and products of choice, is replacing it. There remains a large task of organizing our picture of economic and social processes and adding the new facts needed to shape the theory in an empirically sound way. It is also urgent that new tools now available for (...) conducting empirical inquiry and constructing models be incorporated in social science graduate education. (shrink)

In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the (...) probability distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear. (shrink)

It is known that, on average, people adapt their choice of memory strategy to the subjective utility of interaction. What is not known is whether an individual's choices are boundedly optimal. Two experiments are reported that test the hypothesis that an individual's decisions about the distribution of remembering between internal and external resources are boundedly optimal where optimality is defined relative to experience, cognitive constraints, and reward. The theory makes predictions that are tested against data, not fitted to it. (...) The experiments use a no-choice/choice utility learning paradigm where the no-choice phase is used to elicit a profile of each participant's performance across the strategy space and the choice phase is used to test predicted choices within this space. They show that the majority of individuals select strategies that are boundedly optimal. Further, individual differences in what people choose to do are successfully predicted by the analysis. Two issues are discussed: the performance of the minority of participants who did not find boundedly optimal adaptations, and the possibility that individuals anticipate what, with practice, will become a bounded optimal strategy, rather than what is boundedly optimal during training. (shrink)

A TRADITIONAL VIEW OF UTILITY AND RIGHTS According to a conventional view, no project could be more hopelessly misconceived than the enterprise of attempting a utilitarian derivation of fundamental rights. We are all familiar – too familiar, perhaps – with the arguments that support this conventional view, but let us review them anyway. We may begin by recalling that, whereas the defining value of utilitarianism – pleasure, happiness or welfare – contains no mention of the dignity or autonomy of (...) human beings, it is this value which utilitarianism in all its standard forms invokes as the criterion of right action. Worse, insofar as utilitarian policy must have as its goal the maximization of welfare conceived as an aggregate summed over the utilities of everyone affected, legal and political utilitarianism seems bound to have a collectivist bias, trading on the dangerous fiction of a social entity and ignoring the distinctness of separate selves with their several incommensurable claims. It seems that, if individuals can appear in the utilitarian calculus at all, it will only be as ciphers, abstract place-holders for units of welfare. For, as an aggregative value, utility must be indifferent to distribution, and insensitive to the preeminently distributive considerations marked by claims about rights. So, if whatever has utility can be broken down into units or elements which are subject to measurement or at least comparison by a common standard, then it will always be possible that a very great loss of welfare for one man or a few men can be justified if it produces a great many small increments of welfare for a vast multitude of men. (shrink)

Previous theory and research on bounded rationality has emphasized how limited cognitive resources constrain people from making utility maximizing choices. This paper expands the concept of bounded rationality to consider how people’s rationality may be constrained by their internalization of a qualitatively distinct standard for sound judgment, which is commonly labeled reasonableness. In contrast to rationality, the standard of reasonableness provides guidance for making choices in situations that involve balancing incommensurable values and interests or reconciling conflicting points-of-view. (...) We review recent evidence showing that laypeople readily recognize the distinctions between rationality and reasonableness and thus are able to utilize these as distinct standards to inform their everyday decision-making. The fact that people appear to have internalized rationality and reasonableness as distinct standards of sound judgment supports the notion that people’s pursuit of rationality may be bounded by their determination to also be reasonable. (shrink)

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new (...) generalizations of Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)

An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.

Classical utilitarianism is very demanding and entails some counter-intuitive implications in moral dilemmas such as the trolley problem in deontological ethics and the repugnant conclusion in population ethics. This article presents how one specific modification of utilitarianism can avoid these counter-intuitive implications. In this modified utilitarian theory, called ‘discounted’ or ‘mild’ utilitarianism, people have a right to discount the utilities of others, under the condition that people whose utility is discounted cannot validly complain against such discounting. A complaint made (...) by a utility discounted person is not valid if either the existence of the discounting people in that option is in a specific sense necessary or the existence of the discounted person is in a sense not necessary. According to mild utilitarianism, we should choose the option that maximizes the total validly discounted or complaint-free discounted utility, i e. the sum of everyone’s utility minus the complaint-free discounts. As there are two conditions that make a complaint invalid, this right to discount can be translated into two versions: the right to bodily autonomy and the right to procreation autonomy. The former right relates to the mere means principle in deontological ethics, the latter right is useful in avoiding the repugnant conclusion problem in population ethics. The possibility of democratically imposing an upper bound on the permissible amount of discounting is discussed. (shrink)

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new (...) generalizations of Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized (...) version of the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory. (shrink)

Decision theory seems to offer a very attractive normative framework for individual and social choice under uncertainty. The decisionmaker should think of her choice situation, at any given moment, in terms of a set of possible outcomes, that is, specifications of the possible consequences of choice, described in light of the decisionmaker's goals; a set of possible actions; and a "state set" consisting of possible prior "states of the world." It is this framework for choice which provides the foundation for (...) expected utility theory, as demonstrated in the work of Leonard Savage. Problems arise, however, when the decisionmaker is boundedly rational: when the mental process of thinking about outcomes, actions, and states is itself expensive and time consuming. In the case of the unboundedly rational decisionmaker, decision theory enjoins her to employ maximally specific outcomes; to consider all possible actions; and to use a set of mutually exclusive and collective exhaustive states, each of which is sufficiently finely specified so that each action, together with each state, yields one and only one maximally specific outcome. In the case of the boundedly rational decisionmaker, this procedure is either infeasible or, if feasible, irrational. This paper presents the problem of bounded rationality. It surveys possible solutions, none of which are found to be attractive. And it concludes by discussing the difficulties that the problem of bounded rationality poses for the welfarist program for legal scholarship presented by Louis Kaplow and Steven Shavell in their book, Fairness versus Welfare. (shrink)

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in an expected prospect maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random prospect under constraint that the risk measure is bounded above, he then behaves as a “generalized expected utility maximizer” in the following sense. The DM exhibits ambiguity with respect to a family (...) of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called “maxmin under risk” and studied by Maccheroni (Econ Theory 19:823–831, 2002). As an application, we make the link between an expected prospect maximization problem, subject to conditional value-at-risk being less than a threshold value, and a non-expected utility economic formulation involving “loss aversion”-type utility functions. (shrink)

We extend de Finetti’s (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we demonstrate when the prevision of the difference between two such equivalent random variables must be positive. This result conflicts with the usual approach to theories of Subjective Expected Utility, where preference is defined over lotteries. In addition, we (...) explore similar results for unbounded variables when their previsions, though finite, exceed their expected values, as is permitted within de Finetti’s theory. In such cases, the decision maker’s coherent preferences over random quantities is not even a function of probability and utility. One upshot of these findings is to explain further the differences between Savage’s theory (1954), which requires bounded utility for non-simple acts, and de Finetti’s theory, which does not. And it raises a question whether there is a theory that fits between these two. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result (...) is the identification of the continuity condition necessary for the revelation of linear utility. (shrink)

After having explained why economics introduced utility functions and later the axioms about behaviour in a risky environment, the paper examines the interest for microeco-nomics of the concept of bounded rationality. It starts from a simple model of the labour market on which agents scarch and adapt their demands, contributing unconsciously to the emergence of a unique price. More complex models are thereafter introduced, which enables to draw a picture of the variety of possible trajectories in a dynamic (...) microeco-nomic system. This approach enables to enlarge microeconomics and to explain numerous facts poorly taken into account in the traditional presentations.Après avoir rappelé pourquoi la science économique avait introduit les fonctions d’utilité puis l’axiomatique des comportements en face du risque, l’article examine l’apport en microéco-nomie du concept de rationalité limitée. Il le fait à partir d’un modèle simple du marché du travail où les agents cherchent, et adaptent leurs exigences, contribuant, sous certaines hypothèses et sans en avoir conscience, à l’émergence d’un prix unique. Des modèles plus complexes sont ensuite examinés, ce qui permet de dresser un tableau de la variété des trajectoires possibles dans un système microéconomique dynamique. Cette approche permet d’élargir la théorie microéconomique en rendant compte de nombreux faits mal insérés dans la présentation traditionnelle. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the (...) status quo, then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn ⇒ L∇n ⇒ I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n ⇒ Cr∇n⇒ I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories.

“Rationality” in Simon's “bounded rationality” is the principle that humans make decisions on the basis of step-by-step reasoning using systematic rules of logic to maximize utility. “Bounded rationality” is the observation that the ability of a human brain to handle algorithmic complexity and large quantities of data is limited. Bounded rationality, in other words, treats a decision maker as a machine carrying out computations with limited resources. Under the principle of embodied cognition, a cognitive mind is (...) an interactive machine. Turing-Church computations are not interactive, and interactive machines can accomplish things that no Turing-Church computation can accomplish. Hence, if “rationality” is computation, and “bounded rationality” is computation with limited complexity, then “embodied bounded rationality” is both more limited than computation and more powerful. By embracing interaction, embodied bounded rationality can accomplish things that Turing-Church computation alone cannot. Deep neural networks, which have led to a revolution in artificial intelligence, are both interactive and not fundamentally algorithmic. Hence, their ability to mimic some cognitive capabilities far better than prior algorithmic techniques based on symbol manipulation provides empirical evidence for the principle of embodied bounded rationality. (shrink)

Distortions in memory impose important bounds on rationality but have been largely disregarded in economics. While it is possible to learn, it is more difficult, and sometimes impossible, to unlearn. This retention effect lowers individual utility directly or via reduced productivity, and adds costs to principal-agent relationships. The engraving effect states that the more one tries to forget a piece of information the more vivid it stays in memory, leading to a paradoxical outcome. The effects are based on, and (...) are supported by, psychological experiments, and it is shown that they are relevant in many economic situations and beyond. (shrink)

An increasingly prevalent approach to studying human cognition is to construe the mind as optimally allocating limited cognitive resources among cognitive processes. Under this bounded rationality approach (Icard in Philos Sci 85(1):79–101, 2018; Simon in Utility and probability, Palgrave Macmillan, 1980), it is common to assume that resource-bounded cognitive agents approximate normative solutions to statistical inference problems, and that much of the bias and variability in human performance can be explained in terms of the approximation strategies we (...) employ. In this paper, we argue that this approach restricts itself to an unnecessarily narrow scope of cognitive models, which limits its ability to explain how humans flexibly adapt their representations to novel environments. We argue that more attention should be paid to how we form our cognitive representations in the first place, and advocate for pluralistic framework which jointly optimizes over both representations and algorithms for manipulating them. We identify several fundamental trade-offs that manifest in this joint optimization, and draw on recent work to motivate a unified formal framework for this analysis. We illustrate a simplified version of this analysis with a case study in social cognition, and outline several new directions for research that this approach suggests. (shrink)

This research examined whether youth's forecasted risk taking is best predicted by a compensatory (namely, subjective expected utility) or non-compensatory (e.g., single-factor) model. Ninety youth assessed the importance of perceived benefits, importance of perceived drawbacks, subjective probability of benefits, and subjective probability of drawbacks for 16 risky behaviors clustered evenly into recreational and health/safety domains. In both domains, there was strong support for a noncompensatory model in which only the perceived importance of the benefits of engaging in a risky (...) behavior predicted youths' forecasted engagement in risky behavior. The study overcomes earlier methodological weaknesses by fully decomposing participants' assessments into importance and probability aspects for both benefits and drawbacks. As such, the findings provide clear evidence in support of a boundedrationality perspective on youth decision making regarding risk taking. (shrink)

Popper's well-known demarcation criterion has often been understood to distinguish statements of empirical science according to their logical form. Implicit in this interpretation of Popper's philosophy is the belief that when the universe of discourse of the empirical scientist is infinite, empirical universal sentences are falsifiable but not verifiable, whereas the converse holds for existential sentences. A remarkable elaboration of this belief is to be found in Watkins's early work on the statements he calls “all-and-some,” such as: “For every metal (...) there is a melting point.” All-and-some statements are both universally and existentially quantified in that order. Watkins argued that AS should be regarded as both nonfalsifiable and nonverifiable, for they partake in the logical fate of both universal and existential statements. This claim is subject to the proviso that the bound variables are “uncircumscribed” ; i.e., that the universe of discourse is infinite. (shrink)

Extremist views on normative rationality fail to address differences in responding owing to intellectual ability or epistemic self-regulation. Individual difference research thus raises serious questions concerning the scientific utility of universal rationality and universal irrationality theories. However, recent data indicate that computational capacity theories do not account adequately for within-subject variability in normative responding, memory-reasoning independence, and instances of ability-normative reasoning independence.

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero (...) probability. Chapters 3–6 discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future. (shrink)

In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the point of intersection at infinite distance for parallel lines. We examine contrasting interpretations of these notions in the context of Leibniz’s analysis of asymptotes for logarithmic curves and hyperbolas. We point out difficulties that arise due to conflating these notions of infinity. As noted by Rodríguez Hurtado et al., a significant difference exists between the (...) Cartesian model of magnitudes and Leibniz’s search for a qualitative model for studying perspective, including ideal points at infinity. We show how respecting the distinction between these notions enables a consistent interpretation thereof. (shrink)

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is (...) illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable. (shrink)

Abstract The increasing prevalence of armed drones in the conduct of military operations has generated robust debate. Among legal scholars, the crux of the dispute generally pits those who herald the new technology's unparalleled precision against those who view such newfound capabilities as an inducement to employ excessive force. Largely overlooked in the discussion over how drone strikes can be accomplished lawfully is a more fundamental question: Can a model of warfare that eschews any risk of harm to one party (...) be squared with the ethical framework that informs the law of war? This matter has less to do with the technology per se than with a policy orientation that utilizes such technology as a strategy in itself, as opposed to one military tool in a larger arsenal. A corollary to the incongruity of riskless warfare is to query whether the ensuing breakdown of ethical and legal norms unwittingly encourages the very instability that the law of war attempts to control, thereby endangering the civilian populations of all parties to the conflict. While other authors have previously addressed the challenges posed by asymmetry to the law of armed conflict in different formats, this article explores these issues through a hypothetical scenario and seeks to elucidate some of the potential ramifications of the pursuit of physical impunity in war. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities (...) are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory. (shrink)

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to (...) infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue). (shrink)

In this paper it is shown that the most rational of all creatures, Homo Oeconomicus, can be enticed to freely engage in an activity that is guaranteed to lead to his ruin. It is furthermore shown that this is possible if and only if utility functions are unbounded. The paper thus develops an argument in favour of bounded utility functions.

This paper explores the concept of a social evaluation functional in the case of an arbitrary set of alternatives. In the first part, a characterization of projective social evaluations functionals is shown whenever the common restricted domain is the set of all bounded utility functions equipped with the supremum norm topology. The result makes a crucial use, among others, of a continuity axiom. In the second part, a comparison meaningful property is introduced for a social evaluation functional which (...) allows us for obtaining a more general result with no continuity requirements. Finally, an impossibility theorem, which is reminiscent of that is obtained by Chichilnisky in (Q J Econ 97:337–352, 1982) but without using topological conditions, is offered. (shrink)

Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti-fanatics say you should not. Anti-fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti-fanaticism can be turned into a positive argument (...) for a weak version of fanaticism, but only from significantly more contentious premises. In combination, these facts suggest that those who find fanaticism counterintuitive should favor not anti-fanaticism, but an intermediate position that permits agents to have incomplete preferences that are neither fanatical nor anti-fanatical. (shrink)

The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for instance, the information that there are more white balls than black ones). Some implications are shown with regard to the core of the capacity (...) and to two additive measures which can be derived from capacities: the Shapley value and the nucleolus. Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative information inequalities, and the Shapley value does it more strictly than the nucleolus. (shrink)

This article critically discusses the concept of economic rationality, arguing that it is too narrow and specific to encompass the full concept of practical rationality. Economic rationality is identified here with the use of the optimizing model of decision, as well as of expected utility apparatus to deal with uncertainty. To argue that practical rationality is broader than economic rationality, the article claims that practical rationality includes bounded rationality as a particular case, and that bounded rationality cannot (...) be reduced to economic rationality as defined here. (shrink)

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. Of (...) course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

This paper utilizes the enactivist notion of ‘sense-making’ to discuss the nature of depression and examine some implications for treatment. As I understand it, sensemaking is fully embodied, fundamentally affective, and thoroughly embedded in a social environment. I begin by presenting an enactivist conceptualization of affective intentionality and describing how this general mode of intentional directedness to the world is disrupted in cases of major depressive disorder. Next, I utilize this enactivist framework to unpack the notion of ‘temporal desituatedness,’ and (...) maintain that the characteristic symptoms of depression result from a disruption to the future-directed structure of affective intentionality. This can be conceptualized as a loss of “online intelligence” and a shrinking of the field of affordances. Then, I argue that two of the standard modes of treatments for depression, medication and cognitive behavioral therapy, are not fully sufficient means of restoring online intelligence, and that these limitations stem partly from the approaches’ implicit commitment to a brain-bound, overly cognitivist view of the mind. I recommend expressive arts interventions such as dance-movement therapy and music therapy as important supplementary treatment methods that deserve further consideration. Insofar as they revitalize subjects’ bodies and emotions, cultivate an openness to the future, and promote self-insight and social synchrony, these treatment modes not only reflect key insights of enactivism, but also offer great potential for lasting healing. (shrink)

Papers from the conference on AI Risk (published in JETAI), supplemented by additional work. --- If the intelligence of artificial systems were to surpass that of humans, humanity would face significant risks. The time has come to consider these issues, and this consideration must include progress in artificial intelligence (AI) as much as insights from AI theory. -- Featuring contributions from leading experts and thinkers in artificial intelligence, Risks of Artificial Intelligence is the first volume of collected chapters dedicated to (...) examining the risks of AI. The book evaluates predictions of the future of AI, proposes ways to ensure that AI systems will be beneficial to humans, and then critically evaluates such proposals. 1 Vincent C. Müller, Editorial: Risks of Artificial Intelligence - 2 Steve Omohundro, Autonomous Technology and the Greater Human Good - 3 Stuart Armstrong, Kaj Sotala and Sean O’Heigeartaigh, The Errors, Insights and Lessons of Famous AI Predictions - and What they Mean for the Future - 4 Ted Goertzel, The Path to More General Artificial Intelligence - 5 Miles Brundage, Limitations and Risks of Machine Ethics - 6 Roman Yampolskiy, Utility Function Security in Artificially Intelligent Agents - 7 Ben Goertzel, GOLEM: Toward an AGI Meta-Architecture Enabling Both Goal Preservation and Radical Self-Improvement - 8 Alexey Potapov and Sergey Rodionov, Universal Empathy and Ethical Bias for Artificial General Intelligence - 9 András Kornai, Bounding the Impact of AGI - 10 Anders Sandberg, Ethics and Impact of Brain Emulations 11 Daniel Dewey, Long-Term Strategies for Ending Existential Risk from Fast Takeoff - 12 Mark Bishop, The Singularity, or How I Learned to Stop Worrying and Love AI -. (shrink)

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

A quadratic utility function is introduced in this paper to study the dynamic characteristics of Cournot duopoly game. Based on the bounded rationality mechanism, a discrete dynamical map that describes the game’s dynamic is obtained. The map possesses only one equilibrium point which is Nash point. The stability conditions for this point are analyzed. These conditions show that the point becomes unstable due to two bifurcation types that are flip and Neimark–Sacker. The synchronization property for that map is (...) studied. Through local and global analysis, some dynamics of attracting sets are investigated. This analysis gives some insights on the basis of those sets and the shape of the critical curves. It also shows some lobes found in those attracting sets which are constructed due to the origin focal point. (shrink)

The objective of this book is to produce a theory of rational decision making for realistically resource-bounded agents. My interest is not in “What should I do if I were an ideal agent?”, but rather, “What should I do given that I am who I am, with all my actual cognitive limitations?” The book has three parts. Part One addresses the question of where the values come from that agents use in rational decision making. The most comon view among (...) philosophers is that they are based on preferences, but I argue that this is computationally impossible. I propose an alternative theory somewhat reminiscent of Bentham, and explore how human beings actually arrive at values and how they use them in decision making. Part Two investigates the knowledge of probability that is required for decision-theoretic reasoning. I argue that subjective probability makes no sense as applied to realistic agents. I sketch a theory of objective probability to put in its place. Then I use that to define a variety of causal probability and argue that this is the kind of probability presupposed by rational decision making. So what is to be defended is a variety of causal decision theory. Part Three explores how these values and probabilities are to be used in decision making. In chapter eight, it is argued first that actions cannot be evaluated in terms of their expected values as ordinarily defined, because that does not take account of the fact that a cognizer may be unable to perform an action, and may even be unable to try to perform it. An alternative notion of “expected utility” is defined to be used in place of expected values. In chapter nine it is argued that individual actions cannot be the proper objects of decision-theoretic evaluation. We must instead choose plans, and select actions indirectly on the grounds that they are prescribed by the plans we adopt. However, our objective cannot be to find plans with maximal expected utilities. Plans cannot be meaningfully compared in that way. (shrink)

Interactions between an intelligent software agent and a human user are ubiquitous in everyday situations such as access to information, entertainment, and purchases. In such interactions, the ISA mediates the user’s access to the content, or controls some other aspect of the user experience, and is not designed to be neutral about outcomes of user choices. Like human users, ISAs are driven by goals, make autonomous decisions, and can learn from experience. Using ideas from bounded rationality, we frame these (...) interactions as instances of an ISA whose reward depends on actions performed by the user. Such agents benefit by steering the user’s behaviour towards outcomes that maximise the ISA’s utility, which may or may not be aligned with that of the user. Video games, news recommendation aggregation engines, and fitness trackers can all be instances of this general case. Our analysis facilitates distinguishing various subcases of interaction, as well as second-order effects that might include the possibility for adaptive interfaces to induce behavioural addiction, and/or change in user belief. We present these types of interaction within a conceptual framework, and review current examples of persuasive technologies and the issues that arise from their use. We argue that the nature of the feedback commonly used by learning agents to update their models and subsequent decisions could steer the behaviour of human users away from what benefits them, and in a direction that can undermine autonomy and cause further disparity between actions and goals as exemplified by addictive and compulsive behaviour. We discuss some of the ethical, social and legal implications of this technology and argue that it can sometimes exploit and reinforce weaknesses in human beings. (shrink)