The existence of a Richter–Peleg multi-utility representation of a preorder by means of upper semicontinuous or continuous functions is discussed in connection with the existence of a Richter–Peleg utility representation. We give several applications that include the analysis of countable Richter–Peleg multi-utility representations.

This paper discusses random utility representations of the Luce model. Earlier works, such as McFadden, Yellott, and Strauss have discussed random utility representations under the assumption that utilities are additively separable in a deterministic and a random part. Under various conditions, they have established that a separable and independent random utility representation exists if and only if the random terms are type III extreme value distributed. This paper analyzes independent random utility representations without (...) the separability condition and with an infinite universal set of alternatives. Under these assumptions, it turns out that the most general random utility representation of the Luce model is a utility function that is an arbitrary strictly increasing transformation of a separable utility function with extreme value distributed random terms. (shrink)

A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive (...) aspects of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with (...) infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, (...) the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture (...) space is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, (...) we should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized (...) by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language. (shrink)

In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to (...) expected utility theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces (...) uncertainty rather than probabilistic risk. (shrink)

I contend that Alva Noë’s Enactive Approach to Perception fails to give an adequate account of the periphery of attention. Noë claims that our peripheral experience is not produced by the brain’s representation of peripheral items, but rather by our mastery of sensorimotor skills and contingencies. I offer a two-pronged assault on this account of the periphery of attention. The first challenge comes from Mack and Rock’s work on inattentional blindness, and provides robust empirical evidence for the semantic processing (and (...) hence representation) of some wholly unattended stimuli. The second challenge draws on LaBerge’s theory of attention to provide a substantial advantage to peripheral representations, saving time whenever we shift the focus of our attention to something which had been in the periphery, allowing us to respond to that thing more quickly than would be possible if Noë’s account of perception were correct. (shrink)

We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.

Consider a subjective expected utility preference relation. It is usually held that the representations which this relation admits differ only in one respect, namely, the possible scales for the measurement of utility. In this paper, I discuss the fact that there are, metaphorically speaking, two additional dimensions along which infinitely many more admissible representations can be found. The first additional dimension is that of state-dependence. The second—and, in this context, much lesser-known—additional dimension is that of act-dependence. (...) The simplest implication of their usually neglected existence is that the standard axiomatizations of subjective expected utility fail to provide the measurement of subjective probability with satisfactory behavioral foundations. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended (...) on the basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that (...) include compact spaces. However, we offer a negative result that continuity may not be reached under such hypotheses. (shrink)

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected (...) class='Hi'>utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example. (shrink)

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

The informativity of a computational model of language acquisition is directly related to how closely it approximates the actual acquisition task, sometimes referred to as the model's cognitive plausibility. We suggest that though every computational model necessarily idealizes the modeled task, an informative language acquisition model can aim to be cognitively plausible in multiple ways. We discuss these cognitive plausibility checkpoints generally and then apply them to a case study in word segmentation, investigating a promising Bayesian segmentation strategy. We incorporate (...) cognitive plausibility by using an age-appropriate unit of perceptual representation, evaluating the model output in terms of its utility, and incorporating cognitive constraints into the inference process. Our more cognitively plausible model shows a beneficial effect of cognitive constraints on segmentation performance. One interpretation of this effect is as a synergy between the naive theories of language structure that infants may have and the cognitive constraints that limit the fidelity of their inference processes, where less accurate inference approximations are better when the underlying assumptions about how words are generated are less accurate. More generally, these results highlight the utility of incorporating cognitive plausibility more fully into computational models of language acquisition. (shrink)

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several (...) possible choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

Recent theoretical work has identified a tightly-constrained sense in which genes carry representational content. Representational properties of the genome are founded in the transmission of DNA over phylogenetic time and its role in natural selection. However, genetic representation is not just relevant to questions of selection and evolution. This paper goes beyond existing treatments and argues for the heterodox view that information generated by a process of selection over phylogenetic time can be read in ontogenetic time, in the course of (...) individual development. Recent results in evolutionary biology, drawn both from modelling work, and from experimental and observational data, support a role for genetic representation in explaining individual ontogeny: both genetic representations and environmental information are read by the mechanisms of development, in an individual, so as to lead to adaptive phenotypes. Furthermore, in some cases there appears to have been selection between individuals that rely to different degrees on the two sources of information. Thus, the theory of representation in inheritance systems like the genome is much more than just a coherent reconstruction of information talk in biology. Genetic representation is a property with considerable explanatory utility. (shrink)

Functionalism faces a problem in accounting for the semantic powers of beliefs and other mental states. Simple causal considerations will not solve this problem, nor will any appeal to the social utility of semantic interpretations. The correct analysis of semantic representation is a teleological one, in terms of the biological purposes of mental states: whereas functionalism focuses, so to speak, only on the structure of the cognitive mechanism, the semantic perspective requires in addition that we consider the purposes of (...) the cognitive mechanism's parts. (shrink)

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group R\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of (...) class='Hi'>utility functions as representing preference differences, while being non- etheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism. (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)

Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure (...) outcomes. The paper proposes an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann :199–205, 1963, p. 201). (shrink)

Expected-utility theory has been a popular and influential theory in philosophy, law, and the social sciences. While its original developers, von Neumann and Morgenstern, presented it as a purely predictive theory useful to the practitioners of economic science, many subsequent theorists, particularly those outside of economics, have come to endorse EU theory as providing us with a representation of reason. But precisely in what sense does EU theory portray reason? And does it do so successfully? There are two strikingly (...) different answers to these questions in the literature. On the one hand, there is the view of people such as David Gauthier that EU theory is an implementation of the idea that reason's only role is instrumental. On the other hand, there is the view suggested by Leonard Savage that the theory is a “formal” and noninstrumental characterization of our reasoning process. (shrink)

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In (...) the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy. (shrink)

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. (...) Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)

Numerous studies show that humans tend to be more cooperative than expected given the assumption that they are rational maximizers of personal gain. As a result, theoreticians have proposed elaborated formal representations of human decision-making, in which utility functions including “altruistic” or “moral” preferences replace the purely self-oriented "Homo economicus" function. Here we review mathematical approaches that provide insights into the mathematical stability of alternative ways of representing human decision-making in social contexts. Candidate utility functions may be (...) evaluated with help of game theory, classical modeling of social evolution that focuses on behavioral strategies, and modeling of social evolution that focuses directly on utility functions. We present the advantages of the latter form of investigation and discuss one surprisingly precise result: “Homo economicus” as well as “altruistic” utility functions are less stable than a function containing a preference for the golden rule or for the common welfare that is only expressed in social contexts composed of individuals with similar preferences. We discuss the contribution of mathematical models to our understanding of human other-oriented behavior, with a focus on the classical debate over psychological altruism. We conclude that human can be psychologically altruistic, but that psychological altruism evolved because it was generally expressed towards individuals that contributed to the actor’s fitness, such as own children, romantic partners and long term reciprocators. (shrink)

The aim of this article is to analyse the contemporary ‘futility discourse’ from a constructivist perspective. I will argue that bioethics discourse typically disregards the con text from which controversies emerge and the processes that inform and constrain such discourse. Constructivists have argued that scientific knowledge is expressive of the dominant paradigm within which a scientific community is working. I will outline an analysis of ‘medical futility’ as a construction of biomedical and bioethical communities (and their respective paradigms). I will (...) trace the emergence and utilization of futility in the literature. My analysis of the context (i.e. the historical circumstances, the particular actors involved) within which the futility discourse emerged suggests that medical futility was constructed, in part, as a means of enhancing physician domination of a context wherein medical authority was threatened. The actors in this debate express widely divergent frameworks of ‘the good’, arguing from distinctive representations of moral agency. At times, this controversy has been argued from incommensurate moral horizons wherein the discussants debate incomparable problems. This discussion is related to a study of the ‘practice’ of futility in the clinical context. Further studies on the construction of bioethical problems are a necessary condition for supporting the truth claims of bioethical arguments. (shrink)

Higher-order theories of consciousness posit that a mental state is conscious by virtue of being represented by another mental state, which is therefore a higher-order representation (HOR). Whether HORs are construed as thoughts or experiences, higher-order theorists have generally contested whether such metarepresentations have any significant cognitive function. In this paper, I argue that they do, focusing on the value of conscious thinking, as distinguished from conscious perceiving, conscious feeling, and other forms of conscious mentality. A thinking process is constituted (...) by propositional-attitude states, and during conscious thinking some or all of these states would be targeted by HORs. Since cases of nonconscious thinking are widely accepted, the question arises as to the use of representing one's thoughts during thinking. Contra the views of Armstrong and Rolls, I argue that HORs do not facilitate first-order thinking. Rather, I propose that such representations enable reasoning about one's act of thinking, and I give various examples of this sort of metacognition in support of the theory. I further argue that the general correlation between complex thinking and its being conscious is merely due to the fact that assessing one's mental act is particularly useful during such thinking, not because consciousness somehow facilitates first-order inference-making, as folk psychology implies. My view is thus consistent with recent empirical evidence that complex thinking sometimes yields better results when nonconscious. (shrink)

Standard theories of expected utility require that preferences are complete, and/or Archimedean. We present in this paper a theory of decision under uncertainty for both incomplete and non-Archimedean preferences. Without continuity assumptions, incomplete preferences on a lottery space reduce to an order-extension problem. It is well known that incomplete preferences can be extended to complete preferences in the full generality, but this result does not necessarily hold for incomplete preferences which satisfy the independence axiom, since it may obviously happen (...) that the extension does not satisfy the independence axiom. We show, for incomplete preferences on a mixture space, that an extension which satisfies the independence axiom exists. We find necessary and sufficient conditions for a preorder on a finite lottery space to be representable by a family of lexicographic von Neumann–Morgenstern Expected Utility functions. (shrink)

This article argues that there is a natural solution to carry out interpersonal comparisons of utility when the theory of gambles is supplemented with a group operation of joint receipts. If so, three types of people can exist, and the two types having multiplicative representations of joint receipt have, in contrast to most utility theories, absolute scales of utility. This makes possible, at least in principle, meaningful interpersonal comparisons of utility with desirable properties, thus resolving (...) a long standing philosophical problem and having potentially important implications in economics. Two behavioral criteria are given for the three classes of people. At this point the relative class sizes are unknown. (shrink)

In her landmark book, Language, Thought, and Other Biological Categories (Millikan1984),1 Ruth Garrett Millikan utilizes the idea of a biological function to solve philosophical problems associated with the phenomena of language, thought, and meaning. Language and thought are activities of biological organisms, according to Millikan, and we should treat them as such when trying to answer related philosophical questions. Of special interest is Millikan’s treatment of intentionality. Here Millikan employs the notion of a biological function to explain what it is (...) for one thing in nature, a bee dance (43), for example, to be about another, in this case, the location of a nectar source. My concern in this paper is to understand whether Millikan’s account of intentionality adequately explains how humans achieve reference, in language or thought, to individuals and groups in their environment. In bringing her theory of intentional content to bear on human activities, Millikan focuses largely on natural language. Thus, in what follows, I begin by laying out the biology-based principles that underlie Millikan’s theory of content, then proceed with an explanation of how the theory is to apply to natural language. As it appears, Millikan’s account of how content is determined for natural language terms and sentences rests on the determinacy of intentional content at the psychological level. This leads me to take a careful look at what Millikan says about the content of mental representations, in hopes of finding a sufficient basis there for the application of Millikan’s theory of content to natural language. Ultimately, I conclude that Millikan’s theory faces a problem of vacuity. If we approach the theory as a theory of intentional content, intended to explain the nature of reference, the theory is lacking in an extremely important respect: Millikan explains how it could be one of the biological functions of a mental or natural language term to refer, without telling us precisely what in the natural order constitutes the reference relation.. (shrink)

The battle over the proper place of mental representation in cognitive science is often portrayed as a clash between realism and eliminativism. But this simple dichotomy belies the variety of different ontological positions available. This article investigates the various stances that one can adopt toward the ontology of mental representation, and in so doing, shows that eliminativism is in fact best understood as two distinct positions: a posteriori eliminativism and a priori eliminativism. Furthermore, I show that a priori eliminativism faces (...) two crippling challenges. I argue that once we put a priori eliminativism aside, determining the ultimate ontological status of representation can be postponed while we assess its utility across different domains of cognitive science—something all remaining positions can agree on. (shrink)

One guide to an argument's significance is the number and variety of refutations it attracts. By this measure, the Dutch book argument has considerable importance.2 Of course this measure alone is not a sure guide to locating arguments deserving of our attention—if a decisive refutation has really been given, we are better off pursuing other topics. But the presence of many and varied counterarguments at least suggests that either the refutations are controversial, or that their target admits of more than (...) one interpretation, or both. The main point of this paper is to focus on a way of understanding the Dutch Book argument (DBA) that avoids many of the well-known criticisms, and to consider how it fares against an important criticism that still remains: the objection that the DBA presupposes value-independence of bets. (shrink)

The Cell Cycle Ontology (CCO) has the aim to provide a 'one stop shop' for scientists interested in the biology of the cell cycle that would like to ask questions from a molecular and/or systems perspective: what are the genes, proteins, and so on involved in the regulation of cell division? How do they interact to produce the effects observed in the regulation of the cell cycle? To answer these questions, the CCO must integrate a large amount of knowledge from (...) diverse sources; the irregularity and incompleteness of this information suggests an ontology can act as the means of this integration. The volatility and continued expansion of biological knowledge means the content and modelling of the CCO will have to be frequently changed and updated. The CCO is generated from the input data automatically once every two months. This makes it easy to change the representation to enable certain queries; incorporate new knowledge; and consistently apply design patterns across the CCO. The automatic process also allows the CCO to be delivered in a variety of representations that suit the needs of various CCO customers and the abilities of existing toolsets. In this paper we present the CCO and its characteristics of utility and flexibility, that, from our perspective, make it a beautiful ontology. (shrink)

The question of whether cognition requires representations has engendered heated discussion during the last two decades. I shall argue that the question is, in all likelihood, a spurious one. There may or may not be a fact of the matter concerning whether a given item qualifies as a representation. However, even if there is, attempts to establish whether cognition requires representation have neither practical nor theoretical utility.

Quantum cognition in decision making is a recent and rapidly growing field. In this paper, we develop an expected utility theory in a context of non-classical uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework, we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neumann–Lüders (...) postulate applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion. (shrink)

The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be characterized and (...) its utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox. (shrink)

This paper studies decisions under ambiguity when attention is paid to extreme outcomes. In a purely subjective framework, we propose an axiomatic characterization of affine capacities, which are Choquet capacities consisting in an affine transformation of a subjective probability. Our main axiom restricts the well-known Savage’s Sure-Thing Principle to a change in a common intermediate outcome. The representation result is then an affine combination of the expected utility of the valued act and its maximal and minimal utilities.

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not (...) be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

This paper proposes an exploration of the methodology of utility functions that distinguishes interpretation from representation. While representation univocally assigns numbers to the entities of the domain of utility functions, interpretation relates these entities with empirically observable objects of choice. This allows us to make explicit the standard interpretation of utility functions which assumes that two objects have the same utility if and only if the individual is indifferent among them. We explore the underlying assumptions of (...) such an hypothesis and propose a non-standard interpretation according to which objects of choice have a well-defined utility although individuals may vary in the way they treat these objects in a specific context. We provide examples of such a methodological approach that may explain some reversal of preferences and suggest possible mathematical formulations for further research. (shrink)

Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between acts. The resulting theory can (...) make all the decisions of classical expected utility theory, plus more in cases where expected utilities are infinite or undefined. Although the theory requires similarly strong assumptions to classical expected utility theory, versions of the theory can be developed with slightly weaker assumptions, without having to prove a new representation theorem for the weaker theory. This alternate foundation is particularly useful if probability is prior to preference, as suggested by the recent program to base probabilism on accuracy and alethic considerations rather than pragmatic ones. (shrink)

The paper reconstructs the connections between the evolution of Patrick Suppes’ measurement theory from 1951 to 1958 and the research in utility analysis he conducted between 1953 and 1957 within the Stanford Value Theory Project. In particular, the paper shows that Suppes’ superseding of the classical understanding of measurement, his endorsement of the representational view of measurement, and his conceiving of an axiomatic version of the latter were prompted by his research in utility analysis.