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)

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.

In this essay I dispute the widely held view that utility theory and decision theory are formalizations of instrumental rationality. I show that the decision theoretic framework has no deep problems accommodating the ?reasonable? qua a preference to engage in fair cooperation as such. All evaluative criteria relevant to choice can be built into a von Neumann?Morgenstern utility function. I focus on the claim that, while rational choice?driven agents are caught in the Pareto?inferior outcome, reasonable agents could ?solve? (...) the PD and cooperate. Not so, I argue. If reasonable people find themselves in PD situations they too would follow the dominant ?defect? strategy. The difference between instrumentally rational agents and those who are also reasonable is not that they would behave differently in Prisoner?s Dilemmas, but that reasonable people are more successful at avoiding the Prisoner?s Dilemma and tend to play more cooperative games. (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)

In this article we explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that (...) this is empirically true: i.e. that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when Allais made his case against the neo-Bernoullians. (shrink)

An artificial general intelligence (AGI) might have an instrumental drive to modify its utility function to improve its ability to cooperate, bargain, promise, threaten, and resist and engage in blackmail. Such an AGI would necessarily have a utility function that was at least partially observable and that was influenced by how other agents chose to interact with it. This instrumental drive would conflict with the strong orthogonality thesis since the modifications would be influenced by the AGI’s intelligence. AGIs (...) in highly competitive environments might converge to having nearly the same utility function, one optimized to favorably influencing other agents through game theory. Nothing in our analysis weakens arguments concerning the risks of AGI. (shrink)

In spite of the thousands of articles on stakeholder theory, research on value creation has had a shorter history and narrower breadth. Only a few studies have researched value creation from stakeholder perspective looking at how stakeholders appropiate value or the processes or activities by which stakeholders create value. Consequently to date, certain questions still remain unanswered regarding how a firm should treat stakeholders in order to create value. Several questions arise specifically from the stakeholder's side: What does "value" mean (...) for a particular group of stakeholders and how do firms create these different types of value? How do we measure the value created by stakeholders? The purpose of this paper is to answer these questions from Amartya Sen's Capability Approach, identifying and measuring stakeholders' capabilities in the value creation process. Stakeholder Capability is the adequate concept for understanding stakeholder welfare rather than the utility function concept. The empirical evidence comes from an in-depth case study of the company The Grobo Group and its stakeholders. According to the results, the following stakeholder capabilities are relevant to value creation: being employable, being autonomus, being innovative, being entreprenurial, being responsive, being socially integrated, being emphatic, being "green" and being healthy. (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)

The classical theory of preference among monetary bets represents people as expected utility maximizers with concave utility functions. Critics of this account often rely on assumptions about preferences over wide ranges of total wealth. We derive a prediction of the theory that bears on bets at any fixed level of wealth, and test the prediction behaviorally. Our results are discrepant with the classical account. Competing theories are also examined in light of our data.

We present a method to characterize the preferences of a decision maker in decisions with multiple attributes. The approach modifies the outcomes of a multivariate lottery with a multivariate transformation and observes the change in the decision maker’s certain equivalent. If the certain equivalent follows this multivariate transformation, we refer to this situation as multiattribute transformation invariance, and we derive the functional form of the utility function. We then show that any additive or multiplicative utility function that is (...) formed of continuous and strictly monotonic utility functions of the individual attributes must satisfy transformation invariance with a multivariate transformation. This result provides a new interpretation for multiattribute utility functions with mutual utility independence as well as a necessary and sufficient condition that must be satisfied when assuming these widely used functional forms. We work through several examples to illustrate the approach. (shrink)

A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von Neumann–Morgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.

The results generated by experimentalists in psychology and economics haveled to numerous advances in the study of human decision making under risk.Camerer (1995) and Rabin (1998) provide excellent reviews of the relevantliterature. These results clearly display the gap between normative theoriesof ideal behavior and descriptive theories of observed behavior. The mostprominent result is loss aversion – the observation that a loss is given greatervalue than a gain of an equal size – and the resulting S-shaped utility function.Rabin puts the (...) key point as follows: ``Researchers have identified a pervasive feature of reference dependence: In a wide variety of domains, people are significantly more averse to losses than they are attracted to same size gains''(Rabin 1998, 13–14). In what follows, I will show that the ``wide variety of domains'' is wide indeed. In particular, I will review the effects of the S-shaped utility function on the resolution of the decision to commit a crime, to decision to violate professional ethics, and the decision to participate in a rebellion. (shrink)

The term ‘communitarianism’ is often identified with ‘altruism’: an individual is taken to be communitarian-minded if he or she is concerned with the well-being of others, and not only with his or her own well-being. While communitarianism may embrace altruism, it is most appositely viewed as having a broader connotation. Consider, for example, the puzzle of voting behaviour, discussed by Amitai Etzioni and many others ). Casting one's vote entails a cost, albeit usually a small one: however, if there are (...) large numbers voting, then one's own vote has a negligible effect on the outcome. An altruist might therefore rationally refrain from voting, since he incurs a cost, and neither he nor anybody else receives a benefit. And yet, millions of people the world over regularly vote in elections. Other examples could also be given. ‘Group-oriented’ behaviour has been the focus of a number of recent studies. C. Clague, for example, examines the roles of guilt and shame in discouraging tax evasion, and informally discusses how social influences may affect the strength of these sentiments. R. Naylor and M. Cripps examine the influence of social custom on individuals' propensity to join trade unions, while P. Nelson argues that in choosing which party to vote for people assign some weight to the preferences of persons they associate with. (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 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)

Altruism is a popular economic explanation for a wide range of pro-social decisions and actions. It has been applied frequently in several different streams of literature, and is a descriptively compelling model of behavior. This paper provides a theoretical framework for the existence of ordinal and cardinal altruistic value functions, as well as altruistic utility functions, based on an altruistic preference relation. Representation theorems are developed to specify relatively weak conditions under which altruistic value and utility (...) functions can be shown to exist. In addition, conditions that lead to additive forms of these functions are provided. (shrink)

When a risk is exchanged, the exact value for the minimum price (positive or negative) that the purchaser (investor, or insurer) is willing to pay is given by the certainty equivalent wealth level, which in turn depends on his specific utility function. When this utility function is unknown, then only a sufficient condition on the price can ever be found. This paper provides methods for calculating such a sufficient condition, when only limited information on the utility function (...) is known. (shrink)

If the currently available theories of semantic information and utility-expectation are to be applied in a satisfactory way, they must be combined with a message-processing procedure. This paper presents a model of communication within which such a procedure can be defined. In this model the sender's messages arrive over a period of time, the receiver can reject some messages and retain others, the receiver can change his mind in various ways, and the receiver can apply various evaluation functions (...) to a "usable message total". As one example of message-evaluation, a system for evaluating news-value is presented. (shrink)

One of the reasons for adopting hyperbolic discounting is to explain preference reversals. Another is that this value structure suggests an elegant theory of the will. I examine the capacity of the theory to solve Newcomb's problem. In addition, I compare Ainslie's account with other procedural theories of choice that seem at least equally capable of accommodating reversals of preference.

Current philosophical theorizing about technical functions is mainly focused on specifying conditions under which agents are justified in ascribing functions to technical artifacts. Yet, assessing the precise explanatory relevance of such function ascriptions is, by and large, a neglected topic in the philosophy of technical artifacts and technical functions. We assess the explanatory utility of ascriptions of technical functions in the following three explanation-seeking contexts: why was artifact x produced?, why does artifact x not have (...) the expected capacity to ϕ?, how does artifact x realize its capacity to ϕ? We argue that while function ascriptions serve a mere heuristic role in the first context, they have substantial explanatory leverage in the second and third context. In addition, we assess the relevance of function ascriptions in the context of engineering redesign. Here, function ascriptions also play a relevant role: they enable normative statements of the sort that component b functions better than component a. We unpack these claims by considering philosophical theories of technical functions, in particular the ICE theory, and engineering work on function ascription and explanation. We close the paper by relating our analysis to current debates on the explanatory power of mechanistic vis-à-vis functional explanations. (shrink)

This commentary considers Merker's mesodiencephalic proposal in relation to quantitative measures of neural dynamics suggested to be relevant to consciousness. I suggest that even if critical neural mechanisms turn out to be subcortical, the functional utility of consciousness will depend on the rich conscious contents generated by continuous interaction of such mechanisms with a thalamocortical envelope. (Published Online May 1 2007).

Functional information means an encoded network of functions in living organisms from molecular signaling pathways to an organism’s behavior. It is represented by two components: code and an interpretation system, which together form a self-sustaining semantic closure. Semantic closure allows some freedom between components because small variations of the code are still interpretable. The interpretation system consists of inference rules that control the correspondence between the code and the function (phenotype) and determines the shape of the fitness landscape. The (...) utility factor operates at multiple time scales: short-term selection drives evolution towards higher survival and reproduction rate within a given fitness landscape, and long-term selection favors those fitness landscapes that support adaptability and lead to evolutionary expansion of certain lineages. Inference rules make short-term selection possible by shaping the fitness landscape and defining possible directions of evolution, but they are under control of the long-term selection of lineages. Communication normally occurs within a set of agents with compatible interpretation systems, which I call communication system. Functional information cannot be directly transferred between communication systems with incompatible inference rules. Each biological species is a genetic communication system that carries unique functional information together with inference rules that determine evolutionary directions and constraints. This view of the relation between utility and inference can resolve the conflict between realism/positivism and pragmatism. Realism overemphasizes the role of inference in evolution of human knowledge because it assumes that logic is embedded in reality. Pragmatism substitutes usefulness for truth and therefore ignores the advantage of inference. The proposed concept of evolutionary pragmatism rejects the idea that logic is embedded in reality; instead, inference rules are constructed within each communication system to represent reality, and they evolve towards higher adaptability on a long time scale. (shrink)

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)

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. (...) First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. (shrink)

Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a (...) decision-theoretic norm; we then show that the decision-theoretic norm applied to the epistemic utility function yields the norm for credences that we wish to justify. We survey results already obtained using this strategy, and we suggest directions for future research. (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)