Utility

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.

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)

This book addresses a range of relevant theoretical issues, including the possibility of an interpersonally comparable measure of well-being, or “utility” metric; the moral value of equality, and how that bears on the form of the social welfare function; social choice under uncertainty; and the possibility of integrating considerations of individual choice and responsibility into the social-welfare-function framework. This book also deals with issues of implementation, and explores how survey data and other sources of evidence might be used to calibrate (...) both a utility metric and a social welfare function, and whether distributive goals are ever best pursued through regulation rather than the tax system. In working through this range of theoretical and practical issues, the book draws from a wide variety of literatures, including philosophical scholarship on equality, responsibility, the nature of well-being, and personal identity over time; the social choice literature within economics; applied economic literatures concerning the measurement of inequality and poverty; legal and policy-analysis scholarship on cost-benefit analysis, environmental justice, and the choice between regulation and taxation; and the burgeoning field of “happiness studies”. (shrink)

The essay presents a novel counterexample to Causal Decision Theory (CDT). Its interest is that it generates a case in which CDT violates the very principles that motivated it in the first place. The essay argues that the objection applies to all extant formulations of CDT and that the only way out for that theory is a modification of it that entails incompatibilism. The essay invites the reader to find this consequence of CDT a reason to reject it.

The best justification of time-discounting is roughly that it is rational to care less about your more distant future because there is less of you around to have it. I argue that the standard version of this argument, which treats both psychological continuity and psychological connectedness as reasons to care about your future, can only rationalize an irrational—because exploitable—form of future discounting.

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)

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.

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.

It is widely held that the influence of risk on rational decisions is not entirely explained by the shape of an agent’s utility curve. Buchak (Erkenntnis, 2013, Risk and rationality, Oxford University Press, Oxford, in press) presents an axiomatic decision theory, risk-weighted expected utility theory (REU), in which decision weights are the agent’s subjective probabilities modified by his risk-function r. REU is briefly described, and the global applicability of r is discussed. Rabin’s (Econometrica 68:1281–1292, 2000) calibration theorem strongly suggests that (...) plausible levels of risk aversion cannot be fully explained by concave utility functions; this provides motivation for REU and other theories. But applied to the synchronic preferences of an individual agent, Rabin’s result is not as problematic as it may first appear. Theories that treat outcomes as gains and losses (e.g. prospect theory and cumulative prospect theory) account for risk sensitivity in a way not available to REU. Reference points that mark the difference between gains and losses are subject to framing, many instances of which cannot be regarded as rational. However, rational decision theory may recognize the difference between gains and losses, without endorsing all ways of fixing the point of reference. In any event, REU is a very interesting theory. (shrink)

On the work of Frank Ramsey, emphasizing topics most relevant to philosophy of science.

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)

Sequel to Armendt 1986, ‘A Foundation for Causal Decision Theory.’ The representation theorem for causal decision theory is slightly revised, with the addition of a new restriction on lotteries and a new axiom (A7). The discussion gives some emphasis to the way in which appropriate K-partitions are characterized by relations found among the agent’s conditional preferences. The intended interpretation of conditional preference is one that embodies a sensitivity to the agent’s causal beliefs.

The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already been given. It turns out that it will also (...) produce a reply to the most serious objections made so far against CDT and against the particular version of CDT I will defend. (shrink)

This is a series of lectures on formal decision theory held at the University of Bayreuth during the summer terms 2008 and 2009. It largely follows the book from Michael D. Resnik: Choices. An Introduction to Decision Theory, 5th ed. Minneapolis London 2000 and covers the topics: -/- Decisions under ignorance and risk Probability calculus (Kolmogoroff Axioms, Bayes' Theorem) Philosophical interpretations of probability (R. v. Mises, Ramsey-De Finetti) Neuman-Morgenstern Utility Theory Introductory Game Theory Social Choice Theory (Sen's Paradox of Liberalism, (...) Arrow's Theorem) . (shrink)

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

This sparkling collection of essays both defines and reassesses the concept of Utility. Using it as a touchstone for the consideration of the place of ethics in the recent history of design, the collection offers a way into the issues which concern design decision-makers today. It offers previously unpublished research into diverse topics such as the investigation into the hitherto undiscovered designs for a utility vehicle, and it reveals a fresh perspective on the philosophy behind the concept of Utility as (...) a design theory. (shrink)

In this paper, I intend to deny the morality and instrumentality of the behavior known as bestiality, or the use of non-human animals for sexual gratification by human beings. While to most modern peoples, this hardly even seems like it should be in question, it should be the nature of the human mind to occasionally question long-standing traditional moray in the hopes of finding solutions to problems and the disbanding of superstition. It has been proposed that the moral question, and (...) by extension the legal question, of bestiality is based on traditions long outlived and unnecessary. In an IceNews.is article written in 2008, Norwegian lawyers were growing concerned over the prevalence of animal brothels in Denmark and the precedent it set for Norway [http://www.icenews.is, 2008]. The article, when coupled with the 2001 article title “Heavy Petting” by prominent Utilitarian philosopher, Peter Singer, proves that the issue of bestiality is no longer the purview of jokes and psychological discussions. I will argue against bestiality as a socially acceptable practice based on five standard premises. The standard premises I will present will contain notes in regard to: instrumentality; consent; disease transmission; deviance; and morality. There is significant work available on the harm done to the beast, so aside from brief summary; the question of the good of the beast is not in the focus. I will also ignore any religious concerns, either surrounding morality or freedom of practice. Instead, these arguments are in support of the moral identity of the individual and of society as a whole. (shrink)

Nakata (Theory Decis 71:559–574, 2011) presents a model of acquisition of information where the agent does not know what pieces of information she is missing. In this note, we point out some technical problems in a few of Nakata’s results and show how to correct them.

Probability is a central concept in utilitarian moral theory, almost impossible to do without. I attempt to clarify the role of probability, so that we can be clear about what we are aiming for when we apply utilitarian theory to real cases. I point out the close relationship between utilitarianism and expected-utility theory, a normative standard for individual decision-making. I then argue that the distinction between “ambiguity” and risk is a matter of perception. We do not need this distinction in (...) the theory itself. In order to make this argument I rely on the personalist theory of probability, and I try to show that, within this theory, we do not need to give up completely on the idea that a “true probability” exists. Finally, I discuss several examples of applied utilitarianism, emphasizing the role of probability in each example: reasonable doubt, the precautionary principle in risk regulation, charity, climate change, and voting. (shrink)

Though the Random Utility Model (RUM) was conceived entirely in terms of ordinal utility, the apparatus through which it is widely practised exhibits properties of cardinal utility. The adoption of cardinal utility as a working operation of ordinal is perfectly valid, provided interpretations drawn from that operation remain faithful to ordinal utility. The article considers whether the latter requirement holds true for several measurements commonly derived from RUM. In particular it is found that measurements of consumer surplus change may depart (...) from ordinal utility, and exploit the cardinality inherent in the practical apparatus. (shrink)

For decisions whose consequences accrue over time, there are several possible techniques to compute total utility. One is to discount utilities of future consequences at some appropriate rate. The second is to discount per-period certainty equivalents. And the third is to compute net present values (NPVs) of various possible streams and to then apply the utility function to these net present values. We find that the best approach is to first compute NPVs of various possible income streams and then take (...) the utility of such NPVs. We show the drawbacks of other alternative models of evaluating income streams. The article discusses the advantages of the power and logarithmic forms in the modeling of time preference. These are the only forms for which utility of income and utility of consumption are strategically equivalent. Further, these forms permit the flexibility in the choice of a time period (e.g., monthly or quarterly) without modifying the utility function, thus simplifying analysis. (shrink)

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards; they require that the expected utility for the federation be maximized or that the expected utilities for people from different states be equal. We discuss an analytic result that characterizes the decision rule with maximum expected utility, set up a class of models that display interstate dependencies and run (...) simulations for different dependency scenarios in the European Union. We find that, under positive correlations, the welfare distribution tends to be less sensitive to the choice of the decision rule, whereas it can be important under negative correlations. The results that Beisbart and Bovens (SCW 29, p. 581, 2007) have found for two types of models without interstate dependencies are relatively stable. There are exceptions, though, under which the way the welfare distribution is shaped by a decision rule is significantly affected by dependencies. (shrink)

Utilitarianism, as well as many other political and moral doctrines, presupposes that the problem of interpersonal utility comparisons can be solved. Otto Neurath gave a comparatively early (1912) and explicit statement of this problem, and he suggested that it cannot be solved. This may still be the dominant view. It is argued that recent attempts to solve the problem (by e.g. Schick, Rescher, Harsanyi, Brandt, Jeffrey, Arrow, and Hare) are unsatisfactory, but that the oldest suggestion - i.e. the method of (...) minimal units or just-noticeable differences - is acceptable from the point of view of utilitarianism. (shrink)

This article examines several families of population principles in the light of a set of axioms. In addition to the critical-level utilitarian, number-sensitive critical-level utilitarian, and number-dampened utilitarian families and their generalized counterparts, we consider the restricted number-dampened family and introduce two new ones: the restricted critical-level and restricted number-dependent critical-level families. Subsets of the restricted families have non-negative critical levels, avoid the `repugnant conclusion' and satisfy the axiom priority for lives worth living, but violate an important independence condition.

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.

The classic utility concept in economics, can't explain destructive or seemingly irrational behaviour. I introduce the principle of maximization of originality, which unites any kind of motivation. Maximization of richness / leisure according to budget (=classic utility), also maximizes originality,as the richer I am the fewer people are equally rich (the richest person is only one). Motivation to stand out can be however achieved also by doing an extreme sport, striptease, having big tattoo, etc. This enables to relate any human (...) activity in dependence on intelligence and opportunities (=environment). I also present the law of values' equality, which shows a way how people tend to behave. The article was exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013. (shrink)

Cognitive tests show that identity and symmetry reflect intellect. 'Guess of other guess' creates various symmetries, while only one is right: 'absolute symmetry', which can be outvoted by the majority. Prejudices result from differences between ME (my identity) and others. Unbiased judgement is symmetrical, always in the middle: neither in favor, nor against ME. Intelligence reduces prejudices, but the lack of opportunities can counterbalance it. That's why type of bias differs in various groups: people from war zones, people in therapy, (...) artists, etc.. "The law of values' equity" is a symmetrical principle redefining utility in economics, when people equate all their values. E.g. 2 children averagely rich, is better than one child rich and another poor. If 'a' is an average richness, and 'x' is a difference in richness, and Utility multiplies all values, then: a * a > (a - x) * (a + x), which is: a² > a² - x². It does not however imply egalitarianism, as it is still better to have both children rich than both average or poor. (shrink)

This study uses techniques from economics to illuminate fundamental questions in ethics, particularly in the foundations of utilitarianism. Topics considered include the nature of teleological ethics, the foundations of decision theory, the value of equality and the moral significance of a person's continuing identity through time.

Decision theory has at its core a set of mathematical theorems that connect rational preferences to functions with certain structural properties. The components of these theorems, as well as their bearing on questions surrounding rationality, can be interpreted in a variety of ways. Philosophy’s current interest in decision theory represents a convergence of two very different lines of thought, one concerned with the question of how one ought to act, and the other concerned with the question of what action consists (...) in and what it reveals about the actor’s mental states. As a result, the theory has come to have two different uses in philosophy, which we might call the normative use and the interpretive use. It also has a related use that is largely within the domain of psychology, the descriptive use. This essay examines the historical development of decision theory and its uses; the relationship between the norm of decision theory and the notion of rationality; and the interdependence of the uses of decision theory. (shrink)

I have claimed that risk-weighted expected utility maximizers are rational, and that their preferences cannot be captured by expected utility theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and that my original (...) claims still stand. However, their arguments do highlight some costs of REU theory. (shrink)

The orthodox theory of instrumental rationality, expected utility (EU) theory, severely restricts the way in which risk-considerations can figure into a rational individual's preferences. It is argued here that this is because EU theory neglects an important component of instrumental rationality. This paper presents a more general theory of decision-making, risk-weighted expected utility (REU) theory, of which expected utility maximization is a special case. According to REU theory, the weight that each outcome gets in decision-making is not the subjective probability (...) of that outcome; rather, the weight each outcome gets depends on both its subjective probability and its position in the gamble. Furthermore, the individual's utility function, her subjective probability function, and a function that measures her attitude towards risk can be separately derived from her preferences via a Representation Theorem. This theorem illuminates the role that each of these entities plays in preferences, and shows how REU theory explicates the components of instrumental rationality. (shrink)

Lara Buchak sets out a new account of rational decision-making in the face of risk. She argues that the orthodox view is too narrow, and suggests an alternative, more permissive theory: one that allows individuals to pay attention to the worst-case or best-case scenario, and vindicates the ordinary decision-maker.

Our aim in this paper was to establish an empirical evaluation for similarity effects modeled by Rubinstein; Azipurua et al.; Leland; and Sileo. These tests are conducted through a sensitivity analysis of two well-known examples of expected utility (EU) independence violations. We found that subjective similarity reported by respondents was explained very well by objective measures suggested in the similarity literature. The empirical results of this analysis also show that: (1) the likelihood of selection for the riskier choice increases as (...) the pair becomes more similar, (2) these choice patterns are consistent with well-known independence violations of expected utility, and (3) a significant proportion of individuals exhibit intransitive choice patterns predicted under similarity effects, but not allowed under generalized expected utility models for risky choice. (shrink)