Underlying Utility Function Research Articles

A novel behavioral penalty function for interval goal programming with post-optimality analysis

Goal programming (GP) is a multi-objective extension of linear programming. Interval GP (IGP) is one of the earliest methods to expand the range of preferred structures in GP. The decision maker’s (DM’s) utility or preference in IGP is investigated by incorporating a widening range of underlying utility functions, commonly known as penalty functions. The basic idea of these functions is that undesirable deviations from the target levels of the goals are penalized regarding a constant or variable penalty value. The main concern with introducing the penalty functions is providing a wide range of a priori preference structures. Yet, the evaluation of how undesirable deviations are penalized based on DM’s behavioral preferences is not sufficiently addressed in the penalty function types developed in the GP literature. In real-world scenarios involving risk, the achievement levels of decision-making attributes are typically associated with the behavior of the DM. In such scenarios, the DM’s unavoidable attitude toward risk should be integrated into the decision-making process. We introduce the concept of behavioral penalty functions into the IGP approach, incorporating a risk aversion parameter tailored to the nature of each attribute to address this gap. This concept offers an innovative framework for capturing the preferences of the DMs and their various attitudes toward risk within the IGP approach. In this paper, we first introduce the concept of behavioral penalty functions. Next, we develop a behavioral utility-based IGP model. Finally, we present a portfolio selection case study to demonstrate the applicability and efficacy of the proposed procedure, followed by a post-optimality analysis and comparisons with other GP approaches.

A Dynamic Kelly Criterion for Games with a Maximum Payout

In 1956, J.L. Kelly provided the formula for the optimal portion f of one’s capital to bet on a coin toss with favorable odds. We show that when the bet can be repeated a fixed number of times, but the game has a maximum payout M, the optimal portion f becomes a function of both k, the number of games remaining, and B, the current bankroll. We describe this function f k ( B ) and quantify the advantages gained over the fixed Kelly criterion. We also discuss the impact of changing the underlying utility function from a logarithmic utility to a more linear utility, and thereby optimizing a risk-reward ratio.

Bayesian Contextual Choices Under Imperfect Perception of Attributes

Classic theories show that choices can be represented by a stable utility function when they satisfy consistency axioms, such as transitivity and the independence of irrelevant alternatives. Empirical choice data, however, display several contextual choice effects that violate these axioms. We study a choice model with a fixed underlying utility function and explain contextual choices with a novel type of information friction: the agent’s perception of the options is affected by attribute-specific uncertainty. Under this friction, the agent learns useful information when the agent sees more options. Therefore, the agent chooses contextually, exhibiting intransitivity, joint–separate evaluation reversal, the compromise effect, the phantom decoy effect, the attraction effect, and the similarity effect. Because the uncertainty is attribute-specific and common across alternatives, the classic axioms hold when the alternatives dominate one another in attributes. This paper was accepted by Dmitri Kuksov, marketing.

Comparing utility functions between risky and riskless choice in rhesus monkeys

Decisions can be risky or riskless, depending on the outcomes of the choice. Expected utility theory describes risky choices as a utility maximization process: we choose the option with the highest subjective value (utility), which we compute considering both the option’s value and its associated risk. According to the random utility maximization framework, riskless choices could also be based on a utility measure. Neuronal mechanisms of utility-based choice may thus be common to both risky and riskless choices. This assumption would require the existence of a utility function that accounts for both risky and riskless decisions. Here, we investigated whether the choice behavior of two macaque monkeys in risky and riskless decisions could be described by a common underlying utility function. We found that the utility functions elicited in the two choice scenarios were different from each other, even after taking into account the contribution of subjective probability weighting. Our results suggest that distinct utility representations exist for risky and riskless choices, which could reflect distinct neuronal representations of the utility quantities, or distinct brain mechanisms for risky and riskless choices. The different utility functions should be taken into account in neuronal investigations of utility-based choice.

The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model

This work provides analysis of a variant of the Risk-Sharing Principal-Agent problem in a single period setting with additional constant lower and upper bounds on the wage paid to the Agent. The effect of the extra constraints on optimal contract existence is studied and leads to conditions on the underlying utility functions under which an optimum may be attained. Solution characterization is then provided along with the derivation of a Borch rule for Limited Liability. Finally, some applications, including the CARA utility case, are discussed.

Multiple Reference Points and Length of Ownership in the Housing Market

Reference-dependent utility has been shown to have a significant influence on housing market activity. Sellers facing a nominal loss on their home due to market conditions, tend to inflate the asking price and thus the transaction price of their home, indicative of loss aversion. However, the original purchase price of a home may lose influence as a reference-point as the period of ownership increases, while homeowners rely increasingly on other benchmarks such as neighboring homes’ sales prices as reference points. In other words, a homeowner may have multiple reference points in their underlying utility function, whose relative influences shift in importance over time. We use comprehensive administrative data on residential real estate transactions in Singapore’s private housing market to test the influences of original purchase price and recent neighborhood price as reference points over the length of homeownership. Purchase price and neighborhood price are each valid reference points based on established empirical methods in the behavioral and housing economics literature. By testing for their relative influences as a function of length of ownership, we find that prior purchase price is more influential for the first years of ownership, while neighborhood price becomes more influential during the subsequent holding years. Finally, we provide a theoretical framework for understanding the relative influences of multiple reference points over time, which supports the empirical findings.

Comparing Utility Functions Between Risky and Riskless Choice in Rhesus Monkeys

Decisions can be risky or riskless, depending on the outcomes of the choice. Expected Utility Theory describes risky choices as a utility maximization process: we choose the option with the highest utility, which we compute considering both the value of the option and its associated risk. According to the random utility maximization framework, riskless choices could also be based on a utility measure. Neuronal mechanisms of utility-based choice may thus be common to both risky and riskless choices. This assumption would require the existence of a utility function that accounts for both risky and riskless decisions. Here, we investigated whether the choice behavior of macaque monkeys in riskless and risky decisions could be described by a common underlying utility function. We found that the utility functions elicited in the two choice scenarios were different from each other, even after taking into account the contribution of subjective probability weighting. Our results suggest that distinct utility representations exist for riskless and risky choices, which could reflect distinct neuronal representations of the utility quantities, or distinct brain mechanisms for risky and riskless choices. The different utility functions should be taken into account in neuronal investigations of utility-based choice.

Self-induced class stratification in competitive societies of agents: Nash stability in the presence of envy.

Envy, the inclination to compare rewards, can be expected to unfold when inequalities in terms of pay-off differences are generated in competitive societies. It is shown that increasing levels of envy lead inevitably to a self-induced separation into a lower and an upper class. Class stratification is Nash stable and strict, with members of the same class receiving identical rewards. Upper-class agents play exclusively pure strategies, all lower-class agents the same mixed strategy. The fraction of upper-class agents decreases progressively with larger levels of envy, until a single upper-class agent is left. Numerical simulations and a complete analytic treatment of a basic reference model, the shopping trouble model, are presented. The properties of the class-stratified society are universal and only indirectly controllable through the underlying utility function, which implies that class-stratified societies are intrinsically resistant to political control. Implications for human societies are discussed. It is pointed out that the repercussions of envy are amplified when societies become increasingly competitive.

By force of habit: Self-trapping in a dynamical utility landscape.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization. We propose a stylized model with a history-dependent utility function, where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find, in particular, that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behavior.

By Force of Habit: Self-Trapping in a Dynamical Utility Landscape

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behavior.

The anatomy of distributional preferences with group identity

The increasing diversity of societies raises questions about the consequences for redistributive preferences. This paper assesses the impact of social identity on distributional preferences in a modified dictator game. I estimate individual-level utility functions with two parameters that govern the trade-offs between equity and efficiency and giving to self and to other. Subjects on average put less weight on income of the out-group. The out-group treatment also changes the distribution of equity-efficiency concerns. However, the experiment also uncovers a large individual heterogeneity of preferences. An analysis of GARP violations reveals that choices in both treatments overwhelmingly stem from well-behaved, yet systematically different underlying utility functions. Hence, the evidence presented here suggests that the rational choice approach is a useful tool for understanding the effect of social identity on preferences.

CONSUMPTION, LEISURE, AND MONEY

This paper takes a parametric approach to demand analysis and tests the weak separability assumptions that are often implicitly made in representative agent models of modern macroeconomics. The approach allows estimation and testing in a systems-of-equations context, using the minflex Laurent flexible functional form for the underlying utility function and relaxing the assumption of fixed consumer preferences by assuming Markov regime switching. We generate inference consistent with both theoretical and econometric regularity. We strongly reject weak separability of consumption and leisure from real money balances as well as weak separability of consumption from leisure and real money balances, meaning that the inclusion of a money in economic models would be of quantitative importance. We also investigate the substitutability/complementarity relationship among different categories of personal consumption expenditure (nondurables, durables, and services), leisure, and money. We find that the goods are net Morishima substitutes, but because of positive income effects they are gross complements. The implications for monetary policy are also briefly discussed.

Environmental quality and monopoly pricing

This paper investigates various aspects of a monopolist's pricing and environmental quality choice, as two simultaneous decisions and with each as a separate decision, the other variable being exogenously fixed. Green quality is modeled as in Spence (1975), and the present analysis builds on his pioneering work. We contrast the private and the first-best socially optimal solutions. While the latter follows the intuitive property of assigning a higher price to higher quality, the former solution does so under a natural condition of log-supermodular demand. This condition is studied in some detail, and related to properties of an underlying utility function. We complete this characterization of optimal pricing by providing a counter-intuitive example where the two-dimensional interaction is such that the monopolist ends up charging a lower optimal price than the social planner, as well as producing a lower quality. Finally, we investigate respective sufficient conditions under which (i) the private and first-best solutions coincide, and (ii) either one is larger than the other.

Planning for cars that coordinate with people: leveraging effects on human actions for planning and active information gathering over human internal state

Traditionally, autonomous cars treat human-driven vehicles like moving obstacles. They predict their future trajectories and plan to stay out of their way. While physically safe, this results in defensive and opaque behaviors. In reality, an autonomous car’s actions will actually affect what other cars will do in response, creating an opportunity for coordination. Our thesis is that we can leverage these responses to plan more efficient and communicative behaviors. We introduce a formulation of interaction with human-driven vehicles as an underactuated dynamical system, in which the robot’s actions have consequences on the state of the autonomous car, but also on the human actions and thus the state of the human-driven car. We model these consequences by approximating the human’s actions as (noisily) optimal with respect to some utility function. The robot uses the human actions as observations of her underlying utility function parameters. We first explore learning these parameters offline, and show that a robot planning in the resulting underactuated system is more efficient than when treating the person as a moving obstacle. We also show that the robot can target specific desired effects, like getting the person to switch lanes or to proceed first through an intersection. We then explore estimating these parameters online, and enable the robot to perform active information gathering: generating actions that purposefully probe the human in order to clarify their underlying utility parameters, like driving style or attention level. We show that this significantly outperforms passive estimation and improves efficiency. Planning in our model results in coordination behaviors: the robot inches forward at an intersection to see if can go through, or it reverses to make the other car proceed first. These behaviors result from the optimization, without relying on hand-coded signaling strategies. Our user studies support the utility of our model when interacting with real users.

Streaming Non-Monotone Submodular Maximization: Personalized Video Summarization on the Fly

The need for real time analysis of rapidly producing data streams (e.g., video and image streams) motivated the design of streaming algorithms that can efficiently extract and summarize useful information from massive data "on the fly." Such problems can often be reduced to maximizing a submodular set function subject to various constraints. While efficient streaming methods have been recently developed for monotone submodular maximization, in a wide range of applications, such as video summarization, the underlying utility function is non-monotone, and there are often various constraints imposed on the optimization problem to consider privacy or personalization. We develop the first efficient single pass streaming algorithm, Streaming Local Search, that for any streaming monotone submodular maximization algorithm with approximation guarantee α under a collection of independence systems I, provides a constant 1/(1+2/√α+1/α+2d(1+√α)) approximation guarantee for maximizing a non-monotone submodular function under the intersection of I and d knapsack constraints. Our experiments show that for video summarization, our method runs more than 1700 times faster than previous work, while maintaining practically the same performance.

Income inequality measurement: a fresh look at two old issues

The literature on income inequality measurement is split into (1) the ethical approach, from which the Atkinson–Kolm–Sen and Kolm–Pollak classes of indices are derived, and (2) the axiomatic approach, which mainly leads to the generalised entropies. This paper shows how to rationalise, under utilitarianism, the generalised entropies as ethical indices. In this framework a generalised entropy index is consistent with the principle of transfers if and only if the underlying utility function is increasing. This unconventional interpretation explains the strange behaviour of the generalised entropies for some values of the inequality aversion parameter, as identified by Shorrocks (Econometrica 48:613–625, 1980). In that case, the underlying utility function is convex. Then, it provides a solution to escape the so-called Hansson–Sen paradox (Hansson in Foundational problems in the special sciences. Reidel Publishing Company, Dordrecht, 1977; Sen in Personal income distribution. North-Holland, Amsterdam, pp 81–94, 1978) that affects the standard ethical indices and which corresponds to a counterintuitive increase in inequality as a result of a concave transformation of the utility function. A normalised version of the generalised entropies behaves appropriately after such a transformation.

Polarized preferences versus polarizing policies

Much of contemporary political debate in the United States focuses on the issue of polarization: specifically, its causal antecedents and its consequences for policymaking and political conflict. In this article, we argue that partisan preference polarization—conventionally defined as the difference in the favored policy positions of legislators from the two major parties—is not a sufficient statistic for potential political conflict in national politics . Rather, a well-defined measure of potential conflict must take into account (1) the locations of status quo policies and proposed alternatives; and (2) the shape of underlying utility functions. We propose measures of the likely contentiousness of a given status quo policy and of a proposal to move that policy. We then demonstrate the usefulness of these measures using estimates of utility function and final passage vote parameters on enacted legislation from the 111th US Senate (2009–2011).

Using Discrete Choice Experiments to Inform the Benefit-Risk Assessment of Medicines: Are We Ready Yet?

There is emerging interest in the use of discrete choice experiments as a means of quantifying the perceived balance between benefits and risks (quantitative benefit-risk assessment) of new healthcare interventions, such as medicines, under assessment by regulatory agencies. For stated preference data on benefit-risk assessment to be used in regulatory decision making, the methods to generate these data must be valid, reliable and capable of producing meaningful estimates understood by decision makers. Some reporting guidelines exist for discrete choice experiments, and for related methods such as conjoint analysis. However, existing guidelines focus on reporting standards, are general in focus and do not consider the requirements for using discrete choice experiments specifically for quantifying benefit-risk assessments in the context of regulatory decision making. This opinion piece outlines the current state of play in using discrete choice experiments for benefit-risk assessment and proposes key areas needing to be addressed to demonstrate that discrete choice experiments are an appropriate and valid stated preference elicitation method in this context. Methodological research is required to establish: how robust the results of discrete choice experiments are to formats and methods of risk communication; how information in the discrete choice experiment can be presented effectually to respondents; whose preferences should be elicited; the correct underlying utility function and analytical model; the impact of heterogeneity in preferences; and the generalisability of the results. We believe these methodological issues should be addressed, alongside developing a ‘reference case’, before agencies can safely and confidently use discrete choice experiments for quantitative benefit-risk assessment in the context of regulatory decision making for new medicines and healthcare products.

Monkeys choose as if maximizing utility compatible with basic principles of revealed preference theory

Revealed preference theory provides axiomatic tools for assessing whether individuals make observable choices "as if" they are maximizing an underlying utility function. The theory evokes a tradeoff between goods whereby individuals improve themselves by trading one good for another good to obtain the best combination. Preferences revealed in these choices are modeled as curves of equal choice (indifference curves) and reflect an underlying process of optimization. These notions have far-reaching applications in consumer choice theory and impact the welfare of human and animal populations. However, they lack the empirical implementation in animals that would be required to establish a common biological basis. In a design using basic features of revealed preference theory, we measured in rhesus monkeys the frequency of repeated choices between bundles of two liquids. For various liquids, the animals' choices were compatible with the notion of giving up a quantity of one good to gain one unit of another good while maintaining choice indifference, thereby implementing the concept of marginal rate of substitution. The indifference maps consisted of nonoverlapping, linear, convex, and occasionally concave curves with typically negative, but also sometimes positive, slopes depending on bundle composition. Out-of-sample predictions using homothetic polynomials validated the indifference curves. The animals' preferences were internally consistent in satisfying transitivity. Change of option set size demonstrated choice optimality and satisfied the Weak Axiom of Revealed Preference (WARP). These data are consistent with a version of revealed preference theory in which preferences are stochastic; the monkeys behaved "as if" they had well-structured preferences and maximized utility.

Uncertainty and binary stochastic choice

Experimental evidence suggests that decision-making has a stochastic element and is better described through choice probabilities than preference relations. Binary choice probabilities admit a strong utility representation if there exists a utility function u such that the probability of choosing a over b is a strictly increasing function of the utility difference $$u(a) -u(b) $$ . Debreu (Econometrica 26(3):440–444, 1958) obtained a simple set of sufficient conditions for the existence of a strong utility representation when alternatives are drawn from a suitably rich domain. Dagsvik (Math Soc Sci 55:341–370, 2008) specialised Debreu’s result to the domain of lotteries (risky prospects) and provided axiomatic foundations for a strong utility representation in which the underlying utility function conforms to expected utility. This paper considers general mixture set domains. These include the domain of lotteries, but also the domain of Anscombe–Aumann acts: uncertain prospects in the form of state-contingent lotteries. For the risky domain, we show that one of Dagsvik’s axioms can be weakened. For the uncertain domain, we provide axiomatic foundations for a strong utility representation in which the utility function represents invariant biseparable preferences (Ghirardato et al. in J Econ Theory 118:133–173, 2004). The latter is a wide class that includes subjective expected utility, Choquet expected utility and maxmin expected utility preferences. We prove a specialised strong utility representation theorem for each of these special cases.