Temporal discounting of gains and losses of time: An experimental investigation

This paper investigates “asymmetries” between non-monetary gains and losses in intertemporal choice. We considered gains and losses of spare/working time with respect to a reference duration defined in a working contract. Specifically, we elicited a behavioral model of intertemporal choice that accounts for a gain/loss-dependent discounting function and a reference-dependent utility. Additionally, we did not impose preference for the present (positive discounting) and allowed for both decreasing and increasing impatience. While our results are standard regarding the discount of money (our baseline treatment), our subjects heavily discounted gains of time. More patience was observed for losses of time and a sizable portion of subjects even exhibited negative discounting, i.e. they preferred to expedite losses of time. Our econometric estimations also reveal a much larger heterogeneity of behavior in terms of both utility and discounting for gains and losses of spare time as compared to money.     

Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study

This paper reports the results of an experiment designed to uncover the stochastic structure of individual preferences over lotteries. Unlike previous experiments, which have presented subjects with pair-wise choices between lotteries, our design allowed subjects to choose between two lotteries or (virtually) any convex combination of the two lotteries. We interpret the mixtures of lotteries chosen by subjects as a measure of the stochastic structure of choice. We test between two alternative interpretations of stochastic choice: the random utility interpretation and the deterministic preferences interpretation. The main findings of the experiment are that the typical subject prefers mixtures of lotteries rather than the extremes of a linear lottery choice set. The distribution of choices does not change between a first and second asking of the same question. We argue that this provides support for the deterministic preferences interpretation over the random utility interpretation of stochastic choice. As a subsidiary result, we find a small proportion of subjects make choices that violate transitivity, but the level of intransitive choice falls significantly over time.     

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

Individual laboratory-measured discount rates predict field behavior

We estimate discount rates of 555 subjects using a laboratory task and find that these individual discount rates predict inter-individual variation in field behaviors (e.g., exercise, BMI, smoking). The correlation between the discount rate and each field behavior is small: none exceeds 0.28 and many are near 0. However, the discount rate has at least as much predictive power as any variable in our dataset (e.g., sex, age, education). The correlation between the discount rate and field behavior rises when field behaviors are aggregated: these correlations range from 0.09–0.38. We present a model that explains why specific intertemporal choice behaviors are only weakly correlated with discount rates, even though discount rates robustly predict aggregates of intertemporal decisions.     

The conflict between naive and sophisticated choice as a form of the ‘liberal paradox’

Pareto-inefficient perfect equilibria can be represented by the liberal paradox approach of Sen, appropriately reconfigured to model intertemporal decision-making by an individual. We show that the preference profile used by Grout (1982) to construct a case in which naive choice Pareto-dominates sophisticated choice can be so represented, if tastes change and if the individual can make decisions at time t, which restrict or determine opportunities available in period t + 1 and beyond. This ability to make a decision that binds oneself in the future is a form of rights assignment. We also show how two resolutions of the liberal paradox work out in the individual decision framework.     

Violations of Present-Value Maximization in Income Choice

We report results of an experiment testing for present-value maximization in intertemporal income choice. Two-thirds of subjects did not maximize present value. Through a series of experimental manipulations that impose costs on non-present value maximizers, we are able to reduce the level of violations substantially. We find, however, that a sizeable proportion of subjects continue to systematically violate present-value principles. Our interpretation is that these subjects either cannot or choose not to distinguish between t income and t expenditure in making their choices. Self-management, bounded rationality, and sequence preference are suggested as possible explanations for such behavior.     

Pure hyperbolic discount curves predict “eyes open” self-control

The models of internal self-control that have recently been proposed by behavioral economists do not depict motivational interaction that occurs while temptation is present. Those models that include willpower at all either envision a faculty with a motivation (??strength??) different from the motives that are weighed in the marketplace of choice, or rely on incompatible goals among diverse brain centers. Both assumptions are questionable, but these models?? biggest problem is that they do not let resolutions withstand re-examination while being challenged by impulsive alternatives. The economists?? models all attempt to make a single equilibrium preference predictable from a person??s prior incentives. This was the original purpose of these models?? hyperboloid (???¨C????) delay discount functions, which have been widely justified by the assumption that a person??s intertemporal inconsistency (impulsiveness) can be accounted for by the arousal of appetite for visceral rewards. Although arousal is clearly a factor in some cases of intertemporal inconsistency, it cannot be blamed for others, and furthermore does not necessarily imply hyperboloid discounting. The inadequacy of ?¨C?? functions is particularly evident in models of internal self-control. I have reviewed several of these models, and have argued for a return to pure hyperbolic discount function as originally proposed, the relatively high tails of which can motivate a recursive process of self-prediction and thereby the formation of self-enforcing intertemporal contracts. Such a process does not require a separately motivated faculty of will, or incompatible goals among brain centers; but it also does not permit the prediction of unique preferences from prior incentives.     

Expected discounted utility

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 (Ann Math Stat 34(1):199–205, 1963, p. 201).

     

Intertemporal choice under timing risk: An experimental approach

This paper investigates how individuals evaluate delayed outcomes with risky realization times. Under the discounted expected utility (DEU) model, such evaluations depend only on intertemporal preferences. We obtain several testable hypotheses using the DEU model as a benchmark and test these hypotheses in three experiments. In general, our results show that the DEU model is a poor predictor of intertemporal choice behavior under timing risk. We found that individuals are averse to timing risk and that they evaluate timing lotteries in a rank-dependent fashion. The main driver of timing risk aversion is nothing but probabilistic risk aversion that stems from the nonlinear treatment of probabilities.     

Subjective beliefs and confidence when facts are forgotten

Forgetting can be a salient source of uncertainty for subjective beliefs, confidence, and ambiguity attitudes. To investigate this, we run several experiments where people bet on propositions (facts) that they cannot recall with certainty. We use betting preferences to infer subjects’ revealed beliefs and their revealed confidence in these beliefs. Forgetting is induced via interference tasks and time delays (up to one year). We observe a natural memory decay pattern where beliefs become less accurate and confidence is reduced as well. Moreover, we find a form of comparative ignorance where subjects are more ambiguity averse when they cannot recall the truth rather than never having learnt it. In a different vein, we identify an overconfidence pattern: on average, subjects overpay for bets on propositions that they believe in, but underpay for the opposite bets. We formulate a two-signal behavioral model of forgetting that generates all of these patterns. It suggests new testable hypotheses that are confirmed by our data.

     

Individual decision-making experiments with risk and intertemporal choice

Many decisions require tradeoffs over time and in the presence of risk. To examine interactions between risk and intertemporal effects we developed a laboratory experiment. In the experiment, subjects choose between payoffs that take place at different points in time. We find that very few subjects are consistently risk averse or risk loving. Instead, we find that subjects are less patient in the presence of risk. We also find that increased risk decreases subjects’ patience levels. However, we do not find evidence that the effect of risk on the intertemporal decision depends on the length of the temporal delay.

Social choice in a sequential environment

In a recent paper [2] we presented a model of societies. In the context of that model, we argued that in the field of social choice it is necessary to consider some type of cardinal utility indices if we want to develop a sensible analysis. The main purpose of the present article is to complete and extend an argument initiated in Section 5 of [2] by giving a rigorous formulation and proof of a theorem informally discussed there.To formulate rigorously our theorem a concept of impersonality is introduced that appears to be more general than those which have been used in the economic literature.Our arguments concerning the need to use cardinal utility indices in the field of social choice are shown to be similar to those used by the proponents of decentralization in the controversy regarding centralization and decentralization as alternative ways of organizing the economic activity of a society.An earlier version of this paper was presented at the Econometric Society Winter Meeting held in Toronto, Canada, December 1972.     

The Domain and Interpretation of Utility Functions: An Exploration

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. This revised version was published online in June 2006 with corrections to the Cover Date.     

Using Turn Taking to Mitigate Coordination and Conflict Problems in the Repeated Battle of the Sexes Game

The Battle of the Sexes game, which captures both coordination and conflict problems, has been applied to a wide range of situations. We show that, by reducing distributional conflict and enhancing coordination, (eventual) turn taking supported by a “turn taking with independent randomizations” strategy allows players to engage in intertemporal sharing of the gain from cooperation. Using this insight, we decompose the benefit from turn taking into conflict-mitigating and coordination-enhancing components. Our analysis suggests that an equilibrium measure of the “degree of intertemporal conflict” provides an intuitive way to understand the sources of welfare gain from turn taking in the repeated Battle of the Sexes game. We find that when this equilibrium measure is lower, players behave less aggressively and the welfare gain from turn taking is higher.      

Ambiguity,pessimism, and rational religious choice

Using a subclass of the α-maximin expected-utility preference model, in which the decision maker’s degree of ambiguity and degree of pessimism are each parameterized, we present a theory of religious choice in the Pascalian decision theory tradition, one that can resolve dilemmas, address the “many Gods objection,” and address the ambiguity inherent in religious choice. Parameterizing both the degree of ambiguity and the degree of pessimism allows one to examine how the two interact to impact choice, which is useful regardless of the application. Applying this model to religious choice is a move beyond subjective expected-utility theory, allowing us to show that a change in either the degree of ambiguity or the degree of pessimism can lead a decision maker to “convert” from one religion to another.     

Bounded awareness and anomalies in intertemporal choice: Zooming in Google Earth as both metaphor and model

This paper draws on recent developments in the theory of choice under uncertainty to model anomalies in intertemporal choice. Cognitive limitations leading to hyperbolic discounting and magnitude effects in intertemporal choice may be described in terms of bounded awareness, and represented by phenomena familiar from visualization software such as Google Earth. Cognitive limits on visualization impose constraints on both the area being viewed and the level of detail of the view, with a trade-off between the two. Increasing detail at the expense of limiting the area viewed may be described as zooming. Data from a field experiment were used to assess the theory with an incentive-compatible multiple price list approach involving magnitude levels of 5x, 10x and 20x the basic magnitude level with time horizons of one, three, six and 12 months. Without zooming adjustments in base consumption, very strong hyperbolic and magnitude effects were found, and present bias could not explain the hyperbolic effects. The zooming model provides an explanation of what appear to be significant intertemporal anomalies in the data.     

Nonbinding recommendations: the relative effects of focal points versus uncertainty reduction on bargaining outcomes

This article focuses on the effects of nonbinding recommendations on bargaining outcomes. Recommendations are theorized to have two effects: they can create a focal point for final bargaining positions, and they can decrease outcome uncertainty should dispute persist. While the focal point effect may lower dispute rates, the uncertainty reduction effect is predicted to do the opposite for risk-averse bargainers. Which of these effects dominates is of critical importance in the design of alternative dispute resolution (ADR) procedures, which are increasingly utilized in a variety of settings. We theoretically examine the effects of recommendations on the contract zone using a framework which allows bargainers’ final positions to influence a binding outcome should negotiations fail. This provides a more stringent test of focal points than previously considered. We also present data from controlled laboratory experiments consistent with our model. Recommendations are empirically shown to influence final bargaining positions and negotiated settlement values. In fact, recommendations significantly reduce dispute rates, even where they are completely ignored in final-stage arbitration. This highlights a potentially significant role for the use of nonbinding procedures, such as mediation, as a preliminary stage in more efficient ADR procedures.     

Approaches to cardinal utility

In a previous article (see [3]) a system of axioms is proposed stating conditions which are necessary and sufficient to determine a cardinal utility function on any set, finite or infinite, of outcomes X. The present paper discusses and interprets the meaning of those axioms, and compares this new approach to cardinal utility with the utility differences approach proposed by Alt and Frisch, among others, and with the expected utility approach of von-Neuman and Morgenstern. The notion of repetition of the same choice situation is presented and its interpretation discussed. It is then argued that this notion leads naturally to the system of axioms presented in On Cardinal Utility. It is also argued that this notion must be used if we want to have a more clear understanding of the meaning of the axioms proposed by Alt and Frisch. Finally, it is remarked that since uncertainty is not present in the new approach, it is free of the paradoxes that have plagued the expected utility hypothesis.