Subjective Hazard Rates Rationalize “Irrational” Temporal Preferences

Subjective Hazard Rates Rationalize “Irrational” Temporal Preferences Christian C. Luhmann (christian.luhmann@stonybrook.edu) Department of Psychology Stony Brook, NY 11794 USA Michael T. Bixter (michael.bixter@stonybrook.edu) Department of Psychology Stony Brook, NY 11794 USA Abstract discount rate, and represents the undiscounted subjective value of that same reward (i.e., the value of that reward if it were available immediately). This expression suggests that the subjective value drops by a fixed percentage for each unit of time that those goods are delayed. If a decision maker’s discount rate is 0.1 (and D is measured in years), then $100 available in a year is only worth $90 right now, or 90% of its immediate value. This reward delayed an additional year is only worth $81, reflecting an additional 10% drop in value. Given that exponential discounting represents an obvious normative standard, there has been a large amount of work designed to carefully evaluate how the behavior of human decision makers compares (Ainslie, 1992; Ainslie & Herrnstein, 1981; Green, Fristoe, & Myerson, 1994; Kirby, 1997; Kirby & Herrnstein, 1995; Loewenstein & Thaler, 1989; Rachlin, 1995). Nearly all of this work has demonstrated that decision makers do not discount exponentially. Instead, researchers have largely advocated hyperbolic discount functions as a superior descriptive account. Under hyperbolic discounting, the subjective value of a delayed reward can be expressed as below, with the quantities defined as above. The critical difficulty with hyperbolic discounting is that it tends to result in contradictory preferences. For example, a hyperbolic discounter might prefer $200 delivered in nine years rather than $100 delivered in six years (a patient preference) but also prefer an immediate $100 rather than $200 delivered in 3 years (an impatient preference). The problem, of course, is that the first pair of rewards will become the second pair of rewards in six years time. Such contradictory preferences violate the axiom of stationarity (Koopmans, 1960), and their predictable nature means that such decision makers may be exploited. That is, an exponential discounter can continually offer the hyperbolic discounter a choice between delayed pairs of rewards, only to later offer (sell) the hyperbolic discounter an opportunity to change their selection and profit from the reliable reversal of preference. For this reason, hyperbolic discounting has been characterized as irrational (Kirby, 1997; Soman et al., 2005). Real-world examples of these preference reversals are not difficult to find. For example, the preferences reflected in our New Year’s resolutions (e.g., exercising over the next 12 months) reliably shift once the time comes Delay discounting refers to decision makers’ tendency to treat immediately consumable goods as more valuable than those only available after some delay. Previous work has focused on a seemingly irrational feature of these preferences: the systematic tendency to exhibit more patience when consequences are far in the future but less patience about those same, identical rewards as time passes. One explanation for delay discounting itself appeals to the risk implicitly associated with delayed rewards. The current study investigates whether the implicit risk hypothesis is capable of explaining the seemingly irrational shifts in patience by having participants make subjective risk judgments regarding a variety of real-world scenarios. To reduce the possibility of task demands, participants judged hazard rates rather than survival rates. Results suggest that the seemingly irrational shifts in patience are quite reasonable once participants’ beliefs about the relationship between delay and risk are taken into account. Keywords: discounting; implicit risk; hazard function People must frequently make choices that involve temporal considerations. For example, would you prefer a job with the higher starting salary or a job with greater opportunity for future advancement? Prior work on such temporal decisions has primarily focused on exploring the phenomenon of delay discounting, in which decision makers behave as though immediately consumable goods are more valuable than those only available after some delay. This phenomenon is powerful enough that decision makers are frequently willing to forgo delayed rewards in favor of immediate rewards even when the delayed rewards are objectively more valuable. For example, a decision maker might choose an immediately-available $100 over $200 that would only be delivered in three years. Such a preference is assumed to reflect the subjective value of the $200 option, discounted by the associated three-year delay. The sway of negative events is similarly blunted by delay. For example, working on your taxes next month is likely preferred over working on them tonight. Classical economics has viewed delay discounting from within the framework of discounted utility theory (Samuelson, 1937), according to which the subjective value of goods drops exponentially: where represents the current value of a reward that will be delivered at time D, k represents the decision maker’s