The sunk-time effect: effect of time invested and reward magnitude using within-subject design

Highlights

• Task and design allowed us to observe sunk-time effect on a within-subject design.

• Results show a linear relationship between the subjective value of a reward and time investments.

• Results show a magnitude effect in a sunk-cost scenario.

Abstract

This study examines the sunk cost phenomenon in the temporal domain with human subjects. We used an adjusting procedure to quantitatively assess the effect of time on the value of an alternative. To explore whether a magnitude effect, similar to that documented in delay discounting studies, could be observed in a sunk cost scenario, we used a within-subject design with two different magnitudes. Two questionnaires were applied individually to 47 first-year psychology students. In each questionnaire, a hypothetical situation was presented in which participants were told that they had waited a certain amount of time to buy a guitar. Then, participants had to pay for the guitar and choose whether to keep it or sell it. Each questionnaire included five delay conditions (between one month and sixty months). The two questionnaires differed only in the nominal value of the guitar. In one of the questionnaires, a smaller magnitude was used (520 USD); in the other one, the value of the guitar was larger (3900 USD). The data suggest a sunk time effect and a linear increase in the subjective value of the alternatives proportional to the time invested. We found evidence of generality of the magnitude effect to the sunk cost scenario. Time investments caused a greater change in the value of outcomes of smaller magnitudes. We suggest that future research lines could evaluate the generality of these findings using different types of population, questionnaires, frames, delays, and commodities.

Introduction

In behavior analysis and behavioral economics, persistence in a course of action is said to be affected by prior investments (e.g. Garland and Newport, 1991; Staw, 1981; Thaler, 1981). The concept of sunk cost has been used by some authors to refer to this phenomenon (Arkes and Blumer, 1985; Garland, 1990; Kacelnik and Marsh, 2002), and it has been tested experimentally in different studies. For example, Arkes and Blumer (1985, in Experiment 1) asked their participants to imagine that, several weeks after buying a $100 ticket to spend a weekend in Michigan, they bought another one to Wisconsin for $50. Then, they noticed that both trips were scheduled for the same weekend and faced the choice between going to Wisconsin (the place they would rather go to) or taking the trip to Michigan (after all, they had invested more money in that ticket). Fifty-four percent of the participants in their study chose to go to Michigan, which suggests that prior investments could change a course of action, favoring alternatives that initially were less preferred. In other words, even when prior investments are nonrefundable, they seem to affect future behavior.

Research on sunk cost effect has focused mainly on procedures in which monetary costs are involved. Relatively few studies have evaluated the effect of sunk investments when temporal costs are involved (e.g., Fantino et al., 2008; Navarro and Fantino, 2009; Soman, 2001). Soman (2001) evaluated whether the sunk cost effect brought about by past investments of time was similar to those when investments were expressed as monetary amounts. Soman (2001) reported that the sunk cost effect was not found with time investments but confirmed the sunk cost effect in the monetary domain. In a subsequent study, Navarro and Fantino (2009) carried out seven experiments in which they evaluated the effect of time investments and personal responsibility (i.e. whether the participants or another person was responsible for a project) on persistence in a course of action using a group design. Navarro and Fantino (2009) used an established protocol of sunk cost studies that consisted of questionnaires with hypothetical situations in which participants were asked to imagine that they were leaders of a group that worked in a mine and that, after some days of working, they found a vein of copper. However, a thick wall of quartz was covering the copper and it would take 10 more days to dig through the wall and collect a smaller amount of copper than expected. Participants faced the choice between keep digging 10 more days or leaving the mine. In the first three experiments of their study, Navarro and Fantino (2009) manipulated sunk time among groups. In each experiment, there was a group in which no time had been invested (0 days) and two groups in which a time investment (60 days) had been made. These two groups differed in quality of time. Depending on the experiment, in each of these two groups, different levels of effort (Experiment 1), enjoyment (Experiment 2) and difficulty of the future work (Experiment 3) were tested. A significantly higher percentage of participants continued in the course of action (digging) when some time had already been invested. Similar results were observed regardless of whether the time invested was aversive or enjoyable, of prospective effort, and framing (individual vs. group, Experiment 4). Experiments 5–7 also found a sunk time effect and supported the idea that personal responsibility for voluntarily initiating a project interacts with time invested.

Navarro and Fantino’s study illustrates one of the many effects time may have on preference. Another extensively studied effect is delay discounting. However, whereas time spans are retrospective in sunk cost studies (i.e., they precede the occurrence of an event and act like an investment), they are prospective in delay discounting studies (i.e., they follow behavior and act as a consequence). Additionally, in sunk cost studies the effect of prior time investments are evaluated by determining the percentage of participants that persist in a course of action, while in delay discounting studies adjusting procedures are used to determine the change in the value of an alternative as a function of prospective delays.

Adjusting procedures consist of a series of trials in which participants choose between a smaller immediate or a larger delayed amount of money. From trial to trial, the amount of the immediate alternative is adjusted until participants show indifference between the two outcomes. With adjusting procedures, we can quantitatively assess the effect of time on the value of an alternative and derive mathematical predictions which, in turn, may provide more precise and unambiguous information about choice in such situations. They also allow for the observation of how time interacts with other variables. For example, the subjective value of alternatives associated with larger amounts of money decreases more slowly as a function of time than the subjective value of alternatives associated with smaller amounts, a phenomenon known as the magnitude effect (Benzion et al., 1988; Grace and McLean, 2005; Green et al., 1997; Myerson and Green, 1995). As such, in this paper, we attempted to extend the findings of Navarro and Fantino (2009) about sunk time using an adjusting choice procedure which has been fruitful on research about decision making and choice in similar fields (e.g. delay discounting). This will permit us to evaluate mathematically the changes in value of an outcome associated with the time invested. Additionally, the present study evaluates the effect of time investments using a within-subject design with two different magnitudes to explore whether the magnitude effect is observed in a sunk cost scenario. The initial hypothesis is that time investments will proportionally increase the value of an item. Additionally, based on delay discounting studies, we expect smaller increases in the value of items associated with larger amounts than those associated with smaller amounts.