Error-prone inference from response time: The case of intuitive generosity in public-good games☆
Introduction
To better understand the choices people make, researchers have begun to investigate the decision process that leads to choices. Brain imaging, eye tracking, and measures of heart rate and skin conductance have all been used to understand this process.1 While these physiological measures require special equipment, response time, which is the time it takes individuals to make decisions, is easily acquired and is increasingly used to examine decision-making.2 For example, response time has been used to predict choices between products, to predict indifference points, to more broadly draw inference on preferences, and to understand strategic thinking and behavior (see Spiliopoulos and Ortmann, 2017 for a review).3
Our ability to directly infer preferences from response time, however, hinges on the assumption that observed decisions reflect the underlying preferences, and that the reflection is independent of the time it takes individuals to make a decision. Questioning the validity of this assumption, we find that fast decisions are more prone to error. This holds when response time is endogenously chosen by the decision-maker, and when it is exogenously imposed by the experimenter through time pressure or time delay. Thus, inference on preferences from response time requires that we account for the rate of mistakes.
To demonstrate the potential for false inference from response time we examine the literature on whether individuals are tempted to be generous or to be selfish. This literature extends models on dual selves and dual-processes reasoning to voluntary giving and asks: Is giving impulsive and intuitive or, is it a deliberate and calculated choice?4 Arguing that intuitive decisions can be inferred from fast decisions and that calculated decisions can be inferred from decisions that are made more slowly, this literature explores how contributions to a public good vary with response time. Lending support to generosity being intuitive, these studies demonstrate in constant-return public-good games (aka voluntary contribution mechanism, VCM) that fast decisions involve greater contributions. This comparative static holds both when response time is endogenously chosen by participants and when it is exogenously imposed by the experimenter through time pressure or time delay.5
The concern in using response time to draw inference on preferences is that fast decisions may be more prone to error.6 This concern is particularly relevant in the VCM, where mistakes cannot be distinguished from generosity (Andreoni, 1995; Houser and Kurzban, 2002), and where fast mistakes can be misinterpreted as fast generosity. In the classic VCM n individuals form a group and each allocates an endowment between a private and a public good. A unit allocation to the private good generates a private payoff of 1, while a unit contribution to the public good secures a payoff of r to each group member, where 1/n < r < 1. To maximize own material payoffs, it is a dominant strategy to allocate the endowment to the private good, whereas maximization of the group's aggregate material payoff requires that the endowment is allocated to the public good.7 With the dominant strategy equilibrium of zero contribution to the public good, all equilibrium deviations benefit others and are consistent with generosity. Consequently, quick erroneous deviations from equilibrium will attribute to contributions being greater for fast decision-makers.
To explore the potential role of mistakes, we modify the VCM to a public-good game where mistakes can be identified. We design a game with an interior equilibrium where some deviations from equilibrium decrease both the earnings of the individual and the earnings of other group members.8 As neither a selfish nor a generous person should be selecting such contributions, we classify them as mistakes and examine whether the rate of mistakes varies with response time. To demonstrate the effect mistakes may have on inference from response time, we look at the effect of varying the location of the equilibrium. The equilibrium in one set of treatments lies below the midpoint of the strategy set (as in the VCM) and in another lies above the midpoint. This variation allows us to explore if the finding that fast decision-makers contribute more than slow decision-makers is robust to changing the location of the equilibrium, and thereby assess whether mistakes may have contributed to the earlier finding.
Our main study uses a 2 × 3 between-subject design. We examine two different locations of the equilibrium, and three different time treatments. In one of the time treatments, decision-makers freely choose their response time. Time is instead exogenously manipulated in the two other time treatments by imposing a time delay or a time limit.
The two different locations of the equilibrium allow us to assess the relative generosity of fast versus slow decisions, and the role of mistakes when drawing inference from response time. We refer to the treatment with the equilibrium below the midpoint of the strategy set as the “Low” treatment, and to the treatment with the equilibrium above the midpoint of the strategy set as the “High” treatment. If response time solely reflects preferences, then we should find the same generosity ordering of fast and slow decision-makers in the Low and High treatments. In particular, if fast decisions are more generous, then fast decision-makers should make larger contributions in both the Low and the High treatments. In varying the location of the equilibrium we can also assess the responsiveness to incentives and whether it varies with response time.
Our three time treatments help us assess differences in behavior by fast and slow decision-makers. We examine the effect of response time when decision-makers are free to choose how long they take to decide and when they are forced to make a fast or slow decision. In the endogenous-time treatments we classify fast decision-makers as those who use less than the median time to decide. In two exogenous-time treatments we impose either time pressure or time delay. Decisions in time-pressure treatments must be made before the time limit expires and decisions in time-delay treatments cannot be made until after a time limit has passed. In line with the endogenous-time treatments, we refer to participants in the time-pressure treatment as fast decision-makers and to those in the time-delay treatment as slow decision-makers.
Our results from the Low endogenous-time treatment replicate existing research on intuitive generosity, showing that fast decision-makers contribute more than slow decision-makers. However, this relationship is reversed in the High endogenous-time treatment, where fast decision-makers contribute less than slow decision-makers. We find in both the Low and High endogenous-time treatments that fast decision-makers are more likely to make mistakes. That is, they choose contributions that simultaneously decrease earnings to themselves and to other group members. By contrast, slow decision-makers are more likely to contribute the equilibrium amount, and when they deviate from the dominant strategy they are more likely to make welfare-improving contributions. Comparing the Low and High treatments we find significant differences in the contributions made by slow decision-makers, while those made by fast decision-makers are not distinguishable by treatment. These results are replicated in the treatments with exogenous time-pressure and time-delay. Thus, fast decision-makers appear insensitive to incentives and are more prone to error, irrespective of whether they voluntarily make fast decisions or are forced to do so.
All these findings are from one-shot interactions. We also have data from repeated interactions, which shows that contributions quickly converge toward the interior equilibrium. Convergence of average contributions occurs from above in the Low treatments and from below in the High treatments. These opposing directions of convergence are consistent with overcontribution in the Low treatment and the undercontribution in the High treatment being due to mistakes.
As noted above, our main study examines contributions in a public-good game with an interior equilibrium. Specifically, we rely on piecewise linear payoff functions that allow us to identify mistakes. The resulting payoff structure is less transparent than that of the classic VCM games, and this complexity may increase the rate of mistakes (although such an increase should not affect whether mistakes are more likely to be made by fast or slow decision-makers). We therefore conduct an additional set of experiments where we ask whether similar results arise when the return to giving is constant as in the VCM, but the strategy set includes contributions that are dominated from an individual and group perspective. By adding a private benefit for contributing to the public good, we examine how contributions change when we move the dominant strategy from one of zero contribution to one of full contribution. In the latter case, any contribution below full contribution reduces the earnings of the individual and of all other group members. This High-VCM treatment replicates our results. In contrast to previous (Low-) VCM results, we find that fast decision-makers contribute less than slow decision-makers. As with our interior-equilibrium designs, we also examine how sensitive decisions are to the location of the equilibrium by comparing contributions in the Low-VCM and High-VCM treatments. Consistent with our results in the interior equilibrium experiments, fast choices appear to be insensitive to treatment changes while slow choices vary significantly by treatment.
Examining choices of 476 participants in different variations of our Low and High treatments, we find that choices by slow decision-makers respond to incentives and are sensitive to the location of the equilibrium, while choices made by fast decision-makers are indistinguishable by the respective Low and High treatments. This insensitivity to treatment is particularly intriguing considering the range of dominated actions is much greater in the High than Low treatments. The lack of response to treatment by fast decision-makers indicates that fast choices are unlikely to reflect (solely) preferences over payoffs. Thus, for fast decisions one must be careful in interpreting deviations from equilibrium as evidence of (non-)standard preferences. As in the work on rational inattention and costly information processing by Caplin and Dean (2015) it may be that dominated choices (by fast decision-makers) result from an unwillingness to trade cognitive effort for monetary reward in our endogenous-time treatments, and an inability to do so in our exogenous-time treatments.
In addition to examining the ability to directly infer preferences from response time, our study makes three broader methodological contributions. First, in identifying mistakes we demonstrate that a number of participants fail to internalize the incentives presented to them in the experiment. This resonates with the “failure of game-form recognition” documented by Cason and Plott (2014). Failure to internalize incentives must be considered not only when examining response time, but in any study where confusion or lack of attention and motivation leads to mistakes that may influence inference. Second, and intriguingly, it appears that response time is one way in which we may be able to evaluate the effect of mistakes. Third, our study serves as a demonstration of what is needed for causal inference. Studies of high internal validity eliminate confounding factors, thus securing that inference comes not only from confirmation of a predicted comparative static, but also from elimination of alternatives that generate the same comparative static.
Section snippets
Related literature
The economics literature is increasingly relying on measures of response time to study decision-making. Early work by Wilcox (1993) viewed response time as a proxy for decision cost and analyzed choices in risky environments. The subsequent literature has used response time to investigate the decision process employed by individuals, to make inferences about preferences, and to predict choices within and across domains (see Spiliopoulos and Ortmann, 2017 for a review).9
Identifying mistakes
In the standard VCM it is not possible to determine whether individuals, in making a positive contribution, are making a mistake or aiming to increase the earnings of others. Impeding the identification of mistakes is that any deviation from the dominant strategy of zero contribution increases group payoffs. We design a set of public-good games where mistakes can be identified. This allows us to examine whether preferences can be inferred from response time. More specifically, we examine two
Public-good games with interior equilibria
We first describe the payoff structure of the interior public-good games followed by the procedures and results of the experiment.
Public-good games with equilibria at the boundary (VCM)
To disentangle mistakes from generosity, we implemented public-good games with an interior equilibrium. These games differ from that of the standard VCM. The interior equilibrium public-good game may be more confusing and potentially result in higher rates of error, and our reliance on payoff tables may have triggered a cognitive mind state without regard for others (e.g., Charness et al., 2004). While these differences are unlikely to affect our comparative statics we, nonetheless, examine
Conclusion
Response times are increasingly used to draw inference on individual preferences. We argue that such inference can be misleading when mistakes are correlated with response time. To demonstrate this, we revisit the finding that individuals who make (or have to make) fast decisions give more in the standard VCM. While this finding has been seen as evidence that individuals are intuitively generous, we argue that large fast contributions may instead result from individuals making mistakes.
As
References (83)
- et al.
Multi-dimensional iterative reasoning in action: the case of the Colonel Blotto game
J. Econ. Behav. Organ.
(2012) - et al.
Modeling internal commitment mechanisms and self-control: a neuroeconomics approach to consumption–saving decisions
Games Econ. Behav.
(2005) - et al.
On the private provision of public goods
J. Public Econ.
(1986) - et al.
Seeds to succeed?: sequential giving to public projects
J. Public Econ.
(2011) - et al.
Being of two minds: ultimatum offers under cognitive constraints
J. Econ. Psychol.
(2011) - et al.
Social value orientation and information search in social dilemmas: an eye-tracking analysis
Organ. Behav. Hum. Decis. Process.
(2013) - et al.
Searching for a better deal–on the influence of group decision making, time pressure and gender on search behavior
J. Econ. Psychol.
(2009) - et al.
Learning from (failed) replications: cognitive load manipulations and charitable giving
J. Econ. Behav. Organ.
(2014) - et al.
Time is money – time pressure, incentives, and the quality of decision making
J. Econ. Behav. Organ.
(2006) - et al.
Second thoughts on free riding
Econ. Lett.
(2014)
Fast or fair? A study of response times
Econ. Lett.
Sustaining cooperation in heterogeneous groups
J. Econ. Behav. Organ.
Economics and emotion: institutions matter
Games Econ. Behav.
Bargaining under time pressure in an experimental ultimatum game
Econ. Lett.
Money, depletion, and prosociality in the dictator game
J. Neurosci. Psychol. Econ.
Naive play and the process of choice in guessing games
J. Econ. Sci. Assoc.
Cooperation in public-goods experiments: kindness or confusion?
Am. Econ. Rev.
Measuring altruistic behavior in surveys: the all-or-nothing dictator game
Surv. Res. Methods
Addiction and cue-triggered decision processes
Am. Econ. Rev.
Registered replication report: Rand, Greene, and Nowak (2012)
Perspect. Psychol. Sci.
Strategic risk and response time across games
Int. J. Game Theory
Neuroeconomics: how neuroscience can inform economics
J. Econ. Lit.
Revealed preference, rational inattention, and costly information acquisition
Am. Econ. Rev.
Defaults and Attention: The Drop Out Effect
The dual-process drift diffusion model: evidence from response times
Econ. Inq.
Search and Satisficing
Am. Econ. Rev.
Fairness is intuitive
Exp. Econ.
Promoting cooperation in nonlinear social dilemmas through peer punishment
Exp. Econ.
Misconceptions and game form recognition: challenges to theories of revealed preference and framing
J. Polit. Econ.
The allocation of time in decision-making
J. Eur. Econ. Assoc.
How robust is laboratory gift-exchange?
Exp. Econ.
Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature
Exp. Econ.
Hardnose the dictator
Am. Econ. Rev.
Combining Response Times and Choice Data Using a Neuroeconomic Model of the Decision Process Improves Out-of-Sample Predictions
Look-ups as the windows of the strategic soul: studying cognition via information search in game experiments
Exploiting moral wiggle room: experiments demonstrating an illusory preference for fairness
Econ. Theory
Testing for altruism and social pressure in charitable giving
Q. J. Econ.
Self-Control, Social Preferences and the Effect of Delayed Payments
Dual-processing accounts of reasoning, judgment, and social cognition
Annu. Rev. Psychol.
z-Tree: Zurich toolbox for ready-made economic experiments
Exp. Econ.
Cited by (39)
Measuring tree complexity with response times
2022, Journal of Behavioral and Experimental EconomicsCitation Excerpt :For each game and each subject, Blues and Reds records the following variables: (i) whether or not a subject wins, and (ii) her response time (RT), measured in seconds, at each round. As it is standard in the literature, subject’s RT is considered as a proxy of their cognitive effort; longer RT implies higher effort (e.g., Ofek, Yildiz, & Haruvy (2007), Rubinstein (2007), Fehr & Rangel (2011), Rubinstein (2013), Krajbich, Oud, & Fehr (2014), Caplin & Martin (2016), Clithero (2018), Rubinstein (2016), Gill & Prowse (2017), Spiliopoulos & Ortmann (2017), Recalde, Riedl, & Vesterlund (2018), and Enke & Zimmermann (2019)). At the same time, subject’s winning/losing is the outcome of their exerting that cognitive effort.
On the use of public goods
2022, Mathematical Social SciencesHassle costs and workplace charitable giving: Field experiments with Google employees
2021, Journal of Economic Behavior and OrganizationCitation Excerpt :For instance, the control group relative to the treatment group had more time to reflect on their decision, while they were engaging in the ‘hassle’ of filling out their payment information online. Some studies find that having less time for the decision leads to greater giving (‘spontaneous giving,’ Rand et al. 2012), but recent work has shown that these inferences could also be due to mistakes Recalde et al. (2018). Behavior may also differ because the timing of the payment is different.
Group identity in fairness decisions: Discrimination or inequality aversion?
2021, Journal of Behavioral and Experimental EconomicsClimate urgency: evidence of its effects on decision making in the laboratory and the field
2021, Current Opinion in Environmental SustainabilityA field experiment on fundraising to support independent information
2021, Journal of Economic Behavior and OrganizationCitation Excerpt :This makes motivational crowding out across the board counteracted for large donors by extrinsic incentives a less likely explanation for our findings. To relate to the literature on impulsiveness and generosity (Recalde et al., 2018), we also study whether any of the treatments is associated with a faster response in terms of contributions. We expect that those receiving the tax allowance treatment are going to respond faster as they need to contribute by the end of the year not to lose the opportunity to use the tax allowance in the first available tax filing opportunity, that is 2017, since the field experiment was run in November 2016.
- ☆
We thank seminar and conference participants at SITE (Stanford), SPI (University of Chicago), TIBER (Tilburg), ESA, ASSA, SABE, NeuroPsychoEcon conference (Antwerp), Erasmus University Rotterdam, the University of Pittsburgh, Hamilton College, and FGV Sao Paulo for helpful comments.