Dreading the pain of others? Altruistic responses to others' pain underestimate dread

In experiments most people choose to hasten, rather than delay, inevitable pain (Badia et al., 1966; Cook & Barnes, 1964), and will even increase the severity of pain to avoid delaying it (Berns et al., 2006; Loewenstein, 1987; Story et al., 2013). A preference to experience pain sooner rather than later implies that delayed pain is subjectively worse than immediate pain, and therefore runs contrary to the behavioral economic notion of delay discounting, which posits that delayed events carry less motivational force than immediate ones (Frederick et al., 2002; Loewenstein & Prelec, 1991; Rachlin et al., 1986; Van Der Pol & Cairns, 2000). Existing theories have therefore explained choice of sooner pain as arising from a process distinct from delay discounting. Specifically, since anticipating pain is known to be aversive (Boucsein & Wendt-Suhl, 1976; Grillon et al., 1993; Hodges & Spielberger, 1966; Huang et al., 2017; Koyama et al., 1998; Ploghaus et al., 1999; Richard & Berridge, 2013), expediting pain can be seen as minimizing an unpleasant anticipation of pain, aptly termed dread (Berns et al., 2006; Chapman & Elstein, 1995; Harris, 2012; Story et al., 2013; Tanaka et al., 2014).

Despite empirical support for the existence of dread (Berns et al., 2006), no previous studies have formally examined whether people consider dread when evaluating others' pain. When offered an opportunity to relieve others' pain in experiments, people are highly altruistic (Fehr & Fischbacher, 2003; Hein et al., 2011; Jackson et al., 2005; Lloyd et al., 2004): Experimental participants will suffer pain for themselves to relieve pain in an anonymous other (Batson et al., 1981; Batson et al., 1983; Batson et al., 1988; Davis et al., 2015; Story et al., 2015), and will even pay more money to reduce the pain of another participant than to reduce their own pain by a similar amount (Crockett et al., 2014; Crockett et al., 2015; Crockett et al., 2017). Furthermore, people are known to mount anticipatory responses to upcoming pain in others (Caes et al., 2012). These findings suggest people will also act to relieve others' dread—that is, people will choose to expedite others' pain when that pain is unavoidable. This has relevance for situations, not uncommon in healthcare settings, where one person (often a doctor or nurse) controls the timing of another's pain. For example, a nurse administering a painful injection might attempt to reduce the salient waiting time by preparing equipment before bringing the patient into the room. If a tendency to relieve others' dread is sufficiently strong, people should even be willing to increase another's pain to mitigate delay.

On the other hand, there is good reason to believe a priori that people might underestimate the effect of dread when trying to relieve others' pain. People are known to be systematically inaccurate in predicting how they will behave in emotional states different from their current state, which has been referred to as an empathy gap (Lowenstein, 2005; Nordgren et al., 2011; Read & Van Leeuven, 1998). Evaluating others' dread of pain theoretically requires considering not only others' emotional state (response to pain), but also others' future state (response to pain in the future). In computational terms, this is a challenging interpersonal inference problem. We therefore predicted people would de-emphasize dread when deciding for others, and place more emphasis on the intensity of pain. This would manifest as a diminished tendency to expedite others' pain relative to one's own pain. We refer to this as a hypothesized Dread Empathy Gap, consistent with empathy gaps observed for other abstract aversive states, such as the pain of social exclusion (Nordgren et al., 2011). Although we use the term ‘empathy’ in this context, we remain agnostic as to the underlying subjective or physiological processes, and behaviorally operationalize this hypothesis.

Dread of Delayed Pain In conventional economic models of intertemporal choice, the subjective utility, urn:x-wiley:00225002:media:jeab721:jeab721-math-0001 of an outcome of magnitude urn:x-wiley:00225002:media:jeab721:jeab721-math-0002 due to be received after delay urn:x-wiley:00225002:media:jeab721:jeab721-math-0003 is described in terms of two independent functions. Firstly, an instantaneous utility function, urn:x-wiley:00225002:media:jeab721:jeab721-math-0004, governs an effect of outcome magnitude; secondly, a discount function, urn:x-wiley:00225002:media:jeab721:jeab721-math-0005, governs an effect of delay, giving: urn:x-wiley:00225002:media:jeab721:jeab721-math-0006(1)Empirically, for rewarding outcomes, discount functions are approximately hyperbolic in form (Ainslie, 1974, 1975; Kirby & Marakovic, 1995; Mazur, 1987), giving: urn:x-wiley:00225002:media:jeab721:jeab721-math-0007(2)where urn:x-wiley:00225002:media:jeab721:jeab721-math-0008 is the discount rate. As shown in Figure 1a, an outcome received immediately urn:x-wiley:00225002:media:jeab721:jeab721-math-0009 would have value urn:x-wiley:00225002:media:jeab721:jeab721-math-0010, while delayed outcomes have lower absolute value, since the overall discount factor, given by the term in brackets, is less than 1 for urn:x-wiley:00225002:media:jeab721:jeab721-math-0011. image Dread and Delay Discount Functions

Note. Shaded grey areas denote negative utility. A. Hyperbolic delay discounting of reward of utility urn:x-wiley:00225002:media:jeab721:jeab721-math-0012, with rate K, as shown in Equation 2. Here reward has positive utility, which decreases with delay, motivating choices to speed-up reward. B. Hyperbolic delay discounting of pain of utility urn:x-wiley:00225002:media:jeab721:jeab721-math-0013. Here utility of pain becomes less negative with delay, motivating choices to defer pain. C. Dread of pain as shown in Equation 3: utility of pain becomes more negative with delay, motivating choices to speed-up pain. This figure is reproduced in part from our previous work published in this journal (Story et al., 2020).

As shown in Figure 1b, for a painful outcome, urn:x-wiley:00225002:media:jeab721:jeab721-math-0014 would be negative, and hyperbolic discounting would bring its disvalue closer to zero. By contrast, choices to expedite pain imply its disvalue grows with delay. This growth in disvalue can accounted for by postulating an additional effect of dread. Following previous approaches, we formalize dread as a cost associated with waiting for pain that is added to the discounted value of pain itself (Berns et al., 2006; Loewenstein, 1987). Thus, the disvalue of one's own future pain is given by: urn:x-wiley:00225002:media:jeab721:jeab721-math-0015(3)The first term in brackets represents conventional hyperbolic discounting of pain, while the second term represents the effect of dread. Here dread increases with delay, under an assumption of logarithmic time perception (Han & Takahashi, 2012; Takahashi et al., 2008). The parameter urn:x-wiley:00225002:media:jeab721:jeab721-math-0016 governs how dread depends on delay: at lower urn:x-wiley:00225002:media:jeab721:jeab721-math-0017, dread becomes more linear in delay and increases more steeply with delay. urn:x-wiley:00225002:media:jeab721:jeab721-math-0018 is a scaling parameter that governs the overall contribution of dread. As shown in Figure 1c, under this Hyperbolic Dread model the disvalue of pain increases with delay, albeit at a decreasing rate. Here, consistent with our previous work in this area (Story et al., 2013; Story et al., 2020), we behaviorally operationalize dread, without specifying an underlying process. Dread of Others' Delayed Pain To consider how people evaluate delayed pain in others, we combine effects of dread and social discounting. Social discounting determines the utility of others' outcomes relative to one's own (Jones & Rachlin, 2006; Jones & Rachlin, 2009; Rachlin & Jones, 2008; Rachlin & Locey, 2011). Formally, the social utility to person urn:x-wiley:00225002:media:jeab721:jeab721-math-0019 of outcome urn:x-wiley:00225002:media:jeab721:jeab721-math-0020 for person urn:x-wiley:00225002:media:jeab721:jeab721-math-0021 is given by: urn:x-wiley:00225002:media:jeab721:jeab721-math-0022(4)where urn:x-wiley:00225002:media:jeab721:jeab721-math-0023 is a social discount factor, and urn:x-wiley:00225002:media:jeab721:jeab721-math-0024 a utility function over individual outcomes. For painful outcomes, urn:x-wiley:00225002:media:jeab721:jeab721-math-0025 implies that another's pain carries more disvalue than one's own pain, a pattern previously observed and referred to as hyperaltruistic (Crockett et al., 2014; Crockett et al., 2017; Crockett et al., 2015; Story et al., 2015). Here, we consider the social discount factor, κ, as fully encapsulating a person's generosity towards another person in a given context, regardless of the causes of this behavior. (For a more complete discussion of a behavioral approach to social discounting of pain, the reader is referred to our recent work in this area, Story et al., 2020). Taken together, Equations 3 and 4 predict that others' dread is taken into account as follows: urn:x-wiley:00225002:media:jeab721:jeab721-math-0026(5)We formalize a Dread Empathy Gap as a diminished effect of delay when choosing on behalf of others: urn:x-wiley:00225002:media:jeab721:jeab721-math-0027(6)where urn:x-wiley:00225002:media:jeab721:jeab721-math-0028 is an additional factor which diminishes the contribution of delay. To test for a Dread Empathy Gap, we conducted two experiments wherein participants chose between different painful outcomes, while we varied the subjective intensity, timing and recipient of the pain. Experiment 1

Experiment 1 was carried out in the laboratory with experiential painful outcomes. Participants made binary choices between painful brief cutaneous electric shock stimuli of different intensities, at delays of up to 29 s. In this experiment, we measured participants' skin conductance responses (SCRs) to anticipated shock and actual shock for themselves and for the other participant.

The experiment consisted of four types of choice presented block-wise in a counterbalanced order (Fig. 2). In self-now-self-later choices, participants chose between immediate and delayed shocks for themselves. In other-now-other-later choices one of the participants, the ‘Decider’, chose between immediate and delayed shocks for the other participant, the ‘Receiver.’ In other-now-self-later choices, the Decider chose between immediate shocks for themselves and delayed shocks for the Receiver. Finally in self-now-other-later choices, the Decider chose between immediate shocks for the Receiver and delayed shocks for themselves. There was no opportunity for reciprocity and participants were informed of this fact. In each condition, each choice had a 0.1 probability of being realized. Participants were informed of this at the start of the experiment, however the outcomes were not described in probabilistic terms (see Discussion). In the event of a choice being implemented, there was a fixed intertrial interval of 30 s and the timing of the shock varied within this interval.

image Experimental Protocol for Experiment 1

Note. A In each of four possible conditions (order counterbalanced across participants) the Decider was asked to choose between two possible combinations of intensity, delay and recipient of shock. B. Choices were selected to be realized with a 1/10 probability, in which event participants saw a yellow warning screen followed by a countdown, C, to shock delivery, D. All participants performed self-now-self-later choices (N = 60). Only Deciders (N = 27) performed the remaining conditions. For these conditions Deciders were informed that, in the event that an outcome was chosen to count for real, the Receiver would see the Decider's choice, followed by an identical countdown to the shock outcome

We predicted that participants would be willing to endure a more severe pain themselves to avoid delaying it (self-now-self-later condition), and might even assign extra pain to the Receiver to avoid delaying pain for themselves (other-now-self-later condition). However, in keeping with a Dread Empathy Gap, we predicted that the Decider would be less likely to increase the Receiver's pain to avoid delaying it (other-now-other-later condition), or to incur pain themselves to avoid delaying the Receiver's pain (self-now-other-later condition). The full factorial design enabled us to test separately for the effects of the recipient of immediate pain and the recipient of delayed pain on the choice of the timing of pain. We used Bayesian model comparison to compare how well alternative versions of the model described above reproduced the observed behavior. The statistical method used instantiates a Bayesian mixed effects logistic regression, in which the distribution over model parameters at the group level serves as an empirical prior over individual level parameters. This approach prevents unreliable individual parameter estimates from taking on extreme values.

Method Participants

Sixty-three healthy participants (23 males 40 females; mean age 23.6 years, s.d. = 4.6 years) were recruited from the University College London (UCL) Institute of Cognitive Neuroscience subject database. Experiments took place at the Wellcome Trust Centre for Neuroimaging, UCL. Sessions lasted 2 hr and participants were compensated at a rate of GB£10 per hour. Participants were recruited in pairs. The two participants in each pair did not meet each other, but were informed that they would be interacting through the computer via an intranet link. The reason for this was to maintain anonymity and to ensure that choices were not influenced by characteristics of the other participant, such as their age or gender. Before the experiment, the participants were randomly allocated to the role of either ‘Decider’ or ‘Receiver’, by a method designed to reassure participants that no deception was involved (see Supporting Online Material).

Participant Flow and Exclusions

Of the 63 participants recruited, 54 (27 pairs, therefore 27 Deciders) completed all parts of the study with full datasets. In the remaining cases, either the second participant in the pair did not arrive, time constraints forced the experiment to end before all blocks had been completed, or data were saved incorrectly. Self-now-self-later choices were available from 60 participants.

Ethics Statement

All participants gave full informed consent before taking part in the study, and were free to withdraw their consent at any time. After the experiment participants were debriefed and given the opportunity to provide feedback. The study procedure received approval from the UCL Research Ethics Committee (4418/001).

Pain Stimuli and Thresholding

Cutaneous electrical stimuli were delivered through two silver chloride surface electrodes placed approximately 3 cm apart on the dorsum of the hand, 1 cm distal to the wrist, via a DS5 Digitimer (Letchworth Garden City, London) constant current stimulator. A single ‘shock’ was composed of five 10 ms square-wave pulses at 49 ms intervals. Stimuli of this nature are considered harmless and are frequently used to study pain processing in humans (Seymour et al., 2005; Vlaev et al., 2009). After providing consent, participants underwent a standardized thresholding procedure. The purpose of this procedure was to select physical intensities of shock (voltages) corresponding to equivalent subjective levels of discomfort on a 10-point Visual Analogue Scale (VAS) for each participant (see Supporting Online Material for full details). We note that the scale confounds pain and unpleasantness (see Duncan et al., 1989; Miron et al., 1989; Price et al., 1983); in this case we are primarily interested in pain as a generic noxious stimulus. This procedure was entirely separate from choices made by participants regarding the timing of shocks.

Passive Trials and Physiological Measurements

We used the package COGENT 2000 (University College London) for presentation of choices and response acquisition. Participants first performed 10 ‘passive trials’ in which the outcome was a 7/10 shock. Delays of 0, 2, 4, 8, 16 and 29 s were used for the main experiment. The 0 s delay was not sampled for the passive trials; all other delays were sampled once in a randomized order. Each passive trial commenced with a screen detailing the intensity of the shock, recipient and delay, for example: “7/10 shock for the other participant, delay 8 secs”. After this screen, a countdown timer began, displayed on the screen as a pie chart, with the segment of time remaining decreasing each second up until the shock outcome (see Fig. 2). Participants were informed that the other participant would see an identical countdown timer. During these trials, we recorded the skin conductance response (SCR) of the Decider from two silver chloride surface electrodes attached to the tips of the first and middle fingers, on the same hand to which the shock stimuli were being delivered (see Supporting Material Online).

Experimental Conditions

We presented four experimental conditions after the passive trials, block-wise in a counterbalanced order (Fig. 2). In the first, termed self-now-self-later, participants chose between immediate and delayed shocks for themselves. Both Deciders and Receivers completed these choices. The remaining three conditions were completed by Deciders alone. In the second, termed other-now-other-later, the Decider could choose between immediate and delayed shocks for the Receiver. In the third, termed other-now-self-later, the Decider could choose between immediate shocks for themselves and delayed shocks for the Receiver. Finally in the fourth, self-now-other-later, condition the Decider could choose between immediate shocks for the Receiver and delayed shocks for themselves. There was no opportunity for reciprocity and participants were informed of this fact. In the social conditions the Receiver was shown the options presented to the Decider and which option the Decider subsequently selected.

Choice Structure

Within each condition, choices followed a symmetrical design. Each of the four conditions consisted of 108 choices per participant; 18 choices were presented at each of six delays: 0, 2, 4, 8, 16 and 29 s. For each choice there were two options, immediate and delayed pain. In ‘adjusting immediate pain’ choices, the delayed shock was always of intensity 5/10, while the intensity of the immediate shock varied from one choice to the next, between 1/10 and 9/10. In ‘adjusting delayed pain’ choices, the immediate shock was always of intensity 5/10, while the intensity of the delayed shock varied from one choice to the next, between 1/10 and 9/10. The set of choices, shown in Table 1, was the same for all participants; no adaptive staircasing procedure was used. Choices were presented in a randomized order. Choices in which the immediate shock was the larger were designed to assess dread while choices in which the delayed shock was the larger were designed to assess delay discounting. Similar procedures are widely used in the literature to estimate various expressions of delay discounting (e.g. Kirby et al., 1999). The aim of this choice structure is to measure the subjective cost associated with delay, theoretically indicated by the point at which participants switch from preferring the immediate option to preferring the delayed option, or vice versa. Here, rather than finding indifference points directly, we used model fitting (logistic regression) to find the dread-discounting parameters which best accounted for each participant's choices.

Table 1. Choice Structure Immediate Pain (Intensity /10) Delayed Pain (Intensity /10) Number of Choices at each d Adjusting Immediate Pain Choices 5 1 2 5 3 2 5 5 1 5 7 2 5 9 2 Adjusting Delayed Pain Choices 1 5 2 3 5 2 5 5 1 7 5 2 9 5 2 Total: 18 Note. Within each condition this set of 18 choices between immediate and delayed pain was presented at each of six delays: 0, 2, 4, 8, 16 and 29 seconds, that is, 108 choices per condition.

Since there was an equal number of options in which the delayed shock was more intense, as those where the immediate shock was more intense, the proportion of choices at each delay for which participants chose the delayed shock, p(choose later), provides a measure of preferences for the timing of pain. p(choose later) = 0.5 indicates indifference between immediate and delayed shocks, termed the 50% indifference line. It follows that p(choose later) < 0.5 indicates a preference for sooner pain and p(choose later) > 0.5 a preference for delayed pain. In keeping with our use of logistic regression, we report p(choose later), rather than estimated indifference points, as measure of time preference for pain; p(choose later) also has the advantage of being independent of assumptions about the functional form of dread-discounting.

In some choices, which we term self-now-other-now choices (36 in total per participant), the shock for both participants was immediate. Since there was an equal number of self-now-other-now choices in which the Decider's shock was the more intense, as was the case for when the Receiver's shock was the more intense, the proportion of these choices on which Deciders chose a shock for the Receiver, termed p(choose other) provides an index of altruism. While p(choose other) = 0.5 suggests that participants were indifferent as to the recipient of the shocks, p(choose other) < 0.5 would imply that participants were willing to endure more pain to relieve even a less severe pain for the other participant (a phenomenon termed hyperaltruism) and finally p(choose other) > 0.5 would imply a degree of self-oriented behavior where participants would prefer that the other participant endure more pain to relieve a lesser pain for themselves.

Incentive Compatibility

In each condition, each choice had a 0.1 probability of being realized. In such an instance a yellow warning screen was first displayed to both participants for 2 s, after which the countdown timer appeared (as for the Passive Trials), followed by the occurrence of a shock at the relevant delay. This procedure was fully explained to participants in the instructions, who were asked to choose knowing that each outcome could be played for real. The timing of outcomes for the two participants was synchronized via an intranet link between the two stimulus PCs. Deciders were informed that, in the eventuality that an outcome was chosen to count for real, the Receiver would see the Decider's choice, followed by an identical countdown to the shock outcome. In the eventuality of a choice being implemented, there was a fixed intertrial interval of 30 s and the timing of the shock varied within this interval.

We note that this form of ‘incentive-compatible’ design in which selected choices count for real is standard in studies of reward-guided choice, albeit with the necessary difference that outcomes are realized within the current experiment, rather than at the end as is customary in reward-guided choice experiments. This arrangement was necessary to allow for a sufficient number of experimental trials to be administered within a reasonable timescale. A theoretical consideration here is that, since outcomes were probabilistic, participants may have discounted options according to their probability (e.g., Estle et al., 2006; Jones & Rachlin, 2009). Against this it is worth noting that the probabilistic nature of the outcomes was not displayed on screen during the presentation of choice options, and therefore was not likely to be a salient feature informing participants' behavior. Furthermore, the probability of a choice being realized was constant across all choice options.

Modeling Analysis

We fitted alternate versions of the model shown in Equations 3 and 5 to participants' choices. Each model yielded an estimate of the utility of each choice option, with utilities transformed into probabilities of choosing each option using a softmax function. We used a Bayesian model-fitting routine wherein group-level data is used to generate empirical priors on subject-level parameter estimates (Huys et al., 2011; Huys et al., 2012), preventing unreliable parameter estimates at the individual level from taking on extreme values. This routine instantiates a Bayesian mixed-effects logistic regression; we use a Bayesian methodology here for better alignment with existing computational approaches (Daw, 2011; the reader is referred to Young, 2018, for a discussion of mixed-effects models in a frequentist framework). We performed model comparison at the group level using the integrated Bayesian Information Criterion (BICint), which scores models based on how well they fit the data (likelihood), while penalizing model complexity (number of parameters). As an additional estimate of the goodness of fit of each model we calculated the pseudo-R2 using McFadden's formula. For a full description of the method and derivation of BICint the reader is referred to Huys et al., 2011; Huys et al., 2012; Story et al., 2020. Model fitting was performed using custom code in Matlab (Mathworks, Provo, UT), available on request to the authors.

Results Self-Now-Self-Later Choices

Choosing delayed pain on less than half of choices at any given delay (p(choose later) < 0.5) indicates a preference for sooner pain, at the expense of increased pain intensity, consistent with dread. We calculated for each subject, using the trapezium method, the area between the curve relating p(choose later) to delay and a horizontal line at p(choose later) = 0.5. Such area-under-the-curve (AUC) approaches are commonplace in quantifying discounting for reward (see Myerson et al., 2001). Since the simplest method of calculating AUC is disproportionally sensitive to indifference points at long delays (Gilroy & Hantula, 2018), we calculated AUC with delay plotted on a log scale (Borges et al., 2016). To aid interpretation of this quantity we divided each delay by the longest logged delay, such that AUC = 1 entails always choosing sooner pain, AUC = 0 entails indifference as to the timing of pain, and AUC = -1 entails always deferring pain. The mean of this area across subjects was significantly positive (mean AUC = 0.11, 95% CI [0.07 0.15], t(59) = 5.16, p < .001) indicating a group level preference to expedite pain.

To further characterize an effect of dread we fitted dread-discounting functions to participants' data. In addition to the Hyperbolic Dread model shown in Equation 2, we also tested a model proposed by Loewenstein (1987), based on exponential discounting (see Supporting Online Material for full details). The fit of the Hyperbolic Dread model is shown in Figure 3, illustrating that the model provides a good fit to the data (mean pseudo-R2=.87), but underestimates choices of sooner pain at longer delays. Closer inspection of the data revealed this discrepancy was attributable to participants' showing a greater-than-expected tendency to expedite even very low-intensity delayed pain (Fig. S1, Supporting Material Online). To account for this finding we tested a variant of the above model in which the dread term scales with delay but not with pain intensity: urn:x-wiley:00225002:media:jeab721:jeab721-math-0033(7)Consistent with previous findings using a similar experimental design (Story et al., 2020), this ‘Unscaled’ variant showed better correspondence to the data (mean pseudo-R2 = .90; ΔBICint = 190) compared with Hyperbolic Dread), and also outperformed an exponential model of dread (ΔBICint = 211). The difference between models is not attributable to the shape of the utility function over pain intensity, since it survives whether this function is concave, linear or convex. Both scaled and unscaled versions of the Hyperbolic Dread model have four free parameters: dread-discounting parameters urn:x-wiley:00225002:media:jeab721:jeab721-math-0037, and a softmax inverse temperature parameter, urn:x-wiley:00225002:media:jeab721:jeab721-math-0038, which governs the degree of randomness in choices. image Preference for Sooner Pain in the Self-Now-Self-Later Condition in Experiment 1

Note. Observed mean probability of choosing the delayed shock option (solid green circles) is plotted against the delay to shock (in seconds) for all participants in Experiment 1 (N = 60). p(choose later) was calculated for each participant at each delay; the group means of these participant-level estimates are displayed here. Error bars represent one standard error above and below the group mean. Overlaid are the equivalent probabilities derived from the maximum a posteriori (MAP) policies of alternative models of dread-discounting: Exponential Dread (hollow circles), Hyperbolic Dread (hollow squares) and Nonscaled Hyperbolic Dread (solid gray triangles). A horizontal line at p = .5 represents indifference between immediate and delayed pain; choosing delayed pain less than half the time (points below p = .5) indicates a preference for immediate pain.

Decreased Tendency to Expedite Pain when Choosing for Others

We tested the extent to which participants were altruistic, and incorporated dread when choosing for others by plotting p(choose later) against delay for Deciders (N = 27) across the four experimental conditions, shown in Figure 4a. For other-now-self-later and self-now-other-later conditions, the curves were shifted in the vertical axis due to altruistic behavior.

image Social Modulation of Dread in Experiment 1

Note. A. Mean probability across Deciders (N = 27) of choosing delayed pain at each delay in each condition, overlaid with behavioral policies of the Dread Empathy Gap model, fitted jointly to all four conditions. Error bars show one standard error above and below the mean. B. Mean AUC in the four conditions. Positive AUC indicates preference for sooner pain, consistent with dread. Error bars represent 95% confidence intervals. C. Estimates of urn:x-wiley:00225002:media:jeab721:jeab721-math-0039 in log space. Negative values indicate underweighting of delay when choosing for others. The solid blue bar indicates the group mean; the bright green bar indicates the 95% CI. Black dots show the parameter estimates for individual subjects, with error bars indicating the uncertainty (square root of the second moment around each parameter)

For these conditions AUC was calculated relative to p(choose other) at delay zero, to correct for the degree of social discounting. In support of a self–other difference in dread, two-way ANOVA revealed a significant effect of the recipient of delayed pain on AUC (F(1,26) = 4.53, p = .043, partial η2= 0.148), with no significant effect of the recipient of immediate pain (F(1,26) = 2.33, p = .139, partial η2 = 0.082) and no significant interaction (F(1,26) = 2.69, p = .113, partial η2 = 0.094) (Figs. 4a and 4b).

Mean AUC was positive across both self-now-self-later and other-now-other-later conditions, consistent with a preference for sooner pain for both self and other, although this did not reach statistical significance for the other-now-other-later condition (Fig. 4b, self-now-self-later mean AUC = 0.11, 95% CI [0.04 0.18], one tailed t(26) = 3.18, p = .004; other-now-other-later mean AUC = 0.052, 95% CI [-0.01 0.12], one tailed t(26) = 1.61, p = .12). There was a strong and significant correlation between the tendency to expedite pain for self and others (AUC self-now-self-later vs. AUC other-now-other-later, Spearman ρ=0.81, p < .001), suggesting participants used their own preferences to guide choices about others. Preference for sooner pain was significantly greater in the self-now-self-later condition than in the other-now-other-later condition (AUC self-now-self-later – AUC other-now-other-later: t(26) = 3.39, p = .002), although the difference between other-now-self-later and self-now-other-later was not significant (t(26) = 0.38, p = .710).

Taken together, the above results indicate participants displayed significantly lower dread when choosing pain on behalf of others compared with when choosing pain for themselves. A possible explanation for the null comparison in other-now-self-later and self-now-other-later conditions is that these entail a greater degree of complexity, requiring participants to consider pain intensity, delay and recipient. Participants' choices might therefore have been noisier in these two conditions, tending to diminish the detectability of dread effects and obscuring self–other differences.

Delay is Underweighted when Choosing for Others

We went on to test the Dread Empathy Gap model (shown in Eq. 6). This model accounts for a reduced contribution of dread when evaluating others' pain by means of an additional discount factor, urn:x-wiley:00225002:media:jeab721:jeab721-math-0044 which diminishes the contribution of delay information when processing others' pain. Model fitting further allowed us to test the possibility that participants' choices were noisier when required to trade-off their pain with that of another, by allowing the softmax inverse temperature, , to be diminished by a factor urn:x-wiley:00225002:media:jeab721:jeab721-math-0046 in self-now-other-later and other-now-self-later conditions. To fit these models, we carried forward each participant's parameters from fitting self-now-self-later choices (urn:x-wiley:00225002:media:jeab721:jeab721-math-0047), and freely fitted urn:x-wiley:00225002:media:jeab721:jeab721-math-0048 and the social discount factor urn:x-wiley:00225002:media:jeab721:jeab721-math-0049. Thus we fitted 324 choices across three conditions (other-now-other-later, self-now-other-later and other-now-self-later) with an additional three parameters.

The Dread Empathy Gap model provided a parsimonious fit to the data (mean pseudo-R2=0.75, and outperformed a Null model in which urn:x-wiley:00225002:media:jeab721:jeab721-math-0051 (ΔBICint=340. Mean urn:x-wiley:00225002:media:jeab721:jeab721-math-0053 was significantly below 1 (mean log urn:x-wiley:00225002:media:jeab721:jeab721-math-0055 95% CI [-1.52 -0.20], one tailed t(26) = -2.68,

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