People make numerous decisions every day including perceptual decisions such as walking through a crowd, decisions over primary rewards such as what to eat, and social decisions that require balancing own and others’ benefits. The unifying principles behind choices in various domains are, however, still not well understood. Mathematical models that describe choice behavior in specific contexts have provided important insights into the computations that may underlie decision making in the brain. However, a critical and largely unanswered question is whether these models generalize from one choice context to another. Here we show that a model adapted from the perceptual decision-making domain and estimated on choices over food rewards accurately predicts choices and reaction times in four independent sets of subjects making social decisions. The robustness of the model across domains provides behavioral evidence for a common decision-making process in perceptual, primary reward, and social decision making.
The most basic tenet in standard economic theory is that individuals know their preferences, and those preferences in turn determine their choices. In this approach, preference and choice are one and the same thing. However, this fundamental assumption is at odds with an extensive experimental literature documenting noisy and inconsistent choices, sometimes referred to as preference reversals [1–4]. Based on these experimental findings, theorists have developed random utility maximization models and experimentalists routinely apply probabilistic choice models to fit their data, often without considering the source of the noise in the decisions [5–7]. One prominent conjecture is that individuals do not know their preferences, but instead must construct their preferences at the time of choice. The promise of neuroeconomics has been to use knowledge from neuroscience and psychology to improve our models of economic decision making [8–19]. One obvious direction for improvement is to develop dynamical models that can jointly predict choices and reaction times (RT). RTs are routinely ignored in economics experiments, presumably because they are irrelevant in the static models that dominate the field. However, we know from the literature on sequential sampling models (SSM) that RTs can be used to more accurately predict choice behavior. So there is hope that dynamical models will prove to be a useful alternative to their static counterparts when RT data or other process measures are available. Another direction for improvement is to develop models that can be applied in different domains. Currently we have separate models for risk aversion, temporal discounting, social preference, etc. Because these models take different inputs and result in arbitrarily scaled utilities, there has been little attempt to unify them. However, recent findings from neuroeconomics indicate that value coding in the brain is subject to adaptive coding. This suggests that the range of inputs to the decision mechanism in one task may be very similar to that in a different task, regardless of the actual range of values being considered. For example, an item with a subjective value rating of 5 out of 10 may be encoded at the same level as a $50 reward in a $0–100 experiment or 10 points in a 0–20 point experiment. Thus it may be possible to predict choice probabilities and RTs across tasks if the range of values is accounted for and exogenous factors like time pressure are not too different. The model we use to explore these possibilities is a SSM closely related to the drift-diffusion model (DDM), which has received a great deal of attention for its ability to fit choices, RTs, eye-movements, and measures of neural activity during certain types of decision making [10,12,15,16,20–30]. While most applications of SSMs have been in the perceptual decision-making domain, they have also been applied to some value-based tasks [15,16,22–25,28,31]. Here we build off of this work and explore (a) whether a SSM can capture social decisions, and (b) whether the parameters fit to a binary food choice task can help predict behavior in four separate social-decision tasks. It is important at the outset to address some unique aspects of this work. First, one might assume that individual variability must surely make our attempt to explain out-of-sample choice behavior an exercise in futility. While it is likely true that individual subjects will vary in terms of their parameters, those variations will average out in sufficiently large datasets. Many applications of behavioral models are concerned with aggregate behavior and that is our focus here as well. Accounting for individual variability in behavior is certainly a promising direction, but it is not the aim of this paper. Second, as alluded to above, we do not wish to claim that there are universal parameters that will precisely predict data in every new dataset. Rather we think of these as “baseline” parameters meant to capture the fact that, in the aggregate, experimental subjects will tend to put in similar levels of effort to make quick and accurate decisions, regardless of the task in front of them. Factors like time pressure, performance improvement or degradation over time, and experimental manipulations will certainly alter these parameters, but hopefully in predictable ways. Investigating such alterations is also separate from the aims of this paper. Instead, a primary goal here is to address the criticism that SSMs involve too many free parameters and so could conceivably fit nearly any set of choice and RT data ([32], but see [20,33]). We address this criticism by estimating the parameters in one dataset and then assessing how well the model performs with these parameters in other datasets. Thus, this is not a demonstration of how well we can fit the model to any new dataset, but rather how well the model can perform out-of-sample with minimal or no fitting.
Task 1 provides behavioral data from a task using the Dictator game where 30 subjects in the role of the dictator made 70 binary decisions between two allocations of money, each one specifying an amount for the dictator and an amount for the receiver (Fig 1). For each choice there was a “selfish” option and a “fairer” option. Compared to the fairer option, the selfish option gave more money to the dictator and less money to the receiver (see Methods). Task 2 is a behavioral task consisting of 69 subjects who faced 100 different binary choice problems. These decisions again involved choosing between two allocations of money, but this time there was, apart from the dictator and the receiver, a third subject involved (a “co-dictator”) who always received the same amount as the dictator. As in Task 1, the selfish option always resulted in more money for the dictators and less money for the receiver. An important feature of Task 2 is that while the game consists of three players, there are only two unique sets of payoffs for the dictator to consider. Existing models of social preference would predict that there should be more weight put on the dictator’s payoff compared to the standard Dictator game from Task 1. For example, the widely-used Fehr-Schmidt model predicts that with the extra partner, the weight on the receiver’s payoff should decrease by half [39]. However, as detailed below, our model predicts no change from Task 1. This is because the dictator and co-dictator’s payoffs are identical and we assume that consistently redundant information is ignored in the choice process. So as in Task 1 there are only four payoffs to consider, two for the dictators and two for the receiver. Task 3 (n = 30) was identical to Task 2, except that in Task 3 we removed the redundant column of information so that there were only four payoffs on the screen, two for the dictators and two for the receiver. We anticipated no difference in behavior between Tasks 2 and 3. Task 4 involves the behavioral data from a previously published fMRI study on the Ultimatum game [36]. In the Ultimatum game, one subject (the proposer) offers some division of a fixed amount of money to another subject (the responder). The responder can either accept the offer, or he can reject the offer, leaving both players with nothing. In this game, subjects often reject unfair offers, contrary to economic models assuming pure self-interest. Rejection behavior in these games directly implies that receivers of unfair offers have a negative valuation of the proposer’s payoff. In this study, 18 subjects were asked to respond to 16 Ultimatum offers, each from a total pie of 20 Swiss Francs (~$25), and subjects received offers of 4,6, 8, and 10 Swiss Francs. In a SSM, there exists a latent variable, which we have termed the relative decision value (RDV). Others have referred to this variable simply as “information” or “net evidence”. In our version of the model, the RDV begins each new decision with a value of zero. As the decision maker accumulates evidence, the RDV evolves until it reaches a threshold value of +/- b, at which point he/she chooses the corresponding option. For each step in time (here 1 ms.), the RDV changes by an amount equal to the drift rate plus Gaussian white noise with standard deviation σ. Because the RDV has arbitrary units, we are always free to set the drift rate, the barrier height (b), or the noise (σ) equal to 1. To allow comparison with our previous results on food choice, we fix the decision barriers to one (i. e. b = 1). A critical question in applying SSMs to value-based decisions is how to handle the drift rate. The drift rate represents the average rate of net evidence accumulation for one option over the other. In a standard perceptual experiment, there would be several conditions with different levels of discriminability. A separate drift rate would be fit to each condition and they would reflect the strength of the perceptual evidence, i. e. the task difficulty. In value-based decision making, discriminability is determined not by perceptual qualities of the items, but by the strength of preference for one item over the other. In a typical experiment every decision problem is unique so there can be a continuum of preference levels. In principle one could try to bin certain trials together and fit separate drift rates to different strengths of preference (indeed this is how we visualize the model fits). However, which trials “fit together” can depend on parameters of the model and so the modeler may be forced to make arbitrary decisions about how to bin the data. Moreover, this approach discards valuable information about how changes in preference lead to changes in drift rate. Our approach is to instead let drift rate vary continuously as a function of the strength of preference. This way we fit all of the data at once, using just one drift parameter d, which multiplies the underlying value difference between the two options. For example, a choice between a $1 item and a $2 item would have a drift rate of d, while a choice between a $1 item and a $5 item would have a drift rate of 4d. More concretely, our model can be written as follows: Vt=Vt−1+d (x−y) +εt where V is the RDV, x and y are the underlying values for option X and option Y respectively, and ε is Gaussian noise with mean zero and variance σ2. V starts each trial at 0 and evolves over time until it reaches +/-1. Recent food-choice experiments have used eye-tracking data to demonstrate that visual fixations play an important role in the evidence accumulation process [15,16]. These results led to the introduction of the attentional DDM (aDDM) where evidence is accumulated more quickly for an option when it is being looked at than when it is not. This effect is captured by a fixation-bias parameter θ that discounts the value of the unlooked-at option when calculating the current drift rate, and it leads to a substantial choice bias for options that happen to capture more looking-time over the course of a trial. The estimated bias parameter value in that study (which has been validated in multi-option choice in [16]) was θ = 0. 3, meaning that the values of the unlooked-at food items are discounted by a factor of roughly a third during comparison. Here we hypothesize that, much like the unlooked-at food items, other peoples’ payoffs receive less weight than one’s own payoffs during the choice process. When subjects make choices in an experiment that involves their own monetary payoff and another player’s monetary payoff, they have to compare these payoffs across alternatives to make a decision. For example, if subject i earns xi in alternative X and yi in alternative Y the subject needs to compare these values. Likewise, the subject needs to compare the monetary payoffs xj and yj for subject j in the two alternatives. We can parsimoniously capture these comparisons in an extended DDM as follows: Vt=Vt−1+ds[ (xi−yi) ±θs (xj−yj) ]+εt In this model ds denotes the drift-rate multiplier and θs measures the subject’s discount rate for the other player’s payoff. This aspect of the model is inspired by Decision Field Theory, where attentional weights dictate the influence of different attributes on the decision [23,40]. Note, that the discounted payoff difference θs (xj−yj) for the other player may enter the relative decision value either positively or negatively depending on how the subject values the other player’s payoff. In principle, it is possible to estimate the drift rate ds, the standard deviation of the error term σs, and the discount rate θs for each of our four social-preference experiments. Instead, we would like to pose a different question. Using parameters fit to one task (a food-choice experiment), how well can the aDDM capture choices and RTs in separate, random groups of subjects in social-decision experiments? Because the social-decision datasets do not include eye-tracking data, we need to make a few extensions to the model. First, we assume (based on [16]) that on average subjects allocate equal attention to both choice options. Second, we assume that consistently redundant information is ignored in the choice process (we test this assumption in Tasks 2 & 3). Third, we incorporate adaptive coding [41,42] to account for the fact that each experiment has different units and ranges of value (see Methods). Finally, we assign a weight of θ = 0. 3 to the other subject’s payoff. There are a couple of motivations for this choice. Initially we hypothesized that subjects in these tasks would be focused on themselves and thus discount the other subjects’ payoffs in the same way that unattended items are discounted in the food-choice aDDM. We later confirmed this hypothesis with ex-post model fits of the θ parameter to each dataset. However, we cannot rule out that this may be a coincidence. In order to capture the stochastic nature of the aDDM we simulate the model 1000 times for each choice problem presented to the subjects and create 95% confidence intervals using bootstrapped samples equal in size to the actual datasets. We then compare the simulated choice and RT curves to the real data. Note that the inputs to these simulations are only the monetary values of the options X and Y for each trial (e. g. Fig 1). No data regarding the subjects’ choices or RTs in the social-decision tasks at the individual or group levels were used to generate predictions for these tasks. Figs 2–5 show the predicted choice and RT curves from the aDDM and the actual data. The model does a remarkable job of predicting both the shape and the absolute levels of the choice probability and RT curves in each of the four tasks, as evidenced by the consistent overlap between the 95% confidence intervals of the model and standard error bars of the data. In S1 Fig we also show that the model accurately predicts the entire RT distributions for each dataset [20]. In addition to the figures, the predictive accuracy of the aDDM can also be assessed in quantitative terms. To do so we calculate the mean error magnitudes between the model and the data (Table 1) as well as traditional goodness-of-fit tests for all four tasks (see S1 Table). In Task 1 (Fig 2A-2B) we see that the probability of choosing the selfish option generally tends to increase with the dictator’s own payoff gain (compared to the other option), and to decrease with the receiver’s payoff loss from the dictator’s selfish option. In other words, while dictators are more likely to choose the selfish option if it earns them more money, they are less likely to choose an option that reduces the receiver’s earnings. Looking at the RTs, we see that the quickest decisions generally occur when the selfish option leads to the most money for the dictator and to the smallest loss for the receiver (Fig 2C-2D and S2 Fig). This decrease in RT is about a third of a second or 12% compared to the slowest decisions. Furthermore, in a mixed-effects regression of log (RT) on |p-0. 5|, where p is the mean group probability of choosing the selfish option, we find a highly significant effect (p = 0. 0005). The average error magnitudes between the model and the data (as a function of the dictator’s payoff gain and the receiver’s payoff loss, respectively) are only 3. 1% and 2. 7% for the choice curves (Fig 2A–2B) and 5. 6% and 6. 1% (of the highest mean RT) for the RT curves (Fig 2C and S2 Fig). In Task 2 we hypothesized that adding the co-dictator without adding additional payoffs to consider would not increase the dictator’s focus on that payoff and thus would not change the relative weight between the dictators and the receiver. In other words we predicted that the dictator would treat the decision problem as if there were only two players: the dictator and the receiver. Contrast this with an alternative scenario where the dictator’s and co-dictator’s payoffs are different; in that case the co-dictator’s payoff would receive a weight of 0. 3, just like the receiver’s payoff. Note that in the extreme, the model makes the same prediction for any number of co-dictator or receiver subjects, as long as there are not additional different payoffs to consider. While counterintuitive, this “scope insensitivity” effect has been well documented in the literature on contingent valuation [43]. As expected, in Task 2 (Fig 3) the probability of choosing the selfish option steadily increases with the dictators’ payoff gain, while there is no linear trend as a function of the receiver’s payoff loss. In this task there was systematic variation in the size of the tradeoff between money for the dictator and money for the receiver. For example, trials with losses to the receiver of 10 and 30 had dictator gains of 5 and 10, while trials with losses to the receiver of 20 and 40 had dictator gains of 17 and 23. Thus the selfish option was more appealing in the latter trials and was more likely to be chosen, as seen in Fig 3B. So, what initially looks like random noise in Fig 3B is actually due to systematic variations in the dictator’s gains and is well-predicted by the model (mean error magnitude: 5. 6% for the dictator’s gain (Fig 3A), 3. 4% for receiver’s loss (Fig 3B) ). Fig 3 also shows that RTs increase as both the dictators’ and the receiver’s payoff differences between the two options go to zero (i. e. for the most similar options) and that the model captures these trends well (mean error magnitude: 3. 1% for the dictator’s payoff gain (Fig 3C), 5. 2% for receiver’s loss (Fig 3D) ). The correspondence between predicted and empirically measured RT is also high when using the model to combine dictator and receiver payoffs into a single utility measure (S2 Fig). In Fig 3 we also present simulations of the model with θ = 0. 15 to demonstrate how the model misfits the data if we assume that the receiver’s payoff receives only half of the weight from the normal Dictator game (Task 1), as would be the case, for example, in the Fehr-Schmidt model [39]. Below, we present data on explicit tests of the Fehr-Schmidt model. As expected, behavior in Task 3 closely matched behavior in Task 2. Overall subjects chose the selfish option on 64% of trials in Task 2 and 65% of trials in Task 3 (t = 0. 173, p = 0. 86). At a more detailed level, we observed similar choice and RT curves (Fig 4 and S2 Fig) (choice: mean error magnitude: 9. 1% for the dictator’s gain (Fig 4A), 5. 6% for receiver’s loss (Fig 4B), RT: mean error magnitude: 6. 5% for the dictator’s gain (Fig 4C), 8. 1% for receiver’s loss (Fig 4D) ). In Task 4 we observe the standard behavioral trend that subjects almost always accept “fair” or “almost fair” offers of 40–50% of the total pie, but start to reject lower offers (Fig 5), with an average indifference point in the 20–30% offer range. Again, the model provides accurate predictions for both choices (mean error magnitude: 5. 7%) and RT (mean error magnitude: 6. 3%).
Taken together, our results show that social decisions display relationships between choice probability and RT that are consistent with a dynamical decision process and that these relationships can be quantitatively captured with a sequential sampling model. Additionally, we demonstrated that these four particular datasets were accurately predicted by parameters from a previous food-choice model. These results are consistent with the notion that there is a common computational framework by which value-based decisions are made. More broadly, the established success of SSMs in describing memory and perception suggests that these models are capturing fundamental aspects of decision making. Namely, a decision-maker evaluates options at the time of choice by accumulating evidence for them until one of the options is judged as being sufficiently better than the other (s). In perceptual decision making the stochastic evidence is primarily exogenous while in value-based decision-making the stochastic evidence is generated internally. Nevertheless, similar evidence-comparison processes seem to apply in these different cases. It is important to highlight that the particular model we have used here is simplified in the sense that it does not include additional parameters for variability in drift rate or starting point across trials or subjects. One strength of SSMs is that they predict not just mean RT, but entire RT distributions. While our model captures these distributions reasonably well, additional parameters are likely required to fully capture every facet of the data. While our model may sacrifice some amount of precision in these distributional analyses, we believe this is outweighed by the benefits of simplicity and robustness across different choice environments. The benefits of this robustness are apparent from our ability to predict behavior across the different datasets. Of course, factors like time pressure, performance improvement or degradation over time, and experimental manipulations will likely alter the parameters of the model. It also remains an open question whether these same parameters will predict behavior outside of the lab where focus and its discounting effects on choice can be affected by many uncontrolled factors such as distraction and advertising. For instance, we know already from a large body of work that putting subjects under time pressure causes faster and less accurate decisions, reflected by a change in parameters of the SSM (e. g. [22,46,47]). This means that if one cannot directly control for time pressure in the field environment, the parameters measured in the laboratory may not predict field behavior accurately. Studying how environmental/experimental factors influence these parameters is an important line of investigation to see how far we can stretch these models. It is also important to highlight that the particular model we have used here is just one of the many SSMs in the literature, including the drift-diffusion model, linear ballistic accumulator model, leaky competing accumulator model, Ornstein-Uhlenbeck model, biophysical attractor models, and urgency-gating models [12,27,45,46,48–50]. While there is a good deal of interest and work being done to distinguish between these models, many of them are identical under certain parameter restrictions and otherwise tend to yield only subtle differences in RT distributions [45,51,52]. In other cases, the data themselves must have specific characteristics to allow comparisons between different SSMs. For example, it has been reported that the urgency-gating model is identical to the drift-diffusion model in situations with constant evidence, as in the datasets we test here [50]. Thus it is impossible to distinguish between the urgency-gating model and the aDDM in this setting. However, it is worth noting that the urgency-gating model would presumably not predict the effects of attention on the weighting of self and other payoff, and thus would be equivalent to the aDDM with θ = 1. As can be seen from Fig 6, that model would clearly fail to capture our subjects’ behavior. In principle it is possible to test specific features of different SSMs against each other in value-based tasks, but to do so would likely require considerably more data, as these sorts of model-fitting exercises are typically performed with ~1000 trials per subject, whereas here our tasks ranged from 16 to 100 choices per subject, spread over a continuum of “conditions” (i. e. subjective-value differences). Even with smaller datasets like the ones reported here, the close relationship between choice probabilities and RT provides additional possibilities to test and constrain the models. We tested several alternative models, both in terms of the subjective value function and in terms of the SSM framework. Specifically we compared our aDDM with Fehr-Schmidt and Bolton-Ockenfels social-preference models and an Ornstein-Uhlenbeck SSM [39,44,46]. While each of these models adequately captured some aspects of some tasks, none were able to match the predictions of the aDDM across tasks and measures (choice probability and RT). Furthermore, the Fehr-Schmidt and Bolton-Ockenfels models do not predict RT at all without inserting them into a SSM such as our aDDM. RTs have been woefully understudied in economics, potentially because of a perceived lack of formal models that make use of them. SSMs provide a clear and precise link between RT and the choice problem. Longer RTs are a direct result of smaller differences in subjective value between choice options, with the longest RTs coinciding with a subject’s indifference point (see S2 Fig). This follows from the fact that smaller value differences lead to slower net evidence accumulation and consequently a higher latency to cross a choice threshold. The measurement of indifference points is the basis for inferring preferences and our model implies that using RTs can improve the estimation of preferences, which should be of great interest to the field. Furthermore, the fact that people consistently spend the most time on decisions that matter the least, i. e. where the subjective value difference between the choice options is smallest, has important normative implications for economics [15,22,25,28,31,53] (but see [54,55]for a more nuanced discussion of this issue). The proposed role of focusing effects in social decisions suggests novel interventions, namely the possibility of changing subjects’ behaviorally revealed social preferences by guiding their focus to other players’ payoffs. Such experimental manipulations have been shown to alter choice patterns (e. g. [56]). This possibility stands in sharp contrast to the orthodox view in economics that takes preferences as given and unchangeable [57]. It also stands in contrast to the prevailing social preference models in economics (e. g. [39,44,58,59]) that neglect the focusing effects underlying other-regarding behaviors. There is indeed evidence suggesting that fixations to other subjects’ payoffs is predictive of other-regarding behavior [60], which provides support for our approach. Interestingly, these results are also consistent with findings from individuals with autism and amygdala damage [61,62], who are impaired both in making eye contact and in social behavior. Based on these findings, it has been argued that making eye contact is a way of directing focus to social, rather than selfish outcomes. While manipulating their attention has been successful in improving the social behavior of autistic subjects, it has yet to be shown that such manipulations can alter social preferences in normal subjects. However, manipulating social distance through the wording of the instructions or identity of the subjects has been shown to change social behavior, possibly by focusing subjects’ more on others’ outcomes [63,64]. The SSM framework, as a general model of decision making, provides a means of quantifying the effects of such manipulations on choice behavior.
Subjects gave informed written consent before participating in each of the four studies. All studies were approved by the local ethics committee (Zurich, Switzerland; KEK-ZH 2010–0327). There are four parameters that are standard in all DDMs: the standard deviation of the Gaussian noise (σ), the drift parameter (d), the decision barrier height, and a non-decision time. Because the relative decision value has arbitrary units, we are always free to set one of the first three parameters in the DDM equal to 1. Following the convention from our previous papers, we fix the decision barriers at +/- 1. The first parameter (σ) dictates the amount of noise added to the average drift rate at each millisecond time step, and its value is taken directly from the food-choice experiments (σ = 0. 02). The second parameter is the drift parameter d that multiplies the value difference between the options, in order to determine the average drift rate. Because our formulation of the DDM has fixed decision barriers at +/- 1, the d parameter must be adjusted to the range of values in order to ensure the equivalence of the model across experiments with different units and/or ranges of value. For example, if in a certain experiment the payoffs are expressed in dollars rather than in cents, the nominal payoff range in the experiment with the dollar representation is smaller by a factor of 100 although the real payoffs are identical. It is therefore necessary to adjust the drift parameter d by a factor of 100 because otherwise the model would make wildly different predictions for two identical decisions. Similarly, a dollar difference in value has very different consequences if we are choosing between snack foods or luxury cars [41,42]. Thus, if different experiments involve different payoff ranges there is the need to adjust the drift parameter such that the product of the drift parameter d and the payoff range v¯ remains constant across experiments. Note, that because d⋅v¯ is constant across all experiments this does not introduce any degree of freedom in choosing the value of d in the social-preference experiments examined here. In the social-preference experiments the subjects made choices sequentially and thus could not know the precise range of values that they would face. However, subjects could immediately see the order of magnitude of their payoffs, so we set the value of d such that the product of d and the order of magnitude of v¯ is always equal to 0. 002 ms-1, the value from the food choice studies. See S2 Table for details. From the binary food-choice study we know that fixation durations do not depend on the values of the options so we can assume that, on average, each option is focused on for half of the trial. Therefore, each option (e. g. option X) accumulates evidence at a rate of d·x for half of the trial, and 0. 3·d·x for the other half of the trial, meaning that the average evidence accumulation rate for each option is [0. 5·d·x + 0. 5·0. 3·d·x] = 0. 65·d·x. In the context of the food-choice model this means that the average relative drift rate is equal to 0. 65·d· (x−y). Again, we apply the behavioral insights from the food-choice study (i. e. that fixations do not depend on the values of the options) to the social-preference studies by assuming that each option is fixated on for half of the trial. Therefore, the final parameterized social DDM can be written as: Vt=Vt−1+0. 65d[ (xi−yi) ±0. 3 (xj−yj) ]+ε where x and y are the amounts received by the decision maker (subscript i) and the other player (subscript j) for options X and Y. As before, the RDV evolves over time (in increments of 1 ms) until it reaches a value of +1 or -1. Note that in this extended version of the model, the factor of 0. 3 appears twice, once to maintain the discount on the non-fixated choice options, and a second time to maintain the asymmetry between self and other payoffs. Another way to implement the model would have been to omit the asymmetry between self and other for the non-fixated option, but this alternative model provided worse fits to every dataset. In our previous work [15] the non-decision time was not fit to the data, but instead directly measured from the food-choice data by calculating the average difference between RT and total fixation time. This difference was 355ms. In our simulations of the model we add this “non-decision time” to all the simulated RTs. To simulate each model we used the given utility function to calculate the subjective value for each trial’s choice options (X and Y), and then used the difference between those utilities to determine the model’s drift rate. The model can be written as: Vt=Vt−1+d (U (X) −U (Y) ) +εt The remaining parameters in the model (d, σ and non-decision time) remained the same as in the aDDM. To test alternative SSM implementations we utilized the Ornstein-Uhlenbeck model. For a given choice problem we assume that the input to the model is the difference in subjective values between options X and Y, denoted I = U (X) −U (Y), where Ui (X) = xi ± 0. 3xj as in the main aDDM. Then the Ornstein-Uhlenbeck model can be written as the following differential equation: dV= (λV+kI) dt+σdW where V is the amount of accumulated evidence at time t, dW is independent white noise (Wiener), and λ, k, σ are free parameters. The process proceeds in steps of dt = 1ms. The parameters used to simulate the model [46] are: λ = 2. 3, k = 0. 11ms−1, σ = 0. 6 and a non-decision time of 400ms.
One critical question that concerns all disciplines involved in the study of human decision-making is whether different types of decisions are made in different ways, or whether there exists a common decision mechanism that underlies human choices. If the latter, what are the properties of that mechanism? Here we characterize a dynamical model of decision making that was initially fit to subjects making food choices but was later able to accurately predict choices and reaction times of separate groups of subjects making social decisions. The robustness of the model across different subjects, tasks, and environments supports the idea that the brain uses a consistent process for making decisions.
A Common Mechanism Underlying Food Choice and Social Decisions