Abstract
The onset of the readiness potential (RP)—a key neural correlate of upcoming action—was repeatedly found to precede subjects’ reports of having decided. This was famously taken as evidence against a causal role for consciousness in human decisions making and thus as an attack on free-will. Yet those studies focused on purposeless, unreasoned, arbitrary decisions, bereft of consequences. So, it remains unknown to what degree these neural precursors of action generalize to deliberate decisions, which are arguably more interesting, ecological, and relevant to real life. We therefore directly compared the neural correlates of deliberate and arbitrary decisions during a $1000-donation task to non-profit organizations. While we found the expected RPs for arbitrary decisions, they were strikingly absent for deliberate ones. Our results are congruent with the RP representing the accumulation of noisy, random fluctuations, which drive arbitrary—but not deliberate—decisions. In that they challenge the generalizability of studies that argue for no causal role for consciousness in decision making from arbitrary to deliberate decisions.
Introduction
Humans typically experience freely selecting between alternative courses of action. Yet a series of studies using EEG1–3, fMRI 4–7, intracraniall8, and single-cell recordings9 challenged the validity of this common experience, finding neural correlates of decision processes hundreds of milliseconds and even seconds prior to the time that subjects reported having consciously decided. These findings have been captivating scholars from many disciplines in and outside of academia10–15, with the prospect that the subjective human experience of freely deciding is but an illusion, because human actions might be unconsciously initiated before the conscious decision to act1,15.
However, in the above studies, subjects were only asked to either decide when or which hand to move.12,16 So their decisions were unreasoned, purposeless, and bereft of consequence. This stands in sharp contrast to most real-life decisions that are reasoned, purposeful, and bear consequences17—from which clothes to wear to what route to take to work, and certainly more formative decisions about life partners, career choices, and so on. Such deliberate decisions are also at the center of the philosophical debate on free will18,19, may involve more conscious deliberation, and could thus be more tightly bound to conscious processes.
Interestingly, though deliberate decisions have been widely studied in the field of neuroeconomics 20,21 or in perceptual tasks22, little has been done to assess the relation between decision-related activity and subjects’ conscious experience of deciding. Here, we combine the two fields of research by comparing neural precursors of deliberate and arbitrary decisions in an EEG experiment. Our experiment utilized a donation-preference paradigm, in which a pair of non-profit organizations (NPOs) were presented in each trial. In deliberate-decision trials, subjects’ chose to which NPO they would like to donate $1000, while in arbitrary-decision trials both NPOs received an equal donation of $500, irrespective of subjects’ key presses (Figure 1). Notably, while the visual inputs and motor outputs were identical between deliberate and arbitrary decisions, the decisions’ meaning was radically different: in deliberate blocks, the decisions were meaningful and consequential reminiscent of important, real-life decisions—while in arbitrary blocks, the decisions were meaningless and bereft of consequences— mimicking previous studies of volition.
Results
Behavioral Results
To validate the experimental paradigm, we manipulated decision difficulty as well as decision type (Fig. 1). We reasoned that this should affect only deliberate decisions, and not arbitrary ones. Subjects’ behavior confirmed that the experimental manipulation was successful. Subjects’ reaction times (RTs) were substantially slower for deliberate than for arbitrary decisions (Figure 2, left; F(1,17)=126.11, p<0.0001 for the main effect of decision type; a main effect of decision difficulty was also found: F(1,17)=18.76, p=0.0004; all analyses were performed on log-transformed data, because the raw RTs violated the normality assumption (W=0.94, p=0.001)). Moreover, in deliberate decisions they were slower for hard vs. easy decisions (F(1,17)=20.12, p=0.0003 for the interaction between decision type and decision difficulty; hard vs. easy deliberate decisions: t(17)=4.78, p=0.0002, and not significantly different between hard vs. easy arbitrary decisions: t(17)=1.01, p=0.325). This further demonstrates that in deliberate decisions, subjects were making meaningful decisions, affected by the different values of the two NPOs, while in arbitrary decisions they were not.
The consistency between subjects’ choices throughout the experiment and the NPO ratings they gave prior to the main session was also analyzed (see methods). As expected, subjects were highly consistent with their own, previous ratings when making deliberate decisions, but not when making arbitrary ones (Figure 2, right; F(1,17)=946.55, p<0.0001 for the main effect of decision type. A main effect of decision difficulty was also found: F(1,17)=57.39, p<0.0001. Again, decision type and decision difficulty interacted (F(1,17)=25.96, p<0.0001: subjects were much more consistent with their choices in easy vs. hard deliberate decisions (t(17)=11.15, p<0.0001), than they were in easy vs. hard arbitrary decisions (t(17)=2.50, p=0.028); though subjects were around chance in their consistency in arbitrary decisions (ranging between 0.39 to 0.64; it seems some subjects were slightly influenced by their preferences in arbitrary, easy decisions trials). Finally, no differences were found between subjects’ tendency to press the right vs. left button in the different conditions (both main effects and interaction: F<1).
EEG Results
Readiness Potential (RP)
The RP, generally held to index unconscious readiness for upcoming movement1,12,23,24 (though see 25–27), was measured over electrode Cz in the different conditions by averaging the activity in the 2 s prior to subjects’ movement. Focusing on the last 500 ms before movement onset for our statistical tests, we found a clear RP in arbitrary decisions, yet the RP was completely absent in deliberate decisions (Figure 3; F(1,17)=11.86, p=0.003 for main effect of decision type; in t-tests against zero, an effect was only found for deliberate decisions (hard: t(17)=5.75, p<0.0001; easy: t(17)=5.09, p=0.0001) and not for arbitrary ones (hard: t(17)=1.24, p=0.231; easy: t(17)=1.84, p=0.084)). Notably, this pattern of results persisted also when separating left-hand button presses from right-hand ones (Figure S1), suggesting that it was not affected by the hand that executed the movement.
RTs in deliberate decisions were typically more than twice as long as RTs in arbitrary decisions. We therefore wanted to rule out the possibility that the absence of RP in deliberate decisions stems from the difference in RTs between the conditions. We carried out two analyses for this purpose. First, we divided the subjects into two groups based on their RT—lower and higher than the median for deliberate and arbitrary trials, respectively—and ran the same analysis using only the faster subjects in the deliberate condition (M=1.91s, SD=0.25) and the slowest subjects in the arbitrary condition (M=1.25s, SD=0.23) (Fig. S2A). If RT length affects RP amplitudes, we would expect the RP amplitudes to be more similar between these two groups. However, though there were only half the data points, a similar pattern of results was observed (Figure S2; F(1,32)=5.11, p=0.031), with significant RP found in arbitrary (easy: t(8)=4.57, p=0.0018; hard: t(8)=4.09, p=0.0035), but not deliberate (easy: t(8)=1.92, p=0.09; hard: t(8)=0.63, p=0.54) decisions.
Second, we regressed the difference between RPs (averaged over the last 500 ms before movement onset) in deliberate and arbitrary decisions against the difference between the RTs in these two conditions for each subject (Fig. S2B). Again, if RT length affects RP amplitudes, we would expect differences between RTs in deliberate and arbitrary conditions to correlate with differences between RPs in the two conditions. But no correlation was found between the two measures. Taken together, these results provide strong evidence against the claim that the difference in RP stems from or is affected by the difference in RTs between the conditions.
Lateralized Readiness Potential (LRP)
The LRP, which reflects activation processes within the motor cortex for action preparation after response selection,28,29 was measured by subtracting the difference potentials (C3-C4) in right-hand response trials from this difference in left-hand responses trials and averaging the activity over the same time window.2,28 In this purely motor component, no difference was found between the two decision types (Fig S3; all Fs<1).
Drift Diffusion Model (DDM)
We constructed a drift-diffusion model (DDM) to account for both the deliberate and arbitrary results. Each trial was modeled as a race to threshold between the decision alternative that was congruent and the one that was incongruent with that subject’s initial rating (see Methods). Each race was represented as a leaky stochastic accumulator (see Methods for details and model parameters). We fit the model to our average empirical reaction-times, which were 2.13, 2.52, 0.98 and 1.00 s for the different conditions (henceforth, magnitudes are given for deliberate easy, deliberate hard, arbitrary easy, and arbitrary hard, respectively). The model’s mean RTs were 2.04, 2.46, 0.94, and 0.96 s for these conditions (Fig. 4A, B). The model was further fit to the empirical congruency ratios, which were 0.99, 0.83, 0.54 and 0.49. The model’s congruency ratios were 1.00, 0.84, 0.53 and 0.53. The model then predicted a continuing, RP-like decrease in activity for arbitrary decisions, but only a very slight decrease in activity for deliberate decisions (Fig. 4C; see also Fig S4), which was well in line with our empirical results (Fig. 3A).
Discussion
Since the publication of Libet’s seminal work claiming that neural precursors of action, in the form of the RP, precede subjects’ reports of having consciously decided to act1, a forceful debate has been ranging between neuroscientists, philosophers, and other scholars about the meaning of these findings for the debate on free will (recent collections include 30–32). Some claim that these results have removed conscious will from the causal chain leading to action 15,33,12,33. Others are unconvinced that these results are decisive in the free-will debate 18,19,34 At the heart of much of this debate lies the RP, thought to represent unconscious decision/planning mechanisms that initiate subjects’ decisions prior to their conscious experience of deciding1,23.
Notably, the RP and similar findings showing neural activations preceding the conscious decision to act have typically focused on arbitrary decisions of different types 1,2,4,5,13,35,36. This, among other reasons, rested on the notion that for an action to be completely free, it should not be determined in any way by external factors37—which is the case for arbitrary, but not deliberate decisions (where each decision alternative is associated with a value, and one generally chooses the optimal alternative). But this notion of freedom faces several obstacles. First, most discussions of free will focus on deliberate decisions, asking when and whether these are free38–40. This might be because everyday decisions to which we associate freedom of will—like choosing a more expensive but more environmentally friendly car, helping a friend instead of studying more for a test, donating to charity, and so on—are generally deliberate, in the sense of being reasoned, purposeful, and bearing consequences. In particular, the free will debate is often considered in the context of moral responsibility (e.g., was the decision to harm another person free or not)12,41–44, and free will is even sometimes defined as the capacity that allows one to be morally responsible34,45. Indeed, it seems meaningless to assign blame or praise to arbitrary decisions. Thus, though the scientific operationalization of free will has typically focused on arbitrary decisions, the common interpretations of these studies—in neuroscience and across the free will debate—have alluded to deliberate ones. Here, we show that this type of inference may not be justified, as the neural precursors of arbitrary decisions do not generalize to meaningful ones18,19.
Our finding thus suggests that two different mechanisms may be involved in arbitrary and deliberate decisions, in line with previous studies which focused on either deliberate or arbitrary decisions, and found different neural correlates for the two decision types. Deliberate, reasoned decision-making was mostly studied in the field of neuroeconomics 20 or using perceptual decisions 22, showing elicit activity in the prefrontal cortex (PFC; mainly the dorsolateral (DLPFC) part 46,47 and ventromedial (VMPFC) part/orbitofrontal cortex (OFC) 48,49 and the anterior cingulate cortex (ACC) 50,51. Arbitrary, meaningless decisions were probed in the field of volitional, showing activations in the Supplementary Motor Area (SMA), alongside other frontal areas like the frontomedian cortex52,53 or the frontopolar cortex, as well as the posterior cingulate cortex 4,9 (though see54, which suggests that a common mechanism may underlie both decision types). Possibly then, arbitrary and deliberate decisions may differ not only in respect to the RP, but may be subserved by different underlying neural circuits, which may further weaken attempts at inferences from one class of decisions to the other. Future studies may thus further explore the relations between deliberate decision-making and subjects’ conscious experience of reaching a decision.
Aside from highlighting the differences between arbitrary and deliberate decisions, this study also challenges a common interpretation of the function of the RP. If the RP is not present before deliberate action, it does not seem to be a necessary link in the general causal chain leading to action. Schurger and colleagues25 suggested that the RP reflects stochastic fluctuations in neural activity that lead to action following a threshold crossing when arbitrarily deciding when to move. Our results are in line with that interpretation and expand upon it, suggesting that the RP represents the accumulation of noisy, random fluctuations that drive arbitrary decisions, while deliberate decisions are mainly driven by the values associated with the decision alternatives55. Further studies of the causal role of consciousness in deliberate vs. arbitrary decisions are required to test this hypothesis.
Methods
Subjects
Eighteen healthy subjects participated in the study. They were California Institute of Technology (Caltech) students as well as members of the Pasadena community. All subjects had reported normal or corrected-to-normal sight and no psychiatric or neurological history. They volunteered to participate in the study for payment ($20 per hour). Subjects were prescreened to include only participants who were socially involved and active in the community (based on strength of their support of social causes, past volunteer work, past donations to social causes, and tendency to vote). Two additional subjects were excluded, one due to highly noisy recording and the other due to extremely long RTs, which deviated from the mean by more than two standard deviations. The experiment was approved by Caltech’s Institutional Review Board, and informed consent was obtained from all participants after the experimental procedures were explained to the subjects.
Stimuli and apparatus
Subjects sat in a dimly lit room. The stimuli were presented on a 21” Viewsonic G225f (20” viewable) CRT monitor with a 60-Hz refresh rate and a 1024×768 resolution using Psychtoolbox version 3 and Mathworks Matlab 2014b56,57. They appeared with a gray background (RGB values: [128, 128,128]). The screen was located 60 cm away from subjects' eyes. Stimuli included names of 50 real non-profit organizations (NPOs). Twenty organizations were consensual (e.g., the Cancer Research Institute, or the Hunger project), and thirty were more controversial: we chose 15 causes that are widely debated (e.g., pro/anti guns, pro/anti abortions), and selected one NPO that supports each of the two sides of the debate. This was done to achieve variability in subjects’ willingness to donate to the different NPOs. In the main part of the experiment, succinct descriptions of the causes (e.g., pro-marijuana legalization, pro-child protection; for a full list of NPOs and acronyms, see Table S1) were presented in black Comic Sans MS.
Procedure & Experimental Design
In the first part of the experiment, subjects were presented with each NPO separately. They were instructed to rate how much they would like to support that NPO with a $1000 donation on a scale of 1 (“I would not like to support this NPO at all) to 7 (“I would very much like to support this NPO”). No time pressure was put on the subjects, and they were given access to the website of each NPO to give them the opportunity to learn more about the NPO and the cause it supports.
After the subjects finished rating all NPOs, the main experiment began. It included 360 trials, divided into 40 blocks of 9 trials each. In each block, subjects made either deliberate or arbitrary decisions. Two succinct causes descriptions. representing two actual NPOs, were presented in each trial (Fig. 1). In deliberate blocks, subjects were instructed to choose the NPO to which they would like to donate $1000 by pressing the <Q> or <P> key on the keyboard, for the NPO on the left or right, respectively, as soon as they decided. Subjects were informed that at the end of each block one of the NPOs they chose would be randomly selected to advance to a lottery. Then, at the end of the experiment, the lottery will take place and the winning NPO will receive a $20 donation. In addition, that NPO will advance to the final, inter-subject lottery, where one subject’s NPO will be picked randomly and will be given a $1000 donation. It was stressed that the donations were real and that no deception was used in the experiment. To persuade the subjects that the donations are real, we presented a signed commitment to donate the money, and promised to send them the donation receipts after the experiment. Thus, subjects knew that in deliberate trials, every choice they made was not hypothetical, and could potentially lead to an actual $1020 donation to their chosen NPO.
Arbitrary trials were identical to deliberate trials except for the following crucial differences. Subjects were told that, at the end of each block, the pair of NPOs in one randomly selected trial would advance to the lottery together. And, if that pair wins the lottery, both NPOs would receive $10 each. Further, the NPO pair that would win the inter-subject lottery would receive a $500 donation each. Hence it was stressed to the subjects that there was no reason for them to prefer one NPO over the other in arbitrary blocks, as both NPOs would receive the same donation regardless of their button press. Subjects were told to therefore simply press either <Q> or <P> when they felt the urge to do so. Thus, while subjects’ decisions in the deliberate blocks were meaningful and consequential, their decisions in the arbitrary blocks had no impact on the final donations that were made. In these trials, subjects were further urged not to let their preferred NPO dictate their response. Note that we did not ask subjects to report their “W-time” (time of consciously reaching a decision), because this measure was shown to rely on neural processes occurring after movement onset58 and to potentially be backward inferred from movement time59. Even more importantly, clock monitoring was demonstrated to have an effect on RP size60, so it could potentially confound our results61.
In addition, we manipulated decision difficulty (Easy/Hard) throughout the experiment, randomly intermixed within each block. Decision difficulty was determined based on the rating difference between the two presented NPOs. NPO pairs with 1 or 4 or more rating point difference were designated hard or easy, respectively. Based on each subject’s ratings, we created a list of NPO pairs, half of each were easy choices and the other half hard choices.
Each block started with an instruction written either in dark orange (Deliberate: “In this block choose the cause to which you want to donate $1000”) or in blue (Arbitrary: “In this block both causes may each get a $500 donation regardless of the choice”). Short-hand instructions appeared at the top of the screen throughout the block in the same colors as that block’s initial instructions; Deliberate: “Choose for $1000” or Arbitrary: “Press for $500 each” (Fig. 1). Each trial started with a fixation cross, with a duration drawn from a uniform distribution between 1 and 1.5s. Then, the two cause descriptions appeared on the left and right side of the fixation cross (left/right assignments were randomly counterbalanced), and remained on the screen until the subjects responded with a key press. The cause corresponding to the pressed button then turned white, and a new trial started. If subjects did not respond within 20s, they received an error message and were informed that if this trial would be selected for the lottery, no NPO would receive a donation. However, this did not happen for any subject on any trial.
To assess the consistency of subjects’ decisions during the main experiment with their ratings in the first part of the experiment, subjects choices were coded in the following way: each binary choice in the main experiment was given a consistency grade of 1, if subjects chose the NPO that was rated higher in the rating session, and 0 if not. Then a consistency grade was calculated as the mean over all the choices. A consistency grade of 1 indicates perfect consistency with one’s ratings, 0 – perfect inconsistency, and 0.5 – chance performance.
To better equate memory load, attention, and other cognitive aspects between deliberate and arbitrary decisions—except those aspects directly associated with the decision type, which was the focus of our investigation—we wanted to make sure subjects were carefully reading and remembering the causes also during the arbitrary trials. We therefore randomly interspersed 36 memory catch-trials throughout the experiment (thus more than one catch trial could occur per block). On such trials, four succinct descriptions of causes were presented and subjects had to select the one that appeared in the previous trial. A correct or incorrect response added or subtracted 50 cents from their total, respectively. (Subjects were informed that if they reached a negative balance, no money will be deducted off their payment for participation in the experiment.) Thus, subjects could earn $18 more for the experiment, if they answered all memory test questions correctly. Subjects typically did well on these memory questions, on average erring in 2.5 out of 36 memory catch trials (7% error) and gaining an additional $16.75 (SD=3.19).
ERP recording methods
The EEG was recorded using an Active 2 system (BioSemi, the Netherlands) from 64 electrodes distributed based on the extended 10–20 system and connected to a cap, and seven external electrodes. Four of the external electrodes recorded the EOG: two located at the outer canthi of the right and left eyes and two above and below the center of the right eye. Two external electrodes were located on the mastoids, and one electrode was placed on the tip of the nose. All electrodes were referenced during recording to a common-mode signal (CMS) electrode between POz and PO3. The EEG was continuously sampled at 512 Hz and stored for offline analysis.
ERP analysis
ERP analysis was conducted using the “Brain Vision Analyzer” software (Brain Products, Germany) and in-house Mathworks Matlab scripts. Data from all channels were referenced offline to the average of all channels. The data were then digitally high-pass filtered at 0.1 Hz using a Finite Impulse Response (FIR) filter to remove slow drifts. A notch filter at 59-61 Hz was applied to the data to remove 60-Hz electrical noise. The signal was then cleaned of blink artifacts using Independent Component Analysis (ICA)62. Signal artifacts were detected as amplitudes exceeding ±100 μV, differences beyond 100 μV within a 200 ms interval, or activity below 0.5 mV for over 100 ms (the last condition was never found). Sections of EEG data that included such artifacts in any channel were removed (150ms prior and after the artifact), leaving an average number of 70.38 trials with a range of 36-86 out of 90 trials per condition. Channels that consistently had artifacts were replaced using interpolation (4.2 channels per subject, on average).
The EEG was segmented by locking the waveforms to subjects’ decision onset, starting 2s prior to the decision and ending 0.2s afterwards, with the segments averaged separately for each decision type (Deliberate/Arbitrary x Easy/Hard) and decision content (right/left). The baseline period was defined as the time window between −1000ms and −500ms prior to the beginning of the trial. Baseline adjustment included subtracting the mean amplitude of the activity during the baseline period from all the data points in the segment.
Differences greater than expected by chance were assessed using two-way ANOVAs with decision type (deliberate, arbitrary) and decision difficulty (easy, hard), using IBM SPSS statistics, version 24. For both RP and LRP signals, the mean amplitude from 500 ms before to button-press onset were used for the ANOVAs. Greenhouse–Geisser correction was never required as sphericity was never violated63.
Model and Simulations
All simulations were performed using Mathworks Matlab 2014b. The model was devised off the one proposed by Schurger and colleagues25. Theybuilt a drift-diffusion model64,65 for arbitrary decisions only, which included a leaky stochastic accumulator (with a threshold on its output) and a time-locking/epoching procedure. Their model amounted to iterative numerical integration of the differential equation where I is the drift rate, k is the leak (exponential decay in x), ξ is Gaussian noise, and c is a noise-scaling factor (ws used c = 0.05). Δt is the discrete time step used in the simulation (we used Δt = 0.001, similar to our EEG sampling rate). Here I represents a constant urgency to respond that is inherent in the demand characteristics of the task, evidenced by the fact that no subject took more than 20 s to decide on any trial. The leak term, k, ensures that the model would not be too linear; i.e., it prevents the urgency from setting up a linear trajectory for the accumulator toward the threshold. Hence, due to the leak term, doubling the magnitude of the threshold would make the accumulator rarely reach the threshold, instead of reaching it in roughly twice the amount of time (up to the noise term) without a leak term.
Our model accounted for both arbitrary and deliberate decisions and was built to fit our empirical results, based on with two Schurger-like components. The first one accumulated activity that drove arbitrary decisions (i.e., random fluctuations25). The second component drove deliberate decisions based on subjects’ values associated with the decision alternatives. Henceforth we term these Noise and Value components for ease of description. Our model used its Noise component for arbitrary decisions and its Value one for deliberate decisions.
Schurger and colleagues modeled only the decision when to move. But our subjects decided both when and which hand to move. So, we had to extend the Schurger model in that respect as well. We did this using a race-to-threshold mechanism between the two decision alternatives. In our paradigm, the difference in rating was either 1 (hard decisions) or 4-6 (easy decisions; see “Procedure & Experimental Design” in Methods), so there was always an alternative that was ranked higher than the other. Choosing the higher or lower alternative was termed a congruent or incongruent choice with the initial ratings, respectively.
Using a parameter sweep, we found the values of the thresholds, urgency, and leak that best fit our average empirical reaction times for {easy, hard} x {deliberate, arbitrary} decisions as well as our empirical consistency ratios for those 4 decision types. The model’s reaction time was defined as the overall time (where each step took Δt = 0.001 s) that it took until the first threshold crossing in the race-to-threshold pair. We used the same threshold value of 0.15 and leak value of k=0.5 for all model types. The only parameter that was modulated across {deliberate, arbitrary} x {easy, hard} decisions x {congruent, incongruent} decision alternatives was the urgency, I (Table 1). These parameters were then fixed when fitting the simulated Cz activity across all conditions.
Each simulation consisted of either 120 runs of the model, the same as the number of empirical trials per condition (Fig. 4C), or 10000 runs of the model for a smoother reaction-time distribution for the model (Fig. 4B). For each run of the model, we identified the first threshold crossing point and extracted the last second (1000 steps) before the crossing in each run. If the first crossing was earlier than sample no. 1,000 by n > 0 samples, we padded the beginning of the epoch with n null values (NaN or “not-a-number” in Matlab). These values did not contribute to the average across simulated trials, so the simulated average RP became noisier at earlier time points in the epoch. Our model was therefore similarly limited to the Schurger model in its inability to account for activity earlier than the beginning of the trial. (Fig. 3C).
The authors declare no competing financial interests.
Acknowledgements
We thank Ralph Adolph for his invaluable guidance and support in designing and running the experiment as well as for very useful discussions of the results. We thank Ram Rivlin for various conceptual discussions about deliberate versus arbitrary decision-making and about the initial experimental paradigm design. We thank Caitlin Duncan for her help in patiently and meticulously gathering the EEG data. We thank Daw-An Wu for discussions about EEG data collection and preprocessing and for his help with actual data collection. We thank Daniel Grossman for his help in carefully preprocessing the data and suggesting potential interpretations of it.
This research was supported by Florida State University's Big Questions in Free Will Initiative, funded by the John Templeton Foundation, to U.M. and C.K., by the Bial Foundation, to U.M. and L.M., and by the German-Israeli Foundation for Scientific Research and Development to L.M. The authors declare no competing financial interests.