Thirty experienced drivers (12 female, 18 male, aged 25.8 ± 2.8 years), who held a valid driver's license gave their informed written consent to participate to this experiment. They all had normal or corrected-to-normal vision and were not informed about the purpose of the study. A local ethics committee approved the experiment.

Figure 1 is an overview of the experimental setup. Participants sat in a fixed-base driving simulator (Mobsim, France). Their eye level was 1.1 m above the floor and 1.5 m in front of a large screen (2.5 × 3.2 m), which encompassed 94° of their horizontal field of view. The action of their right foot on the brake and accelerator pedals and their manipulation of the steering wheel (ECCI Trackstar 6000 GTS) were monitored via a USB signal sent to a host computer (Intel® Core™ i7-950 Processor @3.07 GHz; NVIDIA® GeForce® GTX 580 graphics card). Customized OpenGL virtual reality software updated the virtual scene. The virtual scene was rear-projected onto the screen by a video projector (Barco iQ R500) at a frame rate of 60 Hz with a resolution of 1152 × 864 pixels. No speedometer or audio feedback was provided to participants.

A 20% deviation of the accelerator or brake pedal from the neutral position constituted a single constant maximum acceleration or deceleration of the virtual car, respectively until the end of the trial. A 45° clockwise rotation of the steering wheel initiated a single lateral exit of the participant's car onto the roadside, followed by an immediate stop. Participants were only able to select one, unique action (i.e., maximum acceleration, maximum braking or a roadside exit) during the course of one trial. Although it was impossible for participants to control the maneuver once it has been initiated, the experimental setup reproduced real-life constraints in emergency situations where the action initiation time is crucial.

From the participant's viewpoint, the visual scene was composed of an intersection formed by two straight, orthogonal roads, the cockpit of the virtual car, an oncoming car traveling orthogonally to participant's displacement and a blue sky (Figure 1). The driving environment consisted of a conventional two-lane, 7-m wide cement road in a flat rural environment. The right-hand side of lanes was delimited by a continuous white line and the left by a discontinuous white line. A 3.5-m wide gravel bank and a 3.5-m wide pavement bordered by trees were displayed on the right- and left-hand sides of the road, respectively. The participant's lane was crossed orthogonally by a 3.5-m wide single lane road bordered by trees. An oncoming vehicle approached the intersection on this road. A white horizontal line and two checkerboard panels attached to poles marked the beginning of the experimental space. The participant's car and the oncoming car were displayed as 3D blue and red models of a 4 × 4 Hyundai ix35, respectively. Both cars were 4.41 m long, 2.13 m wide, and 1.68 m high.

Participants were divided into three groups according to the maximum deceleration of the virtual car: 5 m/s² D_max (the low group), 10 m/s² D_max (the high group) and ∞ m/s² D_max (the inf group, able to stop instantaneously). The experiment was divided into four phases: deceleration calibration, acceleration calibration, familiarization and the experimental phase. At the beginning of each phase, participants automatically moved through an empty rural environment at a constant velocity along the longitudinal road axis for 5 s before the trial actually started. During this period, any pedal action by participants was ignored by the simulator. A digital 3 s countdown preceded the actual trial. At this point, the oncoming vehicle (or an immobile barrier, see the deceleration calibration in the next section) appeared and the velocity of the participant's car did not change unless they manipulated the pedals or the steering wheel. It is important to note that participants were not allowed to continuously regulate their displacement; they could only initiate either a maximum acceleration or deceleration. The trial ended when the participant's car was 10 m beyond the intersection or had stopped.

The deceleration calibration phase was designed to enable participants to calibrate the maximum deceleration (D_max) of the virtual car. Participants were instructed to stop in front of a red and white barrier placed just before the intersection. Specifically, they were asked to initiate the driving maneuver with the maximum braking capabilities of their car at the last possible moment. The initial distance between the participant's car and the barrier, and the participant's initial velocity were manipulated to create six CT_stop values (depending on the group). CT_stop is defined as the last time to stop safely by braking at D_max (see the Supplementary Material for a mathematical definition, Independent Variables subsection and Table 1 for initial values). In sum, the participant's task was to brake at a time as close as possible to the CT_stop. Conditions were allocated randomly and repeated twice. A trial was recorded as successful when the participant braked at least 0.55 s before the CT_stop or at most 0.20 s after it. A braking time of t = CT_stop – 0.55 s meant that they had stopped 14 m before the barrier (on average). Conversely, a maneuver initiated at t = CT_stop + 0.20 s meant that they had stopped 5 m after it (on average). The superior tolerance was weaker than the inferior tolerance in order to discourage participants from braking after the CT_stop as this decision led to a collision.

The acceleration calibration phase was designed to enable participants to calibrate the maximum acceleration (A_max) of their virtual car. Participants were instructed to cross the intersection before an oncoming car moving at a constant velocity reached the intersection and blocked the crossing. Thus, drivers had to initiate the driving maneuver with the maximum acceleration capabilities of their car at the last possible moment. Their distance to the intersection and their initial velocity, and the distance between the oncoming car and the intersection and its velocity were manipulated to create six CT_cross values (the same for each group). CT_cross is defined as the last time to cross safely the intersection by accelerating at A_max (see the Appendix for a mathematical definition, Independent Variables subsection and Table 1 for initial values). Here, the participant's task was to accelerate as close as possible to CT_cross. These conditions were randomly allocated and repeated twice. A trial was recorded as successful when the participant decided to accelerate at a time at least 0.55 s before the CT_cross or a maximum of 0.20 s after it. If participants decided to accelerate at t = CT_cross – 0.55 s, they crossed the intersection before the oncoming obstacle with a safety margin of 8 m (on average). Conversely, if they initiated the maneuver at a time later than t = CT_cross + 0.20 s, they collided with the oncoming car as the average safety margin was –0.5 m.

In each calibration trial, success was indicated to the participant by a green symbol and failure by a red symbol. Participants performed 12 trials in each calibration sub-phase. The 12-trial sequence ended when the participant had successfully completed at least eight trials. Otherwise, the 12-trial sequence was repeated until they met this criterion.

During the experimental phase, an oncoming car moved orthogonally at a constant velocity (see Table 1 for velocity values) toward the intersection and stopped in the participant's lane, blocking the road. In each trial, participants had to decide whether to cross, stop or exit. They could either try to cross the intersection before the oncoming car arrived by initiating a maximum acceleration before it was too late to cross safely (i.e., before the CT_cross). Otherwise, they could decide to stop before they reached the intersection by initiating a braking maneuver before it was no longer possible to stop safely (i.e., before the CT_stop). As a last resort, they could decide to bail out by steering into the emergency lane to ensure their safety. In any given trial, they selected one of these three actions, which were indicated in real time by “GO,” “STOP,” and “OUT” messages displayed on the screen to provide an augmented feedback about the maneuver selected. At the end of each trial a green symbol informed the participants that they had not collided with the oncoming car, while a red symbol indicated a collision. No feedback was provided when participants bailed out; this was to discourage them from abusing this emergency alternative. The entire experiment lasted approximately one and a half hours. A short familiarization phase preceded the experimental phase. In this phase, the participant was exposed once to the 18 experimental conditions.

The independent variables and their respective contribution to the success of participant's maneuver are illustrated in Figure 2. The maximum acceleration of the virtual car (A_max) was set to 2 m/s² for all groups. The maximum deceleration (D_max) was a between-group variable. As mentioned above, participants were divided into three groups according to the maximum deceleration of the virtual car: 5 m/s² D_max (the low group), 10 m/s² D_max (the high group) and ∞ m/s² D_max (the inf group). As the inf group was able to stop instantaneously at any given moment, they only had to decide whether to cross. Consequently, differences in the behavior of the inf group and the other groups made it possible to compare the influence of a single cross-ability affordance and choice between cross-ability and stop-ability affordances.

The CT_cross (i.e., the critical time at which the minimum satisfying acceleration to safely cross the intersection, denoted MSA, exceeds the driver's maximum acceleration capabilities A_max) and the CT_stop (i.e., the critical time at which the minimum satisfying deceleration to safely stop, denoted MSD, exceeds the driver's maximum braking capabilities D_max) were between-trials variables. The computations of these variables are defined in the Supplementary Material.

The experimental conditions were created by adjusting the extrinsic features of the intersection between trials. Hence, we manipulated the distance from the drivers to the intersection and their initial velocity, and the distance between the oncoming car and the intersection and its velocity for each of the three groups (Table 1). This created 18 intersection-crossing combinations, which were randomly sorted and repeated five times. These combinations resulted in three CT_cross values (the latest time it was possible to cross safely by accelerating at A_max) that were applied to each group (0.00, 1.50, and 2.50 s), and six CT_stop values (the latest time it was possible to stop safely by braking at D_max) that ranged from −1.50 to 4.25 s depending on the braking capability of the virtual car (the ranges were different for each group). The ratio between the initial distance of the oncoming car and the initial distance of the participant's car was adjusted so that the oncoming car was always initially located 35° to the left of the participant's field of view.

CT_cross and CT_stop values specified the last moment (relative to the beginning of the trial) at which the maximum acceleration and deceleration had to be initiated in order to cross or stop safely, respectively. Therefore, from a functional point of view, positive, negative and null values of CT_cross and CT_stop indicated safe crossing and stopping after, before and at the beginning of the trial, respectively. For example, a CT_stop equal to 2.50 s meant that the driver could initiate a deceleration at a maximum of 2.50 s after the beginning of the trial (i.e., later than in a trial with a CT_stop value equal to 1.50 s). Conversely, a CT_stop value equal to −1.50 s meant that at the beginning of the trial, it was already impossible to stop safely (by 1.50 s).

The dependent variable was the decision selected by each participant (i.e., to cross, stop, or to exit), the time at which the pedal corresponding to the selected decision was pushed and the number of collisions with the oncoming car. We computed the individual frequency of each decision as the ratio of the number of decision types over the number of trials and focused on crossing frequency as a function of CT_cross and CT_stop conditions. We computed the individual average decision time for the overall trials (independently of the occurrence of collisions).

Our initial hypothesis was that the selection of driving maneuvers was driven by the perception of the corresponding affordance. In other words, crossing frequency would increase with the viability of crossing possibilities and stopping frequency would increase with the viability of stopping possibilities. Finally, drivers were expected to exit the road when it was not possible to either cross or stop.

Based on the frequency of crossing maneuvers, we tested the hypothesis of the choice between cross-ability and stop-ability affordances when drivers have to select the best maneuver at the approach to an intersection. From an extrinsic viewpoint, all groups of drivers experienced identical intersection-crossing situations. However, from an intrinsic viewpoint, stopping possibilities (CT_stop) were manipulated between groups by varying maximum braking capabilities (D_max). Crossing possibilities (CT_cross) were not manipulated between groups as maximum acceleration (A_max) was kept constant. Therefore, if the stop-ability affordance played a role in decision-making, the manipulation of D_maxwas expected to affect the average crossing frequency. More specifically, the low D_max group was expected to cross the intersection at a higher frequency on average than the high D_max group because the former had lower braking capabilities.

We investigated the choice between affordances hypothesis in more detail by examining, for each group, the effect of CT_cross and CT_stop. As described earlier, the three CT_cross values (0.00, 1.50, and 2.50 s) were combined with six different CT_stop values, yielding a total of 18 intersection-crossing situations. Depending on the intersection-crossing situation and D_max, drivers encountered CT_stop values ranging from −1.50 to 1.75, 0.50 to 3.00, and 2.50 to 4.25 s for the low, high and inf groups, respectively. We predicted that in the inf group (that only had to handle the cross-ability affordance, given that drivers could stop instantly) crossing frequency would increase with CT_cross, while CT_stop would have no effect. For the low and high groups, we expected to see a combined effect of CT_cross and CT_stop on the average crossing frequency. This would demonstrate that CT_cross and CT_stop, as formalized in this experiment, contribute to choice between affordances. We expected that the crossing frequency would increase with increasing CT_cross in the same way for each group, and would increase with decreasing CT_stop, more so for the low group exposed to low CT_stop values (CT_stop = 0.33 s on average) than for the high group exposed to higher CT_stop values (CT_stop = 1.75 s on average).

Our first analysis checked that all groups had successfully calibrated their virtual maximum deceleration (D_max) and acceleration (A_max) during the calibration phase. Drivers were assumed to have calibrated their A_max and D_max when they succeeded in 8 out of 12 trials in acceleration and braking calibration tasks. We analyzed the number of 12-trial sequences required to achieve this criterion and the overall success rate for all groups. Participants in the three groups calibrated D_max in 2.30 ± 0.95, 1.90 ± 0.88, and 1.10 ± 0.32 sequences of 12 trials with a final success rate equal to 9.40 ± 1.17, 9.00 ± 0.94, and 10.50 ± 1.08 trials, for the low, high and inf groups, respectively. Participants calibrated A_max in 3.00 ± 1.05, 3.00 ± 1.70, and 3.50 ± 1.08 sequences of 12 trials with a success rate in the last 12-trial sequence equal to 9.10 ± 1.79, 8.80 ± 0.92, and 9.10 ± 1.37 trials, for the low, high and inf groups, respectively. In sum, participants quickly calibrated their maximum action capabilities. The calibration time for D_max increased as D_max decreased, while the calibration time for A_max was constant across groups. Finally, the similarity in the final success rates achieved by all groups suggests that all participants had a similar level of competence before the experimental phase.

Our analyses then investigated differences in collision frequency according to group and decision type. Despite the similar success rates at the end of the crossing and stopping calibration phases, the three groups of participants collided with the oncoming car at different frequencies (24.56 ± 5.25, 14.00 ± 3.40, and 8.22 ± 4.92% for the low, high and inf groups, respectively). Moreover, the decision to cross led to more collisions (17.00 ± 4.69, 9.22 ± 3.78, and 8.22 ± 4.92%) than the decision to stop (7.56 ± 3.66, 4.78 ± 2.35, and 0% for the low, high and inf groups, respectively). Overall, these results show that the risk of collision due to the decision to cross increased with a decrease in maximum braking capabilities.

Thirdly, analyses aimed at investigating the changes in driver's decision time depending on groups, decision type and intersection-crossing situations. Decision time did not appear to differ between the low and high groups (0.81 ± 0.20 and 0.91 ± 0.21 s) but increased for the inf group (1.53 ± 0.42 s). Moreover, decision time for crossing, stopping and exiting (0.78 ± 0.27, 1.29 ± 0.61 and 1.48 ± 0.47 s, respectively) was in most cases in an ascending order (consistent with instructions), with the inf group showing a large tendency to decide stopping later than crossing. This suggests that the participants of the inf group exploited their braking possibility as a last resort, in opposition to the other groups that had to choose between affordances.

We further focused on the influence of intersection-crossing situations on the average decision time. We noted that CT_stop and TTC_s (Time to Contact of the driver's car referred to the intersection) co-varied in our intersection-crossing situations (Table 1). Their respective contributions on decision time was thus assessed for the three groups with comparisons of percentage of variance of decision time provided by separate linear regressions between these two predictors and decision time, respectively. TTC_s was found to better account for the variations of decision time than CT_stop (85.54, 80.63, and 77.37% vs. 35.15, 65.59, and 77.37% the low, high and inf groups, respectively). The decision time increased with the increase of TTC_s (ranging from 0.66 to 1.05, 0.71 to 1.15, and 1.11 to 2.00 s for the low, high and inf groups, respectively). However, the influence of TTC_s was more important for the inf group than for the other groups. Finally, the decision time of the inf group decreased and was equal to 1.72, 1.49, and 1.37 s when CT_cross increased and were equal to 0.00, 1.50 and 2.50 s, respectively. On the contrary, the decision time remained quite constant for the low (0.87, 0.78, and 0.77 s) and high groups (0.99, 0.87, and 0.85 s) across manipulations of CT_cross.

In sum, we reported that the decision time tends to decrease when CT_cross increased for the inf group. Moreover, decision time increased when TTC_s increased with a more important intensity for the inf group than for the other groups. The low and high group being limited in their maximum acceleration and deceleration capabilities took their behavioral decision earlier than the inf group which was only limited by a maximum acceleration.

The final and most important analysis investigated changes in the frequency of driving maneuvers across groups depending on their crossing and stopping possibilities during the experimental phase. Figure 3 shows that the frequency of all driving maneuvers (crossing, stopping and exiting) varied as a function of the between-group manipulation of D_max. As deceleration capability (D_max) increased, drivers attempted less often to cross the intersection (65.22 ± 12.78, 50.00 ± 13.66, and 42.89 ± 17.48% for the low, high and inf groups, respectively). In parallel, as D_max increased, drivers decided to stop more frequently (21.78 ± 13.12, 46.56 ± 13.75, and 57.00 ± 17.51% for the low, high and inf groups, respectively). Finally, as D_max increased, drivers exited less often (13.00 ± 11.10, 3.44 ± 4.64, and 0.11 ± 0.35% for the low, high and inf groups, respectively).

These differences in the frequency of stopping and exiting suggest a mixed perception of related affordances. The increase in the frequency of the decision to stop as D_max increased corresponded to an increase in stopping possibilities, as average CT_stop values increased with D_max. Similarly, the decrease in the frequency of the decision to exit as D_max increased corresponded to a decrease in intersection-crossing situations where there were no crossing or stopping possibilities (i.e., CT_cross and CT_stop were less than or equal to zero at the start of the trial). Exiting maneuvers were observed in 13% of trials for the low group, while 11% of intersection-crossing situations prevented both safe crossing and stopping. On the other hand, the frequency of exiting in high and inf groups, which never encountered such situations, was close to zero.

However, the observed changes in crossing frequency with D_max suggested that there was a choice between a cross-ability affordance, directly related to the crossing action, and a stop-ability affordance that was a priori irrelevant to the decision to cross. As CT_cross conditions were identical for all groups, changes in crossing frequency as a function of CT_cross would tend to confirm that crossing possibilities influenced the decision to cross, independently of the group. In parallel, given that stopping possibilities were a priori only relevant to braking maneuvers and that they co-varied with D_max, the D_max effect on crossing frequency would suggest that there is a choice between stopping and crossing possibilities when performing the crossing maneuver.

In order to investigate the choice between crossing and stopping affordances, a Two-Way ANOVA (CT_cross [0.00, 1.50, 2.50] × group [low, high, inf]) with CT_cross as a repeated measure was performed on crossing frequencies. Post-hoc comparisons were conducted using Newman–Keuls a posteriori tests. The ANOVA showed a significant main effect of CT_cross [F_{(2, 54)} = 67.16, p < 0.05]. Post-hoc analyses showed that crossing frequency significantly increased with each increase of CT_cross (p < 0.05). The ANOVA also showed a significant main effect of group [F_{(2, 27)} = 5.96, p < 0.05]. Post-hoc analyses showed that the crossing frequency was significantly higher for the low group than for the other groups. The group × CT_cross interaction was not significant [F_{(4, 54)} = 1.39, p > 0.05].

In brief, our results showed that crossing frequency increased with CT_cross for all groups. Between-group differences were observed in crossing frequency, although all groups experienced identical intersection-crossing situations and had identical maximum acceleration capabilities. Taken together, these results suggest that both crossing and stopping possibilities play a role in the decision to cross.

As CT_stop co-varied with D_max and CT_stop conditions were different for each group (see Table 1), the influence of CT_stop can only be investigated by carrying out three separate Two-Way ANOVAs (CT_cross × CT_stop) with repeated measures on CT_cross and CT_stop on crossing frequency. Figure 4 depicts the change in average crossing frequency as a function of CT_cross and CT_stop. For each group, the ANOVAs again revealed a main effect of CT_cross [F_{(2, 18)} = 25.06; F_{(2, 18)} = 20.96 and F_{(2, 18)} = 25.85, p < 0.05 for the low, high and inf groups, respectively]. For all groups, post-hoc analyses revealed that the crossing frequency observed for CT_cross = 0 was significantly lower than that seen in the other CT_cross conditions (p < 0.05). The ANOVA also revealed a main effect of CT_stop for low and high groups [F_{(5, 45)} < 9.59; F_{(5, 45)} = 3.59, p < 0.05 for the low and high groups, respectively]. Post-hoc analyses showed that the crossing frequency displayed by the low group during the negative CT_stop conditions (CT_stop = −1.50 and −0.50) were significantly higher (p < 0.05) when compared separately to those displayed in other CT_stop conditions (except for CT_stop = 0.45). Concerning the high group, the crossing frequency observed for the lowest CT_stop value (CT_stop = 0.50) was significantly higher than in all conditions for which CT_stop ≥ 1.50 (p < 0.05, except for CT_stop = 2.00). No significant main effect of CT_stop was found for the inf group [F_{(5, 45)} = 0.30, p > 0.05]. Finally, no significant CT_cross × CT_stop interaction was found [F_{(10, 90)} = 0.55; F_{(10, 90)} = 1.42; F_{(10, 90)} = 1.75, p > 0.05 for the low, high and inf groups, respectively].

In sum, drivers attempted to cross the intersection more often, not only as CT_cross increased (for all three groups), but also as CT_stop decreased (for the low and high groups). As predicted, only the crossing affordance seemed to influence the inf group (where braking capabilities were infinite). Concerning the other groups, the increase in crossing frequency was higher in the low group (where the CT_stop was low) than the high group (where the CT_stop was higher). It seems that the frequency of crossing maneuvers results from a choice between crossing and stopping affordances (characterized by CT_cross and CT_stop, respectively) for the low and high groups.

Based on our statistical results and mathematical constraints, we designed an a posteriori model able to quantify this choice between crossing and stopping affordances using the average inter-individual crossing frequency for the three groups. In the model, crossing frequency was only influenced by main effects of CT_cross and CT_stop. Indeed, in the low and high groups crossing frequency increased with CT_cross and decreased with CT_stop with no significant CT_cross × CT_stop interaction. Consequently, for the low and high groups, the crossing frequency was modeled as a sum of two functions: an increasing CT_cross function, denoted f, and a decreasing CT_stop function, denoted g. The behavior of the inf group, which was assumed to be immune from choice between CT_cross and CT_stop affordances due to its infinite D_max, was modeled differently. The ANOVA analysis of this group's behavior revealed a main positive effect of CT_cross but no main effect of CT_stop. We thus modeled the crossing frequency of the inf group with a single increasing CT_cross function, denoted f. We used the same function f for the three groups as the group × CT_cross interaction was found to be non-significant.

The best mathematical formula found to describe f and g were sigmoid-type functions. Such functions were widely used to model verbal (Oudejans et al., 1996; Fajen and Matthis, 2011) and motor responses (Ishak et al., 2008) to affordances (see Franchak and Adolph, 2014 for a review about the use of probabilistic functions to model affordances; and Gescheider, 1997 for classical literature from which this habit was borrowed). A visual inspection of Figure 4 suggested that the negative effect of CT_stop on crossing frequency was exponential, with a plateau in crossing frequency for the lowest and highest CT_stop values. The change in crossing frequency as a function of CT_stop is given by the following formula: g(CTstop)=11+e−b·CTstop, where b ≤ 0 is a coefficient modulating the slope of the crossing frequency (i.e., the lower b the lower the slope of the sigmoid). We used a similar sigmoid formula to model the positive effect of CT_cross on crossing frequency: f(CTcross)=11+e−a·CTcross where a ≥ 0 is the coefficient that modulates the slope of the crossing frequency. It should be noted that other mathematical functions would have been equally good candidates to fit this three point pattern. Moreover, in order to model the crossing frequency in the theoretical 0–100% range, another mathematical constraint was added. We modulated the action of f and g functions such that their sum never exceeded 100 using w and 1 − w weightings, with w ranging from 0 to 1. The choice between CT_cross and CT_stop on predicted crossing frequency was finally modeled as follows: (1)F˜cross=100×[w1+e−a·CTcross+1−w1+e−b·CTstop]

We used the Gauss–Newton algorithm to estimate the set of coefficients a, b, and w that minimize the sum of squares of residuals between the data and our model. With an identical set of coefficients for each group (a = 1.67, b = −1.69, and w = 0.57), the model offers a coefficient of determination equal to 0.84 and thus accurately reproduces our observations (Figure 4). The quality of this adjustment to our data can be further established by noting that this R² is close to the maximal theoretical R² equal to 0.92. This theoretical R² can be computed using, as a model for crossing frequency, a sum of a polynomial of degree 17 in CT_stop (6 CT_stop modalities × 3 groups – 1, corresponding to the degrees of freedom related to CT_stop) and a polynomial of degree 2 in CT_cross (3 CT_cross modalities −1, corresponding to the degrees of freedom related to CT_cross). We considered the maximum theoretical value to be 0.92 as we did not observe a significant CT_cross × CT_stop interaction, theoretically explaining 8% of variance. Moreover, the low standard deviations of the coefficients (std = 0.56, 0.50, and 0.03 for a, b, and w coefficients, respectively) demonstrated their stability and confirmed that the model provided relevant predictions. A Student's t-test based on a t-distribution with n − k = 51 degrees of freedom (n and k refer to the number of points and the number of coefficients, respectively) tested the null hypothesis that each coefficient is equal to zero and demonstrated their significance.

First, the 1−w1+e−b·CTstop term accounts for the observed exponential increase in crossing frequency with CT_stop, especially for the low group exposed to CT_stop values ranging from 1.75 to −1.50 s. The predicted crossing frequency exponentially increases as CT_stop values decrease until a maximum crossing frequency is reached when CT_stop values drop below −1.50 s. Second, this term is close to zero when CT_stop exceeds 2.00 s and no longer influences the crossing frequency. Therefore, in accordance with the statistical analysis, the crossing frequency model (Equation 1) can be reduced to a simpler formalization for the inf group exposed to CT_stop times higher than 2.50 s: F˜cross=100×[w1+e−a·CTcross]. Third, the w1+e−a·CTcross term accounts for a similar increase in the modeled crossing frequency with CT_cross among the three groups. This is explained by their identical exposure to the three CT_cross times (0.00, 1.50, and 2.50 s) for a given CT_stop value.

In conclusion, the proposed model accurately reproduces our observations and predicts choice between CT_cross and CT_stop affordances for the average inter-individual crossing frequency. The model not only showed that manipulations of CT_cross induced changes in crossing frequency but also that manipulation of CT_stop modulated variation in crossing frequency. Finally, the model is able to account for the crossing frequency for all three groups with different action capabilities but identical coefficients. This supports the formalization of CT_cross and CT_stop as affordances, which are extrinsic properties of the intersection-crossing situations scaled to the driver's maximum acceleration and deceleration capabilities, respectively.

Do driving maneuvers at the approach to an intersection emerge from choice between driving possibilities? Theoretically, drivers assess the viability of crossing the intersection based on traffic constraints and the acceleration of their car. However, at the same time, they assess the viability of performing a safe stop before the intersection based on their braking capability. Inspired by the original concepts of FST and MSZ introduced by Gibson and Crooks (1938), we formalized the viability of crossing as the critical time at which safe crossing is no longer possible (CT_cross) and the viability of stopping as the critical time at which it is no longer possible to stop safely before the intersection (CT_stop). In other words, CT_cross is the critical time at which the minimum satisfying acceleration for safe crossing (MSA) exceeds the driver's maximum acceleration (A_max). In the same way, CT_stop is the critical time at which the minimum satisfying deceleration for safe crossing (MSD) exceeds the driver's maximum braking capabilities (D_max). We tested the hypothesis that the decision taken by the driver is the result of choice between these crossing and stopping possibilities. We thus investigated the respective contribution of CT_cross and CT_stop to the decision taken by a driver when approaching an intersection in a driving simulator.

Three groups of participants drove cars with identical acceleration capabilities but different braking capabilities and were asked to try to cross an intersection before an oncoming car traveling orthogonally blocked the route. Alternatively, they could decide to stop before the intersection to let the oncoming car cross. Finally, as a last resort, they could decide to exit on the roadside. Since acceleration capability (A_max) was constant for the three groups, between-group intersection-crossing situations offered identical crossing possibilities (CT_cross). However, between-group differences in braking capabilities (D_max) created different stopping possibilities (CT_stop). We hypothesized that frequency of the decision to cross would increase as the viability of stopping decreased, although the viability of crossing was constant for all groups.

We consistently observed that crossing frequency increased as the critical time for crossing (CT_cross) increased, irrespective of the group and the between-trial manipulation of CT_stop. This result suggests that drivers perceive CT_cross as a variable that specifies the viability of crossing and underlines the driver's sensitivity to affordances that rely on maximum acceleration capabilities (Fajen and Matthis, 2011). Moreover, we found between- and within-group differences which showed that crossing frequency increased as CT_stop decreased. Although previous studies have shown that drivers are sensitive to affordances based on maximum deceleration capabilities, such as in a braking task (Fajen, 2005b,c), it is surprising to see the influence of braking capabilities on crossing decisions in our results. Finally, we found that the frequency of exiting increased when the combination of CT_cross and CT_stop ruled out crossing and stopping possibilities. Overall, these observations confirm that drivers take both the viability of crossing and stopping into account at the approach to an intersection.

The influence of the car's braking capabilities on crossing frequency is the core result of this experiment. It raises questions about the mechanisms that combine crossing and stopping possibilities in making the final decision. What mechanism, underlying choice between the possibilities for action, could explain the influence of the driver's stopping possibilities on crossing frequency? In theory, all groups of drivers have an identical perception of their crossing possibilities, but our results show that in practice their stopping possibilities play a role in this assessment. Drivers appear to decide to cross an intersection not only because crossing is a very viable possibility, but also because stopping is not. This result is supported by our model, which suggests that drivers simultaneously assess crossing and stopping possibilities and weigh each of them. Moreover, our model is compatible with results from traditional affordance paradigms, as it explains behavior when drivers are exposed to a unique affordance (the inf group in our experiment). The following paragraphs evaluate candidate mechanisms which may explain these results.

We first ruled out a mechanism that consisted of the manipulation of the experimental instructions, i.e., drivers first assessed their crossing possibilities and then their stopping possibilities. This hypothesis would have led to similar between-group crossing frequencies for intersection-crossing situations where the safe crossing possibilities were identical. Moreover, stopping and exiting frequencies of all groups would have varied depending on stopping possibilities in situations with identical crossing possibilities. Although the observed stopping and exiting frequencies are compatible with this hypothesis, the different between-group crossing frequencies invalidate it.

It could be argued that the combined effect of crossing and stopping possibilities on crossing frequency is due to the fact that drivers do not perceive their crossing possibilities in the same way. In this case, a single affordance (perhaps including crossing and stopping possibilities) would sum up the decision-making process. Our implementations of critical times at which it is no longer safe to cross or stop in reference to the driver-intersection system are well-suited for the investigation of this kind of hypothesis. Indeed, considering that decision-making is based on critical times for both safe crossing and stopping possibilities is compatible with the idea that crossing possibilities are perceived in reference with the stopping possibilities. For instance, if CT_cross = 1.5 s and CT_stop = 3 s, these values will specify that safe stopping is afforded 1.5 s longer than safe crossing. Nevertheless, our statistical analysis, supported by a model that explains behavior given an identical set of CT_cross and CT_stop coefficients, suggests that these variables are separate affordances, among which drivers choose. In other words, drivers would identically perceive their possibilities to cross the intersection but would act in a different way depending on their stopping possibilities.

Alternatively, the final decision to select a given driving maneuver could be understood using a behavioral dynamics framework (Warren, 1998, 2006). In this framework, the final decision is consistent with a dynamic system. The possibility that offers the best chance of success among other available possibilities is the attractor for the final selection of a maneuver. On the other hand, the possibility that offers the least chance of success acts as a repeller in the final decision. This framework has been shown to account for route selection when steering, and avoiding obstacles in a complex environment (Fajen and Warren, 2003). Therefore, in our study, competing driving possibilities may act as the angular acceleration of the goal and the obstacle in the Fajen and Warren's steering task study and motivate the final decision as a function of their respective attractive or repulsive power. Further work needs to be carried out to confirm this hypothesis.