**Abstract**:

**Abstract**
**Objects in the environment differ in their low-level perceptual properties (e.g., how easily a fruit can be recognized) as well as in their subjective value (how tasty it is). We studied the influence of visual salience on value-based decisions using a two alternative forced choice task, in which human subjects rapidly chose items from a visual display. All targets were equally easy to detect. Nevertheless, both value and salience strongly affected choices made and reaction times. We analyzed the neuronal mechanisms underlying these behavioral effects using stochastic accumulator models, allowing us to characterize not only the averages of reaction times but their full distributions. Independent models without interaction between the possible choices failed to reproduce the observed choice behavior, while models with mutual inhibition between alternative choices produced much better results. Mutual inhibition thus is an important feature of the decision mechanism. Value influenced the amount of accumulation in all models. In contrast, increased salience could either lead to an earlier start (onset model) or to a higher rate (speed model) of accumulation. Both models explained the data from the choice trials equally well. However, salience also affected reaction times in no-choice trials in which only one item was present, as well as error trials. Only the onset model could explain the observed reaction time distributions of error trials and no-choice trials. In contrast, the speed model could not, irrespective of whether the rate increase resulted from more frequent accumulated quanta or from larger quanta. Visual salience thus likely provides an advantage in the onset, not in the processing speed, of value-based decision making.**

*independent model*, we assumed that the two accumulators did not interact, while the other accumulator models implemented mutual inhibition between them. The

*speed model*assumed that salience influenced the rate with which value information was accumulated by modulating the strength of the incoming value information. The

*onset model*was motivated by the observation that salience can reduce visual processing time (Ratcliff & Smith, 2011; White & Munoz, 2011) and assumed an earlier accumulation onset time rather than an increased accumulation rate. The full model combined both ways for salience to affect the accumulation process. Comparison between model predictions and behavior suggested that mutual inhibition and salience-induced differences in accumulation onset time, but not accumulation rate, are necessary to explain the behavior of the human participants.

*t*test, df = 34,

*p*< 10

^{−9}), low salience (

*t*test, df = 34,

*p*< 10

^{−10}), congruent (

*t*test, df = 34,

*p*< 10

^{−8}), and incongruent (

*t*test, df = 34,

*p*< 10

^{−6}) (Figure 3). The correlation coefficients were significantly smaller than zero as tested by the

*t*test in all cases; the larger the chosen value, the shorter the reaction time. This result reflected most likely the motivational drive of the chosen target value on the speed of decision making and response execution processes. Interestingly, the relative importance of this motivational drive was weaker on no-choice trials than on choice trials (slope of no-choice trials: high salience: −0.78 ms/point, low salience: −1.6 ms/point; slope of choice trials: high salience: −4.82 ms/point, low salience: −5.19 ms/point, congruent: −4.33 ms/point, incongruent: −4.25 ms/point), and in no-choice trials, the correlation between value and reaction time was significant only for low salience (

*t*test, df = 43,

*p*= 0.03), but not high-salience trials (

*t*test, df = 43,

*p*= 0.1) (Figure 3).

*p*< 10

^{−4}, low-salience trials: df = 42,

*p*= 0.015, congruent trials: df = 42,

*p*= 0.016, incongruent trials: df = 42,

*p*= 0.002). This relationship was also negative (slope high-salience trials: −0.57 ms/point, low-salience trials: −0.33 ms/point, congruent: −0.33 ms/point, incongruent: −0.42 ms/point): the larger the value difference, the shorter the reaction time. This finding supports the view that participants compared the values of both targets before making a choice. Larger value differences made it easier to discriminate the more valuable target and resulted in faster responses, while smaller differences decreased the discriminability and required more time to select the correct response.

*p*< 10

^{−10}) than for low-salience trials (mean: 726 ms).

*p*= 0.032) than in low-salience trials (mean: 913 ms). Moreover, the congruency between differences in value and reward salience had a strong effect on the target selection process. In congruent as well as in incongruent trials, the two targets varied both in value and in salience. In congruent trials, the more valuable target had also more salient reward information. Thus, both the difference in value and in salience supported the same target. In contrast, in incongruent trials the more valuable target had less salient reward information. Here, the difference in value and in salience supported different targets. Accordingly, across all value levels, the reaction time on congruent trials (mean: 822 ms) was significantly faster (K-S test,

*p*< 10

^{−13}) than on incongruent trials (mean: 953 ms; Figure 4). This difference could not be explained merely by the fact that the chosen targets differed in salience. The reaction time on congruent trials was still significantly faster (K-S test,

*p*= 0.01) than that on high-salience trials (Figure 4), even though the salience of the chosen targets were the same. Likewise, the reaction time on incongruent trials was also significantly slower (K-S test,

*p*< 0.01) than that on low-salience trials (Figure 4).

*p*= 0.25) than the one for high-salience-trials. This indicated that the participants were still able to identify the color of the low-salience targets, although those targets were harder to identify. In contrast, the error rate for incongruent trials was much higher (13.1%). This is higher than the error rates for high salience (K-S test,

*p*= 0.01) and congruent trials (K-S test,

*p*= 0.01), as well as for low-salience trials although the latter difference was not significant (K-S test,

*p*= 0.07).

*p*= 0.28 and

*p*= 0.25, respectively), the difference is significant (K-S test,

*p*= 0.048) for the combined population. In congruent trials, this difference became larger. The reaction time for error trials (mean RT: 955 ms) was significantly longer (K-S test,

*p*= 0.001) than for correct trials (mean RT: 823 ms). In contrast to all other trial types, in incongruent trials the reaction time for error trials (RT: 876 ms) was significantly shorter (K-S test,

*p*= 0.01) than for correct trials (mean RT: 953 ms). Note that this shorter reaction time on error trials was not confounded by the chosen value on those trials. First, on error trials (by definition) a smaller value was chosen than on correct trials. Second, the error rate did not increase as the chosen value increased (Figure 5B). The chosen value on error trials was therefore on average not larger than the chosen value on correct trials. This specific difference in the reaction time distributions between congruent and incongruent trials turned out to be important, because, as we shall see below, it allowed us to distinguish between different types of accumulator models of the decision process.

*v*and

_{chosen}*v*are the point values of the chosen and non-chosen targets (

_{nonchosen}*v*∈ (0, 0.1, 0.2, 0.4, 0.8)), and

_{i}*S*and

_{chosen}*S*are the salience values of the chosen and non-chosen targets (

_{nonchosen}*S*∈ (0, 1)), respectively. All four parameters (but none of the other four possibilities listed above) contributed significantly to the regression, including: (a) value of the chosen target (

_{i}*t*test:

*p*< 10

^{−7}), (b) salience of the chosen target (

*t*test:

*p*< 10

^{−5}), (c) value difference between chosen and non-chosen target (

*t*test:

*p*< 10

^{−4}), and (d) salience difference between chosen and non-chosen target (

*t*test:

*p*= 0.001). Table 1 shows the BIC values, Akaike value, and evidence ratio (relative to the best-fitting model) for different models ranked by their fit to the behavioral data. From the evidence ratios it is clear that there were actually approximately 12 different regression models all containing four variables that all fitted the data almost as well as the best-fitting model. This phenomenon is likely related to the fact that the variables we chose were most likely not completely independent of each other such as the equation containing

*S*and

_{chosen}*S*can be equally expressed as an equation containing

_{nonchosen}*S*and

_{chosen}*dS*. However, there was a clear drop in evidence for alternative three- or five-variable models.

Rank | Variables resulting in model | BIC | AIC | Evidence ratio |

1 | v, _{chosen}s, _{chosen}dv, ds | −8711 | −8734 | 1 |

2 | v, _{chosen}s, _{non-chosen}ds, v_{non-chosen} | −8711 | −8734 | 1 |

10 | v, _{chosen}s, _{chosen}dv, v_{non-chosen} | −8710 | −8733 | 1.23 |

13 | v, _{chosen}s, _{chosen}dv | −8708 | −8726 | 3.90 |

17 | v, _{chosen}s, _{chosen}dv, ds, v × _{non-chosen}s_{non-chosen} | −8705 | −8732 | 23.90 |

*χ*

^{2}fit (7.08) was significantly larger than that for the other two constrained models (Model 2: mean

*χ*

^{2}fit, 2.44;

*t*test, df = 29,

*p*< 10

^{−8}, Model 3: mean

*χ*

^{2}fit, 2.24;

*t*test, df = 29,

*p*< 10

^{−10}). More importantly, the predicted reaction times in no-choice trials did not fit the observed reaction times (Figures 10A and B). Specifically, a very general characteristic of the observed reaction time data was the increased reaction time latency on choice trials as opposed to no-choice trials (Figure 7). In contrast, the independent model predicted that the reaction times for choice trials were as fast as those in no-choice trials, due to the lack of inhibition from the non-chosen target. In addition, Model 1 overestimated the error rate on incongruent trials (Figure 10C) and it failed to predict the observation that on incongruent trials the reaction times on error trials were shorter than those on correct trials (Figure 10D). For no-choice trials, the mean

*χ*

^{2}value (12.84) of Model 1 was significantly larger than that of the other two models (Model 2:

*χ*

^{2}: 8.38,

*t*test, df = 29,

*p*< 10

^{−15}, Model 3:

*χ*

^{2}: 3.61,

*t*test, df = 29,

*p*< 10

^{−34}). In sum, the analysis of Model 1 showed very clearly that mutual inhibition between two choices is important for target selection.

*χ*

^{2}

*= 2.44) was slightly poorer than that of Model 3 (mean*

_{fit}*χ*

^{2}

*= 2.24), the difference was not significant (*

_{fit}*t*test, df = 29,

*p*= 0.86). The simulated reaction times of both Models 2 and 3 were correlated with the difference between chosen and non-chosen values, chosen values, non-chosen values, and the congruence between value and salience, which was consistent with the behavioral data.

*χ*

^{2}

*= 3.61) in no-choice trials was significantly (*

_{test}*t*test, df = 29,

*p*< 10

^{−15}) better than that of Model 2 (mean

*χ*

^{2}

*= 8.38). In particular, the human participants showed consistently longer reaction times in no-choice trials with low-salience targets compared to trials with high-salience targets. Consequently, the comparison of predicted to observed reaction times in Figures 11B and 12B showed that for most no-choice trials (indicated by the red circles) the predicted RTs of Model 2 are too short, while the predictions of Model 3 for no-choice trials were as accurate as for choice trials.*

_{test}*p*= 0.004; Model 3: K-S test,

*p*= 0.003). On incongruent trials, however, Model 2 predicted that the reaction time on erroneous trials was also significantly longer (K-S test,

*p*= 0.002) than on correct trials (Figure 11D). This is because an error can only occur when the accumulator associated with the low-value target happens to reach the threshold earlier than the one associated with the high-value target. Since in Model 2 the low-value accumulator tended to rise slowly, this could only happen if the competing high-value accumulator also rose slowly. Thus, in this model the reaction time on error trials had to be longer than on correct trials (Figure 9B).

*t*test, df = 47,

*p*< 10

^{−8}, Sobol Index: 0.43) with the reaction time differences between error and correct trials on incongruent trials (Figure 13). In Model 3, errors were due to the earlier onset of accumulation for the low-value targets. This onset time difference, especially when it was large, created a window of opportunity for the low-value accumulation process during which it experienced no competition from the high-value accumulation process. Therefore, in this model the reaction times on error trials tended to be shorter than on correct trials (Figure 9C). The fact that this prediction, which was specific for Model 3, was confirmed by the behavioral data gives further support for the hypothesis that differences in the onset latency of accumulation (as in Model 3) rather than in the rate of accumulation (as in Model 2) explains the salience effect in our behavioral choice task.

*χ*

^{2}

*= 3.50), and it resulted in decreased accuracy when predicting the reaction time in the testing set (no-choice trials, mean*

_{fit}*χ*

^{2}

*= 8.20) over Model 3. This provided additional support for Model 3.*

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*n*is the number of trials (a constant in our case),

*k*is the number of fitting parameters, and

*RSS*the residual sum of squares after fitting (Burnham & Anderson, 2002; Busemeyer & Diederich, 2010). A lower numerical BIC value indicates better fit of a model, with a lower residual sum of squares indicating better predictive power, and a larger

*K*penalizes less parsimonious models. This procedure is related to a likelihood-ratio test, and equivalent to choosing a model based on the

*F*statistic (Sawa, 1978). It provides a Bayesian test for nested hypotheses (Kass & Wasserman, 1995).

*w*

_{1}is the BIC weight for the best model that equals to one. Δ

*is the BIC difference for each model: in which*

_{i}*BIC*is the model with the smallest

_{min}*BIC*value.

*F*tests, but this approach, while exact, requires the assumption of data with a normal distribution that is not true for the reaction time distribution. We decided therefore to use model selection criteria based on information theories, because they were computationally straightforward and potentially more robust. An additional advantage was that we could compare all 255 models simultaneously, using a consistent criterion (Burnham & Anderson, 2002).

**)**. In choice trials, it consists of two integrators

*m*and

_{1}*m*that accumulate evidence in favor of the two possible choices as described by a stochastic differential equation: In the simulations, we always chose

_{2}*dt*= 1

*ms*. The first term in Equation A5 describes how each integrator accumulates evidence from its corresponding target. It has four factors. The first,

*I*

_{1}_{,}and

*I*, is the mean quanta of accumulation. We assumed that this quanta is determined by the normalized value of the target,

_{2}*v*∈ (0, 0.1, 0.2, 0.4, 0.8). The second, (1 +

_{i}*dw*) introduces variability for each accumulated quantum. As

_{i}*dw*is drawn from a normal distribution, at each time the instantaneous accumulation,

_{i}*I*(1 +

*dw*) comes from a Gaussian distribution whose mean is equal to its standard deviation and both are determined by and

_{i}*a*

_{0}and

*a*

_{1}are fitted coefficients. We equated standard deviation and mean of the distribution to minimize the number of free parameters.

*H*(

*t*−

*t*) in Equation A5.

_{i}*H*(

*t*) is the Heaviside step function:

*t*is negatively correlated with the salience of the target.

_{i}*t*=

_{i}*t*

_{0}+

*t*, where

_{i}s_{i}*s*is the salience of target

_{i}*I*, and

_{i}*t*

_{0}, and

*t*are fitted coefficients.

_{1}*λ*

_{0}and

*λ*are fitted coefficients. No accumulation occurs in accumulator

*m*. if

_{i}*N*= 0 and the probability of this happening is determined by

_{i}*s*through Equation 8. The mean rate of accumulation is determined by

_{i}*I*(

_{i}*λ*

_{0}+

*λs*). By having the probability of accumulation term, the salience of value information could influence accumulation rate in a way that is orthogonal to the effect of value itself. That is the influence of salience is independent of the strength of value information.

_{i}*u*in Equation A5 is the inhibition coefficient. It determines the strength of inhibition between two integrators.

*u*(Equation A5) was set to zero in this model. Information for each integrator is therefore accumulated according to the simplified version: Models 2, 3, and 4 are feed-forward inhibition models (Purcell et al., 2010; Shadlen & Newsome, 2001). We assume that the amount of momentary evidence for accumulation is positively correlated with the value of the corresponding targets and we take into account the influence of the salience of the target based on two different hypotheses. In Model 2 (speed model) (Figure 8B), we assume that salience influences the rate, but not the onset time of accumulation. Therefore, onset difference,

*t*, was set to zero for Model 2. The stochastic differential equations for integrators accumulating evidence can then be simplified as: In contrast, in Model 3 (onset model) (Figure 8C) we assume that salience influences the onset time rather the rate of accumulation. The accumulation rate was determined by the probability to receive momentary evidence,

_{i}*P*(

*N*(

_{i}*dt*)). Accordingly, in this model the probability of accumulation for each integrator in a given time interval, and therefore the rate of accumulation of this accumulator, is independent of the salience level of the corresponding target. The stochastic differential equations for integrators accumulating evidence can be simplified as Traditionally the accumulators in decision making have been modeled as a Wiener process and a continuous accumulation of information. Since we want to test the hypothesis that value influences accumulated quanta magnitude and salience accumulated quanta rate, we have to use the more general description presented above. However, it should be noted that in Model 3, the accumulation quanta frequency is independent of stimulus properties and thus could be mapped more easily to a Wiener process.

*m*

_{1}) is defined. Thus, there is only one integrator

*m*

_{1}and only one input unit, with all values corresponding to the second target set to zero.

*o*is the observed proportion of RTs in these bins,

_{i}*p*is the corresponding proportions from the respective model, and

_{i}*n*is the number of correct trials in a given experiment that is the total number of data points in the observed (and simulated) RT distribution. The advantage of this fitting method is that it maximizes the proportion of correctly fitted responses in addition to matching the distribution of observed RTs (Purcell et al., 2010; Van Zandt et al., 2000).

*χ*

^{2}values separately for correct choice trials [

*u*,

*a*

_{0},

*a*

_{1},

*t*

_{0},

*t*

_{1},

*a*,

*λ*

_{0}, and

*λ*in Equations 5–8) to specify which parameters contributed to the differences between models and to what extent.