Normalization is a general neural mechanism for context-dependent decision making

Abstract

Understanding the neural code is critical to linking brain and behavior. In sensory systems, divisive normalization seems to be a canonical neural computation, observed in areas ranging from retina to cortex and mediating processes including contrast adaptation, surround suppression, visual attention, and multisensory integration. Recent electrophysiological studies have extended these insights beyond the sensory domain, demonstrating an analogous algorithm for the value signals that guide decision making, but the effects of normalization on choice behavior are unknown. Here, we show that choice models using normalization generate significant (and classically irrational) choice phenomena driven by either the value or number of alternative options. In value-guided choice experiments, both monkey and human choosers show novel context-dependent behavior consistent with normalization. These findings suggest that the neural mechanism of value coding critically influences stochastic choice behavior and provide a generalizable quantitative framework for examining context effects in decision making.

Fig. 1.

Model of normalized value coding in stochastic choice. (A) Structure of the trinary-choice model. Value inputs (V₁,V₂, and V₃) were converted into mean firing rates (μ) representing each choice option and variability was introduced as noise terms added to the mean firing rates. In a given trial, the option with the maximum firing rate was designated as the chosen option. (B) Example difference between absolute and relative value-coding representations. Each curve shows the probability density function of the neural activity associated with one of three choice options. Under relative value coding, increasing distracter value (red) reduces the distance between target option distributions and decreases the relative choice ratio for the better target. Relative value parameter settings: K = 100, σ_H = 50, w = 1, σ_fixed = 1, S = 0. (C) Two forms of context dependence in stochastic choice behavior. Points show relative choice ratio between two targets (V₁ = 150 and V₂ = 140, arbitrary units) as a function of distracter value under absolute or relative value coding (error bars, bootstrap 95% CI).

Fig. 2.

Relative value coding generates context dependence in model choice behavior. (A) Example trinary-choice behavior. Each point in the simplex plot represents average choice behavior for a given triplet of value conditions, color-coded by distracter value (V₃). The choice probability of a given option is represented by the linear distance between its associated vertex and the opposite edge; for example, a point at the bottom vertex would represent 100% choice of option 3 (p₁ = 0, p₂ = 0, p₃ = 1) and a point in the midpoint of the top edge would represent 0% choice of option 3 (p₁ = 0.5, p₂ = 0.5, p₃ = 0). The legend shows the different value conditions, with each trial using a single value triplet (V₁, V₂, and V₃). Choice behavior under fixed target-value pairs (V₁ and V₂) are connected with blue lines and deviate markedly from the linear constant relative ratio lines predicted by rational-choice theory (gray lines). Example simulation parameters: K = 100, σ_H = 50, w = 1, σ_fixed = 8, S = 0. (B) Context-dependent relative target choice functions. Lines are color-coded by distracter value, as in A. (C) Relative target choice efficiency plotted as a function of distracter value. Efficiency is defined as the average choice probability for the better target across all target-value differences, a quantity that varies inversely with stochasticity. To quantify the normalization-driven context dependence, we measured the decrement in efficiency (−ΔE) between V₃ = 0 and V₃ = 100.

Fig. 3.

Context dependence in monkey value-guided choice. Context-dependent behavior in a trinary-choice task. Points show average relative choice behavior between the two high-value target options in the presence of a low- (blue) or high- (red) value distracter. Curves plot logistic functions fit to the conditional choice data (either target chosen).

Fig. 4.

Human choice behavior experiment. (A) Trinary-choice task. In each bid trial, subjects indicated the maximum price they would pay for a snack-food item. Subjects completed two bid trials for each of 30 food items. In each choice trial, subjects were presented with three food items and selected the one they most preferred. (B) Example bid data. Consistent with a stable valuation, subjects’ bids for individual items were highly correlated across repetitions (example subject: r = 0.96, P = 1.62 × 10⁻¹⁷; population: mean r = 0.87, P = 3.31 × 10⁻³⁶, t test). (C) Example bid distribution and choice-set construction. The 10 highest-valued items were assigned to be target items; 10 distracter items were sampled evenly from the 20 lowest-valued items.

Fig. 5.

Context dependence in human value-guided choice. (A) Choice behavior varies with distracter value. Points show relative choice probability of the higher-value target as a function of normalized distracter value averaged across the subject population (error bars, binomial CI). Target choice probability is significantly dependent on distracter value (r = −0.80, P = 0.006). (B) Individual subject choice behavior depends on distracter value. Each point shows the average relative choice of the better target option in high- versus low-distracter-value trials. Individual subjects’ choices were classified as high or low according to normalized distracter value. (C) Biphasic effect on choice efficiency. Points show the population logistic function slope parameter as a function of normalized distracter value (lines, 95% CI of the parameter estimation). (D) Context-dependent choice curves. Curves show logistic functions fit to the population data, color-coded by distracter value for the range of decreasing efficiency (0–0.8). As distracter value initially increases from low magnitudes, the choice functions grow shallower and choice grows increasingly inefficient.