D1 Dispersion, gap, social weight and regime

Topic

The starting point remains the individual, represented as a generalized actor who makes choices—regarding consumption, labor supply, savings, migration, childbearing, trust, or participation in collective action—based on a cost-benefit decision function applied to the set of options presented by the context. This cost-benefit decision function relies on a vector of personal characteristics—preferences, available resources, identity, and risk tolerance—while resource constraints limit the individual to choosing from a restricted subset of those options. This individual does not, in isolation, constitute a population behavior trajectory; rather, it is the unit that, when repeated and aggregated within a shared context, generates the population-level behavior measured by the six collective behavior trajectories.

Three indicators can be observed simultaneously within this individual decision space, each measuring it from a different angle. The dispersion of the characteristic vector describes the heterogeneity of the population before any decisions are made. The gap between the expected private net benefit and the actual decision taken measures the extent to which the individual's decision deviates from the prediction of their private cost-benefit decision function alone. Finally, the relative weight of the social term directly measures how much of that gap is attributable to the decision-making context rather than to the individual themselves. Taken together, these three indicators make it possible to distinguish whether a collective behavior trajectory is driven by heterogeneous individuals making decisions in isolation, or by individuals who are already homogeneous and coordinated by a shared threshold.

The dispersion of the characteristic vector across the population measures the degree of heterogeneity among individuals regarding their preferences, resources, identity, and risk tolerance. Its sustained shift toward homogeneity is the precondition that facilitates the coordination of many individuals around the same shared threshold—meaning that the distortion caused by group influence spreads across an entire population rather than remaining isolated within a few individuals.

For each person, the gap between the expected net private benefit and the actual decision taken measures the extent to which their effective decision deviates from what their private cost-benefit decision function alone would predict. When this gap appears suddenly and locally in a specific individual or subgroup, it serves as a signal of an isolated individual distortion. Conversely, when the same gap appears widely and simultaneously across a large segment of the population, it functions instead as a signal of distortion driven by group influence.

The relative weight of the social component within the population's aggregate decision function can be estimated—among other methods—by fitting a statistical model to observed decisions that calculates the probability of individuals choosing between available alternatives. When this weight surpasses that of the private cost-benefit component, the individual's decision shifts into a regime of socially embedded decision-making; this marks the precise point where the population ceases to operate as a collection of independent individuals and begins to generate the population-level behavior measured by the six channels of collective behavior. Ultimately, this set of three indicators serves to diagnose—from a distance and without observing each individual's decision—what explains the behavior of a given collective pattern: whether it involves a population of individuals with diverse characteristics who are deciding independently—regarding consumption, work, saving, migration, childbearing, trust, or participation in collective action—or whether that same population has become homogeneous and coordinated, individual by individual, through the same crossing of the threshold between private cost-benefit considerations and the social context.

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