Lucas Sage

Selected Publications

1. PNAS

   Reinforcement generates systematic differences without heterogeneity

   Alexandros Gelastopoulos, Lucas Sage, Arnout van de Rijt

   Proceedings of the National Academy of Sciences 2025

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   Inequality in outcomes may emerge through a reinforcement process in which stochastic variation in values is determined by prior values but may also originate in preexisting differences in unobserved factors. A common approach toward differentiating between these origins in longitudinal data is to attribute systematic differences between units—differences in means or differences proportional to a time-varying group average—to unobserved heterogeneity. We show that any longitudinal data with systematic differences can also be produced by a reinforcement-driven data generating process. This result reconciles findings in three distinct research areas—science of science, personal culture, and sexual networks—where reinforcement is a strong theoretical prior, yet longitudinal data analyses advance an explanation of interpersonal differences based on heterogeneity. Future studies may bound the role of heterogeneity and reinforcement from below by measuring fixed traits that systematically vary with the outcome and isolating random events that trigger emergent differences.

2. PLoS ONE

   The spreading of SARS-CoV-2: Interage contacts and networks degree distribution

   Lucas Sage, Marco Albertini, Stefani Scherer

   PLoS ONE 2021

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   Notable cross-country differences exist in the diffusion of the Covid-19 and in its lethality. Contact patterns in populations, and in particular intergenerational contacts, have been argued to be responsible for the most vulnerable, the elderly, getting infected more often and thus driving up mortality in some context, like in the southern European one. This paper asks a simple question: is it between whom contacts occur that matters or is it simply how many contacts people have? Due to the high number of confounding factors, it is extremely difficult to empirically assess the impact of single network features separately. This is why we rely on a simulation exercise in which we counterfactually manipulate single aspects of countries' age distribution and network structures. We disentangle the contributions of the kind and of the number of contacts while holding constant the age structure. More precisely, we isolate the respective effects of inter-age contact patterns, degree distribution and clustering on the virus propagation across age groups. We use survey data on face-to-face contacts for Great Britain, Italy, and Germany, to reconstruct networks that mirror empirical contact patterns in these three countries. It turns out that the number of social contacts (degree distribution) largely accounts for the higher infection rates of the elderly in the Italian context, while differences in inter-age contacts patterns are only responsible for minor differences. This suggests that policies specifically targeting inter-age contacts would be little effective.

3. JASSS

   Can Ethnic Tolerance Curb Self-Reinforcing School Segregation? A Theoretical Agent Based Model

   Lucas Sage, Andreas Flache

   Journal of Artificial Societies and Social Simulation 2021

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   Schelling and Sakoda prominently proposed computational models suggesting that strong ethnic residential segregation can be the unintended outcome of a self-reinforcing dynamic driven by choices of individuals with rather tolerant ethnic preferences. There are only few attempts to apply this view to school choice, another important arena in which ethnic segregation occurs. In the current paper, we explore with an agent-based theoretical model similar to those proposed for residential segregation, how ethnic tolerance among parents can affect the level of school segregation. More specifically, we ask whether and under which conditions school segregation could be reduced if more parents hold tolerant ethnic preferences. We move beyond earlier models of school segregation in three ways. First, we model individual school choices using a random utility discrete choice approach. Second, we vary the pattern of ethnic segregation in the residential context of school choices systematically, comparing residential maps in which segregation is unrelated to parents' level of tolerance to residential maps reflecting their ethnic preferences. Thirdly, we introduce heterogeneity in tolerance levels among parents belonging to the same group. Our simulation experiments suggest that ethnic school segregation can be a very robust phenomenon, occurring even when about half of the population prefers mixed to segregated schools. However, we also identify a sweet spot in the parameter space in which a larger proportion of tolerant parents makes the biggest difference. This is the case when the preference for nearby schools weighs heavily in parents' utility function and the residential map is only moderately segregated. Further experiments are presented that unravel the underlying mechanisms.