Current research

Ranking-based reinforcement

In many contexts where people have to make decisions, their choices are informed by what many other people are doing. Some examples are whether to vaccinate one’s children or not, which book to read, which word form to use, and so on. This often creates a positive feedback loop, where popularity of a choice serves as a signal that reinforces itself, leading to dynamics that in different literatures are known as cumulative advantage, the rich get richer, preferential attachment, or the Matthew effect. Such dynamics, which reinforce initial (and often random) differences in popularity, are known to be able to sustain multiple equilibria, including states of inferior “lock-in”, where a majority of people adopts an intrinsically less appealing option, and this majority remains stable over time.

In a series of papers that range from mathematically-oriented to applied, my colleagues and I have been studying the dynamics of popularity and the possibility of lock-in when people’s choices are primarily driven by the way the various options rank in terms of popularity, rather than by quantitative differences in popularity. Specifically, in the first of these papers, we study the dynamics of rankings in the context of Markov processes and derive fundamental results regarding their long-term behavior. In a follow-up paper, we are specializing this study to popularity rankings and show how this leads to a unified framework for studying choice by a large number of people under a variety of behavioral assumptions that are relevant in economics. And in a third paper, we are showing both mathematically and by analyzing past experimental data that the tendency of people to pay disproportionate attention to who is in the lead (independently of the exact differences in popularity) renders a system likely to lock in in cases that it wouldn’t do so otherwise.

Collaborators: Pantelis P. Analytis, Francesco Cerigioni, Gaël Le Mens, Hrvoje Stojic, Arnout van de Rijt

Reinforcement vs. heterogeneity in longitudinal data

In analyses of longitudinal records, it is standard practice to attribute systematic differences across individuals (e.g., differences that remain on average constant over time) to heterogeneity in unobserved characteristics. In this paper, we show that such systematic differences might instead be the result of a reinforcement mechanism acting on pure chance events. We use three case studies from different research areas to show that what had been previously thought to reveal differences in talent, fixed beliefs, or predispositions to have many sexual partners, could at least partially be the outcome of chance events whose effects snowball. We then show that this is a very general phenomenon: any longitudinal data that is consistent with differences in intrinsic characteristics is equally consistent with a reinforcement mechanism acting on ex ante identical individuals.

Collaborators: Lucas Sage, Arnout van de Rijt

The disjunction effect and the Law of Total Probability

The disjunction effect refers to an empirical violation of the Sure-Thing Principle, which states that if a person is willing to take an action independently of the outcome of some event, then they must be willing to do so even when the outcome of the event is unknown. A standard practice for inferring a disjunction effect, especially in between-subjects experiments, consists in showing a population-level version of this phenomenon, specifically that fewer people are willing to take the proposed action when the outcome of the event is unknown than for any possible known outcome. Although this does not imply the original definition, this population-level has received a lot of attention, because it presumably violates the Law of Total Probability and thus requires non-classical theories in order to be explained. In this working paper, we show that this condition is in fact unrelated to the Law of Total Probability and thus entirely irrelevant for the study of the disjunction effect and decision making in general. This calls for a reevaluation of experimental results that have been interpreted as showing a disjunction effect based on the above condition. We then revisit the question of whether an individual-level disjunction effect can be shown in between-subjects experiments. We derive a relation that is both necessary and sufficient for a disjunction effect to be inferrable from between-subjects data.

Collaborators: Gaël Le Mens

Earlier work

Brain oscillations and working memory

As a PhD student, I used dynamical systems models of biological neural networks to study the brain’s oscillatory activity. The work had both a neuroscientific focus and a mathematical one. On the neuroscience side, I studied the properties of a network that is believed to form part of the brain’s parietal cortex, and suggested that it may form a physiological substrate for a working memory buffer in humans. The work was published in PNAS (link) and has attracted attention from neuroscientists studying human memory.

On the mathematical side, I studied the mechanisms that underlie the behavior of the above network and that allow it to process new input without disrupting its ongoing activity. The results suggested a novel form of interaction of neural oscillations of different frequencies and were published in the Journal of Mathematical Neuroscience (link).

Collaborators: Nancy Kopell (PhD thesis supervisor), Miles A. Whittington.

Preprints and submitted articles

• Gelastopoulos, A., Analytis, P. P., Le Mens, G., & van de Rijt, A. (2024). The marginal majority effect: when social influence produces lock-in. arXiv preprint arXiv:2310.01096.
• Gelastopoulos, A., & Le Mens, G., P. P., The disjunction effect does not violate the Law of Total Probability. PsyArXiv. (2024).
• Analytis, P. P., Cerigioni, F., Gelastopoulos, A., & Stojic, H. (2022). Sequential choice and self-reinforcing rankings. Pompeu Fabra University, Economics Working Paper Series, No. 1819.

Peer-reviewed journals

• Gelastopoulos, A., Sage, L., & van de Rijt, A. (2025) Reinforcement generates systematic differences without heterogeneity. Proceedings of the National Academy of Sciences, 122 (23) e2408163122.
• Analytis, P. P., Gelastopoulos, A., & Stojic, H. (2023). Ranking-based rich-get-richer processes. The Annals of Applied Probability, 33(6A), 4366-4394.
• Gelastopoulos, A., & Kopell, N. J. (2020). Interactions of multiple rhythms in a biophysical network of neurons. The Journal of Mathematical Neuroscience, 10, 1-43.
• Gelastopoulos, A., Whittington, M. A., & Kopell, N. J. (2019). Parietal low beta rhythm provides a dynamical substrate for a working memory buffer. Proceedings of the National Academy of Sciences, 116(33), 16613-16620.
• Analytis, P. P., Wu, C. M., & Gelastopoulos, A. (2019). Make-or-Break: Chasing Risky Goals or Settling for Safe Rewards?. Cognitive science, 43(7), e12743. link

Conference Proceedings

• Kontalexi, M, Gelastopoulos, A., & Analytis, P. P. (2025) Social Influence Distors Ratings in Online Interfaces. Companion Proceedings of the ACM on Web Conference 2025 (WWW '25). Association for Computing Machinery, New York, NY, USA, 1086–1090.
• Analytis, P. P., Stojic, H., Gelastopoulos, A., & Moussaïd, M. (2017). Diversity of preferences can increase collective welfare in sequential exploration problems. arXiv preprint arXiv:1703.10970.

Expository articles

• What are the real numbers? (Part I) - This article introduces the rigorous definition of real numbers through Dedekind cuts in an approachable way, assuming only some familiarity with calculus.
• Entropy and Mutual Information - Information theory is widely applied across the sciences. Despite being very mathematical in nature and building upon the theory of probability, mathematicians are often unfamiliar with it, as it doesn't form part of a typical mathematics curriculum. This article, written as a project for a graduate course in Probability Theory, is a brief introduction to information theory intended for mathematicians, or anyone with a solid background in probability.

Courses taught

As main instructor

• Spring 2023: Introduction to Game Theory, Pompeu Fabra University
• Summer 2017: Probability, Boston University

As teaching assistant

• Fall 2018: Elementary Statistics, Boston University
• Fall 2016: Introduction to Analysis 1, Calculus 1 for Social Sciences, Boston University
• Spring 2013: Functional Analysis, Applied Differential Equations, Jacobs University Bremen
• Fall 2012: Linear Algebra 1, Perspectives of Mathematics 1, Jacobs University Bremen
• Spring 2012: Analysis 2, Jacobs University Bremen
• Fall 2011: Analysis 1, Jacobs University Bremen

Guest lectures

• Modeling and detecting cumulative advantage in the social sciences, BIGSSS Computational Social Science Summer School on Democratic Debate, Constructor University - July 2023
• Architecture and information processing in biological neural networks, M.Sc. in Data Science Program, University of Southern Denmark. - May 2022
• The mathematics of juggling, 1st Neo-meta-cabaret artists convention, Libertatia social center, Thessaloniki, Greece. - June 2021
• Principles of Biological Neural Networks, M.Sc. in Data Science Program, University of Southern Denmark. - April 2021
• Gambling, Circuits, and Facebook (with A. Kehagias and R. Grigoriou), 3rd Electrical and Computer Engineering Student Conference, Aristotle University of Thessaloniki - April 2009