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This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the…
This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of…
Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased…
This paper studies the persuasion of a receiver who accesses information only if she exerts costly attention effort. A sender designs an experiment to persuade the receiver to take a specific action. The experiment affects the receiver's…
In proportional elections with open lists the excess of preferences received by candidates with respect to the list average is known to follow a universal lognormal distribution. We show that lognormality is broken provided preferences are…
The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry…
We present a limit theorem describing the behavior of a probabilistic model for square-free numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval $[0,1]$. We also…
We investigate a variation of the classical voter model in which the set of influencing agents depends on an individual's current opinion. The initial population consists of a random sample of equally sized sub-populations for each state,…
The wisdom of crowds has been shown to operate not only for factual judgments but also in matters of taste, where accuracy is defined relative to an individual's preferences. However, it remains unclear how different types of social signals…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
While Large Language Models (LLMs) have shown exceptional performance in various tasks, one of their most prominent drawbacks is generating inaccurate or false information with a confident tone. In this paper, we provide evidence that the…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
Even though the forecasting literature agrees that aggregating multiple predictions of some future outcome typically outperforms the individual predictions, there is no general consensus about the right way to do this. Most common…
We present a toy model of opinion spreading in a society which combines a self-reinforcing mechanism with diffusion. The relative strength of these two mechanisms - called the affectability of the system - is a free parameter of the model.…
We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that…
When different information sources on a given topic are combined, they interact in a nontrivial manner for a rational receiver of these information sources. Suppose that there are two information sources, one is genuine and the other…
Language is not only used to transmit neutral information; we often seek to persuade by arguing in favor of a particular view. Persuasion raises a number of challenges for classical accounts of belief updating, as information cannot be…
We study a sequential social learning model in which there is uncertainty about the informativeness of a common signal-generating process. Rational agents arrive in order and make decisions based on the past actions of others and their…
Large language models (LLMs) offer unprecedented opportunities for analyzing social phenomena at scale. This paper demonstrates the value of LLMs in psychological measurement by (1) compiling the first large-scale dataset of election rumors…