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Formal models of opinion formation commonly represent an individual's opinion by a value on a fixed opinion interval. We propose an alternative modeling method wherein interpretation is only provided to the relative positions of opinions…
We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in ${\cal D}(n,p)$ for nearly optimal $p$ (up to a $\log ^cn$ factor). In particular, we show that given $t = (1-o(1))np$ Hamilton cycles $C_1,\ldots ,C_{t}$,…
An important question when eliciting opinions from experts is how to aggregate the reported opinions. In this paper, we propose a pooling method to aggregate expert opinions. Intuitively, it works as if the experts were continuously…
We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges…
This paper introduces a generalised opinion model that extends the standard DeGroot model by representing agents' opinions and influences as soft constraints rather than single real values. This allows for modelling scenarios beyond the…
A Hamilton cycle in a digraph is a cycle that passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of…
We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…
We generalize the classic multi-agent DeGroot model for opinion dynamics to incorporate the Spiral of Silence theory from political science. This theory states that individuals may withhold their opinions when they perceive them to be in…
We consider a type of pull voting suitable for discrete numeric opinions which can be compared on a linear scale, for example, 1 ('disagree strongly'), 2 ('disagree'), $\ldots,$ 5 ('agree strongly'). On observing the opinion of a random…
We present a protocol to selectively decouple, recouple, and engineer effective couplings in mesoscopic dipolar spin networks. In particular, we develop a versatile protocol that relies upon magic angle spinning to perform Hamiltonian…
This paper investigates how interacting agents arrive to a consensus or a polarized state. We study the opinion formation process under the effect of a global steering mechanism (GSM), which aggregates the opinion-driven stochastic agent…
It is widely believed that society is becoming increasingly polarized around important issues, a dynamic that does not align with common mathematical models of opinion formation in social networks. In particular, measures of polarization…
We analyze the asynchronous version of the DeGroot dynamics: In a connected graph $G$ with $n$ nodes, each node has an initial opinion in $[0,1]$ and an independent Poisson clock. When a clock at a node $v$ rings, the opinion at $v$ is…
We provide a variational interpretation of the DeGroot-Friedkin map in opinion dynamics. Specifically, we show that the nonlinear dynamics for the DeGroot-Friedkin map can be viewed as mirror descent on the standard simplex with the…
A covering of a digraph $D$ by Hamilton cycles is a collection of directed Hamilton cycles (not necessarily edge-disjoint) that together cover all the edges of $D$. We prove that for $1/2 \geq p\geq \frac{\log^{20} n}{n}$, the random…
We study a DeGroot-like opinion dynamics model in which agents may oppose other agents. As an underlying motivation, in our setup, agents want to adjust their opinions to match those of the agents of their 'in-group' and, in addition, they…
The paper proposes an analysis of liquid democracy (or, delegable proxy voting) from the perspective of binary aggregation and of binary diffusion models. We show how liquid democracy on binary issues can be embedded into the framework of…
This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude…
In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between…
This paper considers a discrete-time opinion dynamics model in which each individual's susceptibility to being influenced by others is dependent on her current opinion. We assume that the social network has time-varying topology and that…