Mathematical Models in Social Psychology

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

“…The basic assumption in these models of opinion dynamics is that if an individual communicates with another, then his/her opinion is attracted by the other's. If one translates this assumption into a set of differential equations, then one gets system (1), as already proposed in [1]. This dynamics asymptotically leads to consensus, i.e.…”

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

“…This new model is a very simple modification of (1), which has no pretension to describe social dynamics precisely, but has the aim to make the role of quantization evident. As we shall see in this paper, the main feature that distinguishes it from (1) is that consensus is not achieved in general.…”

“…Surveys of the opinion dynamics literature can be found in [11,23,34]: all of these bring forward the need for theories that can explain both agreement and disagreement, as recognized since [28,1]. Different explanations of persistence of disagreement have been proposed: among them, we recall in [24] the persisting influence of the initial opinions; in [27] the bounded confidence of the individuals; in [32,2] the presence of stubborn individuals; and in [3] the occurrence of antagonistic interactions.…”

“…Let us consider again the dynamics (9) on the 4-node path graph. Consider the parametrized segment x a = (a, 1 2 , 1 2 , 1 − a) ⊤ for a ∈ [0, 1 2 ], which interpolates between the Krasovskii equilibria x 0 = x A and x 1 2 = x B . For every a ∈ (0, 1 2 ) it holds true that…”

Some models of balance applied to children's perceptions of international relations

“…The work of those authors who have dealt extensively with the question of the 'objective balance' of sociometric data (e.g. Flament, 1963, andAbelson, 1967) is not completely relevant to the study of the 'subjective balance' of the judgments of subjects. Unless and until triads of a sort which definitely do not conform to Heider's balance theory are discovered, it seems reasonable to assume that all cases where unilateral affective relations can be conceived to exist between members of a triad are candidates for explanation by balance theories.…”