Repulsive Markovian models for opinion dynamics

We consider the problem of modeling a decision-making process in a network of stochastic agents, each described as a Markov chain. Two approaches for describing disagreement among agents as social forces are studied. These forces modulate the rates at which agents transition between decisions. We define similarity conditions between the two disagreement models and derive a method for obtaining two model instances that fulfill this property. Moreover, we show that a condition for significantly reducing the state-space dimension through marginalization can be derived for both models. However, using a counterexample, we also demonstrate that similarity is not generally possible for models that can be marginalized. Finally, we recommend which disagreement model to use based on the results of our comparison.