Abstract
We introduce a Voter Model variant, inspired by social evolution of musical preferences. In our model, agents have preferences over a set of songs and upon meeting update their own preferences incrementally towards those of the other agents they meet. Using the spectral gap of an associated Markov chain, we give a geometry dependent result on the asymptotic consensus time of the model.
Highlights
The terminology of Finite Markov Information Exchange (FMIE) models has been introduced [1] [3] as a catch-all for the interpretation of Interacting Particle Systems (IPS) models as stochastic social dynamics
We will introduce and study a generalized Voter Model - inspired by the evolution of musical preferences among a group of friends - as an FMIE process
1.1 The iPod Model Here we introduce the iPod FMIE model
Summary
The terminology of Finite Markov Information Exchange (FMIE) models has been introduced [1] [3] as a catch-all for the interpretation of Interacting Particle Systems (IPS) models as stochastic social dynamics. Between every pair of agents i, j we associate a Poisson process with rate νi,j whose times we refer to as meetings between i and j. A special feature of the model (Proposition 2.3) is that the average (over agents) preference for a given song evolves as a martingale, analogous to the total proportion of agents with a given opinion on the voter model. This distinguishes the iPod model from many other variants of the voter model that have been studied [4]. Our bounds (on the analogous consensus time as a function of the spectral gap) in our setting are sharper by a factor of ln(N ), but we are unsure whether our methods would apply in their setting
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