Understanding the social conditions that tend to increase or decrease polarization is important for many reasons. We study a network-structured agent-based model of opinion dynamics, extending a model previously introduced by Flache and Macy (2011), who found that polarization appeared to increase with the introduction of long-range ties but decrease with the number of salient opinions, which they called the population's "cultural complexity." We find the following. First, polarization is

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... ly path dependent and sensitive to stochastic variation. Second, polarization depends strongly on the initial distribution of opinions in the population. In the absence of extremists, polarization may be mitigated. Third, noisy communication can drive a population toward more extreme opinions and even cause acute polarization. Finally, the apparent reduction in polarization under increased "cultural complexity" arises via a particular property of the polarization measurement, under which a population containing a wider diversity of extreme views is deemed less polarized. This work has implications for understanding the population dynamics of beliefs, opinions, and polarization as well as broader implications for the analysis of agent-based models of social phenomena.