# Information Cascade and Phase Transition

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## Abstract

In this chapter, we discuss a voting model with two candidates. We set two types of voters – herders and independents. The voting of independent voters is based on their fundamental values; on the other hand, the voting of herders is based on the number of votes. Herders always select the majority of the previous *r* votes, which is visible to them. We call them digital herders. As the fraction of herders increases, the model features a phase transition beyond which a state where most voters make the correct choice coexists with one where most of them are wrong. Here we obtain the exact solutions of the model. The main contents of this chapter are based on Hisakado and Mori (J Phys A 22:275204, 2011).

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