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We consider a situation where one has to choose an option with multiplier m.The multiplier is inversely proportional to the number of people who havechosen the option and is proportional to the return if it is correct. If onedoes not know the correct option, we call him a herder, and then there is azero-sum game between the herder and other people who have set the multiplier.The max-min strategy where one divides one's choice inversely proportional to mis optimal from the viewpoint of the maximization of expected return. We callthe optimal herder an analog herder. The system of analog herders takes theprobability of correct choice to one for any value of the ratio of herders,p<1, in the thermodynamic limit if the accuracy of the choice of informedperson q is one. We study how herders choose by a voting experiment in which 50to 60 subjects sequentially answer a two-choice quiz. We show that theprobability of selecting a choice by the herders is inversely proportional to mfor 4/3 < m < 4 and they collectively adopt the max-min strategy in that range.

Collective Adoption of Max-Min Strategy in an Information Cascade Voting Experiment