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

Shintaro Mori, Masato Hisakado, Taiki Takahashi

posted on 15 November 2012

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We consider a situation where one have to choose an option with multiplier m. The multiplier is inversely proportional to the number of people who have chosen the option and is proportional to the return if it is correct. If he does not know the correct option, we call him herder and it is a zero-sum game between the herder and other people who have set the multiplier. Game theory proves that the max-min strategy where one divides one's choice inversely proportional to m is optimal from the viewpoint of the maximization of expected return. We call the optimal herder analog herder. We study the prediction by a voting experiment in which 50 to 60 subjects answer a two-choice quiz sequentially. We show that the probability of selecting a choice by the herders is inversely proportional to m for 4/3<=m<=4 and they adopt the max-min strategy in the range. The system of analog herder maximizes the probability of correct choice for any value of the ratio of herder p in the thermodynamic limit. Even in limit p->1, the system can take the probability to one. The herders in the experiment cannot maximize the probability as there is a bias in their choices for m<4/3 and m>4.