Effective group size of majority vote accuracy in sequential decision-making

Abstract

We investigate a sequential decision-making situation wherein, with a certain probability, each voter imitates the decision of another voter who has already made a decision; otherwise, she makes a decision independently. After all individuals reach decisions, the group decision is determined using the simple majority rule. To evaluate the collective performance in this situation, we introduce the concept of effective group size, which measures how many independent voters are needed to obtain the same majority vote accuracy realized by non-independent sequential votes. We have found the deterioration of majority vote accuracy by imitation behavior of voters, and quantified it by a decrease in the effective group size. We argue that this decline in the majority vote accuracy is caused by the two factors: a decrease in the number of independent voters and an increase in the disparity of influences of voters on succeeding voters’ decisions.