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.
Highlights
Human society heavily depends on the performance of group decision making
Using the concept of effective group size, we demonstrate that the smaller the frequency of independent voters, the worse the majority vote accuracy becomes; this phenomenon does not explain the full range of our results (Sect. 3.2)
We evaluate the resulting disparity among independent voters’ influence on succeeding voters, which proves to be the other factor causing the deterioration of majority vote accuracy (Sects. 3.3 and 3.4)
Summary
Human society heavily depends on the performance of group decision making. Decisions on what kind of international treaty to conclude, which presidential candidate to choose, and whether to raise a tax or not influence our quality of life. Theoretical studies on information cascade have often dealt with non-simultaneous decision-making timings In their influential study, Bikhchandani et al [7] considered the sequential decision-making situation where each individual intends to choose a correct option by referring to the decisions of all predecessors. To obtain better insight on the accuracy of non-simultaneous collective decision making, we introduce a novel concept in this research field, effective group size. This concept helps us to quantitatively decompose the deterioration of majority vote accuracy in the process of sequential decision-making into two factors. If we focus only on the final frequencies of independent voters and imitators, Model 1 is qualitatively the same as Model 2, which we analyze in Appendix A
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