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How Individuals Weigh Their Previous Estimates to Make a New Estimate in the Presence or Absence of Social Influence

Abstract. Individuals make decisions every day. How they come up with estimates to guide their decisions could be a result of a combination of different information sources such as individual beliefs and previous knowledge, random guesses, and social cues. This study aims to sort out individual estimate assessments over multiple times with the main focus on how individuals weigh their own beliefs vs. those of others in forming their future estimates. Using dynamics modeling, we build on data from an experiment conducted by Lorenz et al. [1] where 144 subjects made five estimates for six factual questions in an isolated manner (no interaction allowed between subjects). We model the dynamic mechanisms of changing estimates for two different scenarios: 1) when individuals are not exposed to any information and 2) when they are under social influence.

Keywords: Estimate aggregation, collective judgment, and social influence.

1 Introduction

The present study examines individuals' mechanisms for revising their estimates in the presence and absence of social influence. How do people weigh their previous estimates while forming new estimates? How do they account for the judgment of others in their next estimate? We base our modeling and estimation work on the data of an experiment by Lorenz et al. [1] where each individual, in 12 groups of 12 people, makes five estimates for six factual questions. Lorenz et al. [1] study different scenarios when individuals do not receive any feedback about others' estimates and when they are given feedback to some degree. Before reviewing their experiment (in Section 2) and presenting our modeling work (in Section 3), we review the key findings of the literature regarding this topic and identify the research questions to which we contribute.

1.1 Aggregation of Individual Estimates

One of the main research areas relevant to our study is the impact of aggregation of individual estimates. In general, individuals aggregate their opinion by averaging [2, 3]. Although nineteenth century scientists did not trust averaging [3], recent studies have shown that the average of multiple estimates from different individuals is more accurate than the average of multiple estimates from one individual [4-11]. Surowiecki [12] demonstrates that the results of aggregating individual estimates are superior to even those provided by experts.

Averaging increases accuracy, because different individuals' estimates often bracket the true value and thus averaging yields a smaller error than randomly choosing one estimate. Only if significant bias is present across all individuals, and thus the estimates do not bracket the truth, the average would be as accurate as a random estimate [3, 5, 8, 9]. Research shows that averaging ensures that the result has lower variability, lower randomization error, lower systemic error, and converges towards the true forecast [see: 5, 13, 14]. Additionally, averaging not only increases the accuracy, but also some form of averaging is almost nearly optimal. Yaniv [6] notes the “independency of individual” as a central condition for obtaining optimal accuracy, and Hogarth [15] presents that groups containing between 8 and 12 individuals have predictive ability to the optimum. This simple mathematical fact of averaging individual estimates, the so-called “wisdom of crowds”, can be easily missed or even if it is seen, it can be hard to accept [12].

1.2 Weighing Process in Aggregation

Research shows that people make decisions by weighing their own opinions with advice from other sources [16]. In the process of giving and receiving advice, individuals discount advice and weigh their own opinions more because they are usually egocentric in revising their opinions and have less access to reasons behind the advisor's view [6, 17, 18]. Harvey and Harries [19] observe a similar behavior in their experiment, where individuals put more weight on forecasts that are their own rather than on equivalent forecasts that are not theirs. In short, differential access to reasons (e.g. advisor's reasons) and egocentric beliefs are the two common causes of overweighing one's own opinions; however, Soll and Mannes [3] show that neither of these two can fully account for the tendency to overweigh one's own reasons.

Yaniv and Milyavsky [20] note that individuals with less information change their opinions based on advice more than more knowledgeable individuals. In their experiment, individuals were less likely to change their initial opinion if they had a strong and formed opinion than others who had not. Additionally, Mannes [21] believes that when individuals recognize the wisdom of crowds and place more weight on their opinions, their revised belief becomes more valid.

In sum, studying the effects of social influence on individual decision making is important to evaluate the reliability of their specific predictions. In fact, the internal mechanisms that drive individuals to update their estimates are not fully specified in the literature, especially when they are under social influence. To be more clear, social influence occurs when an individual changes her attitude because of the attitudes of others; that is, when an individual's beliefs, feelings, and behaviors are affected by other people [22].

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