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2 The Experiment

Lorenz et al. [1] ask 144 students to answer six quantitative questions on geographical facts and crime statistics in Switzerland, including (1) population density, (2) border length, (3) the number of new immigrants, (4) the number of murders, (5) the number or rapes, and (6) the number of assaults. The participants were split randomly into 12 experimental sessions, each consisting of 12 participants. Each question was repeatedly answered in five rounds (time periods). The questions were designed in such a way that individuals were not likely to know the exact answer, but could still have some clue. Participants did not interact with each other and the only information they received about the others' estimates was provided by experimental manipulation (no information, aggregated information, and full information) through the software interface. Individuals were also asked about their confidence levels in their first and fifth estimates for each question on a six-point Likert scale (1, very uncertain; 6, very certain). The confidence level values were not provided to the others.

Three different scenarios were tested regarding information exposure, including “no information”, “aggregated information”, and “full information”. In the no information scenario, individuals were not aware of others' estimates and, therefore, the five consecutive estimates were made with no additional information. In the aggregated information scenario, each subject was provided with the arithmetic average of others' estimates in the previous round. Finally, in the full information scenario, individuals received a figure of the trajectories of all others' estimates along with their numerical values from the previous round. For each group, two questions were posed in each information scenario. The order of questions in each information condition was randomized.

Subjects were encouraged to answer questions precisely by offering them financial rewards. Individuals received increasing monetary payments if their estimates fell into the 40%, 20%, or 10% intervals around the truth; otherwise, they received no reward. The correct answer and rewards were disclosed at the end of the experiment to avoid giving away a priori knowledge about the right answer.

3 Modeling

In this study we design two scenarios, no information (No Info) and aggregated information (Aggregated Info), to reproduce the dynamic mechanism of changing estimates, over five estimation making rounds. No Info and Aggregated Info models are discussed in Sections 3.1 and 3.2 respectively. Parameter estimation is then presented in section 3.3.

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