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Symmetric conformity functions make decision-making processes independent of the distribution of learning strategies
Arkadiusz Jędrzejewski, Laura Hernández
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Two main procedures characterize the way in which social actors evaluate the qualities of the options in decision-making processes: they either seek to evaluate their intrinsic qualities (individual learners), or they rely on the opinion of the others (social learners). For the latter, social experiments have suggested that the mathematical form of the probability of adopting an option, called the conformity function, is symmetric in the adoption rate. However, the literature on decision-making includes models where social learners employ either symmetric or nonsymmetric conformity functions. We generalize a particular case studied in a previous work, and we show analytically that if the conformity function is symmetric, the details of the probability distribution of the propensity of the agents to behave as a social or an individual learner do not matter, only its expected value influences the determination of the steady state. We also show that in this case, the same steady state is reached for two extreme dynamical processes: one that considers propensities as idiosyncratic properties of the agents (each agent being an individual learner always with the same probability), and the opposite one, which allows them to change their propensity during the dynamics. This is not the case if the conformity function is nonsymmetric. This fact can inspire experiments that could shed light on the debate about mathematical properties of conformity functions.
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