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Multistability of impact, utility and threshold concepts of binary choice models

机译:二元选择模型的影响,效用和阈值概念的多重稳定性

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摘要

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability. (C) 2008 Elsevier B.V. All rights reserved.
机译:通过影响函数,效用函数和阈值模型方法来考虑二元选择背景下的决策问题。检查了广义影响函数和效用函数的性质;结果表明这两种方法是等效的。研究它们与阈值模型的关系,并显示各个累积分布函数之间的对应关系。在平均场近似范围内确定与热力学平衡相对应的静止状态。稳态的多重稳定性用冲击/效用函数的随机变量的分布函数表示。讨论了与伊辛模型的统计物理学预测的对应关系:逻辑分布导致均值场结果,即居里-魏斯近似。社会性格,自我支持,社会互动的非线性等分布函数和/或其他模型参数的变化,将打破与伊辛模型统计物理学的直接对应关系,在某些情况下会导致多稳定性结构更丰富。 (C)2008 Elsevier B.V.保留所有权利。

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