Summary
The motivation for this paper arises out of the authors experiences in modelling real decision makers where the decisions show not only a continuous response to a continuously changing environment but also sudden or discontinuous changes. The theoretical basis involves a parametric characterisation of the environment, a decision makers perception of it in terms of a twice differentiable Distribution Function and a bounded Loss Function. Under a specified, minimizing dynamic, the resultant Expected Loss Function satisfies the conditions for a potential function and Thoms Catastrophe Classification Theorem may be used to assess the singularity points and the thresholds at which jump decisions are taken. The paper describes the theory, summarises some results on unimodal distributions illustrated by jump decisions and population polarisation. Mixture distributions are then examined and the E* models defined. These are then briefly illustrated by reference to models which have been constructed in relation to Prison Riots, Agricultural and Economic modelling.
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Harrison, P.J., Smith, J.Q. Discontinuity, decision and conflict. Trabajos de Estadistica Y de Investigacion Operativa 31, 99–140 (1980). https://doi.org/10.1007/BF02888349
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DOI: https://doi.org/10.1007/BF02888349