Motivated by the psychological literature on the peak-end rule for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents future choices depend on the peak memory of their past experiences. In particular, we use this approach to investigate whether increased noise/disruption always leads to more switching between decisions. Here extreme value theory illuminates different classes of dynamics indicating that the long-time behaviour is dependent on the scale used for reflection; this could have implications, for example, in questionnaire design.
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