Flat Maxima in Linear Optimization Models

Abstract

Expected value functions as functions of decisions and decision strategies are flat around their maxima. This so called flat maximum phenomenon has been discovered in sensitivity analyses in virtually all decision theoretic paradigms. But until now most of the research on flat maxima explored more or less general examples and limiting considerations. Two basic questions remained unanswered: what are the mathematical reasons for the restricted shape of the evaluation functions; and can these restrictions be interpreted as flatness in a psychological sense. While the second question calls for psychological experimentation, the first question can be answered with mathematical tools. The present article shows that the mathematical characteristics of linear optimization models impose severe restrictions on the functions evaluating choice alternatives such as gambles, multi-attributed outcomes, or consumption streams.

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Document Details

Document Type
Technical Report
Publication Date
Nov 02, 1973
Accession Number
AD0770569

Entities

People

  • Detlof V. Winterfeldt
  • Ward Edwards

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Decision Theory
  • Detection
  • Engineering
  • Human Factors Engineering
  • Linear Programming
  • Mathematical Analysis
  • Michigan
  • Military Research
  • Numbers
  • Optimization
  • Probability
  • Psychology
  • Random Variables
  • Real Numbers
  • Signal Detection
  • Statistical Decision Theory
  • Theorems

Readers

  • Computational Modeling and Simulation
  • Educational Psychology
  • Team-Based Human-Centered Cognitive Task Decision Making and Information Performance.