成对比较

成对比较(英语:Pairwise comparison)用于确定两件事之间哪个更好,对于每个可能的对象做比对。在某些情况下,两者可能同样好。成对比较用于研究偏好。

总览

每当在两件事之间表达偏好时,就可以进行成对比较。 如果例如两个选择分别是x和y ,以下这三个成对比较是可能的:

x优于y :“ x>y" 或 "xPy"

y优于x:“ y>x" 或 "yPx"

x和y一样好:“ x=y“ 或 "xIy"

传递性

对于给定的决策代理,传递性规则如下:

如果xPy并且满足yPz,则xPz

如果xPy并且满足yIz,则xPz

如果xIy并且满足yPz,则xPz

如果xIy并且满足yIz,则xIz

优先顺序

例如,如果有三个选择a , b和c ,然后有十三种可能的优先顺序 (可能的个人喜好):

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应用

成对比较的一个重要应用是受到广泛使用的层级分析法,这种方法将复杂的问题系统化,帮助人们处理复杂的决策。它使用有形和无形因素的成对比较来构建可帮助决策的比率量表[1][2]

参见

层次分析法 偏好(经济学) 孔多塞法: 这种方法将每个选项与所有其他的选项成对比较确定多数人的偏好

参考文献

  1. ^ Saaty, Thomas L. Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. Pittsburgh, Pennsylvania: RWS Publications. 1999-05-01. ISBN 978-0-9620317-8-6. 
  2. ^ Saaty, Thomas L. Relative Measurement and its Generalization in Decision Making: Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors – The Analytic Hierarchy/Network Process (PDF). Review of the Royal Academy of Exact, Physical and Natural Sciences, Series A: Mathematics (RACSAM). June 2008, 102 (2): 251–318 [2008-12-22]. doi:10.1007/bf03191825. (原始内容 (PDF)存档于2009-11-23). 
  • Sloane, N.J.A. (ed.). "Sequence A000142 (Factorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  • Sloane, N.J.A. (ed.). "Sequence A000670 (Number of preferential arrangements of n labeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  • Y. Chevaleyre, P.E. Dunne, U. Endriss, J. Lang, M. Lemaître, N. Maudet, J. Padget, S. Phelps, J.A. Rodríguez-Aguilar, and P. Sousa. Issues in Multiagent Resource Allocation. Informatica, 30:3–31, 2006.

延伸阅读

  • Bradley, R.A. and Terry, M.E. (1952). Rank analysis of incomplete block designs, I. the method of paired comparisons. Biometrika, 39, 324–345.
  • David, H.A. (1988). The Method of Paired Comparisons. New York: Oxford University Press.
  • Luce, R.D. (1959). Individual Choice Behaviours: A Theoretical Analysis. New York: J. Wiley.
  • Thurstone, L.L. (1927). A law of comparative judgement. Psychological Review, 34, 278–286.
  • Thurstone, L.L. (1929). The Measurement of Psychological Value. In T.V. Smith and W.K. Wright (Eds.), Essays in Philosophy by Seventeen Doctors of Philosophy of the University of Chicago. Chicago: Open Court.
  • Thurstone, L.L. (1959). The Measurement of Values. Chicago: The University of Chicago Press.
  • Zermelo, E. (1928). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung, Mathematische Zeitschrift 29, 1929, S. 436–460