查看“︁成对比较”︁的源代码

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'''成对比较'''（{{lang-en|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)：

*<math>a>b>c</math>
*<math>a>c>b</math>
*<math>b>a>c</math>
*<math>b>c>a</math>
*<math>c>a>b</math>
*<math>c>b>a</math>
*<math>a>b=c</math>
*<math>b=c>a</math>
*<math>b>a=c</math>
*<math>a=c>b</math>
*<math>c>a=b</math>
*<math>a=b>c</math>
*<math>a=b=c</math>

== 應用 ==
成對比較的一個重要應用是受到廣泛使用的[[層級分析法]]，這種方法將複雜的問題系統化，幫助人們處理複雜的決策。它使用有形和無形因素的成對比較來構建可幫助決策的比率量表<ref name='DMFL'>{{cite book | last = Saaty | first = Thomas L. | authorlink = | title = Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World | publisher = RWS Publications | date = 1999-05-01 | location = Pittsburgh, Pennsylvania | pages = | doi = | id = | isbn = 978-0-9620317-8-6 }}</ref><ref name='RACSAM'>{{cite journal|title=Relative Measurement and its Generalization in Decision Making: Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors &ndash; The Analytic Hierarchy/Network Process|journal=[[Spanish Royal Academy of Sciences|Review of the Royal Academy of Exact, Physical and Natural Sciences, Series A: Mathematics (RACSAM)]]|date=June 2008|first=Thomas L.|last=Saaty|authorlink=Thomas L. Saaty|volume=102|issue=2|pages=251&ndash;318|id=|url=http://www.rac.es/ficheros/doc/00576.PDF|format=|accessdate=2008-12-22|doi=10.1007/bf03191825|archive-date=2009-11-23|archive-url=https://web.archive.org/web/20091123050803/http://www.rac.es/ficheros/doc/00576.PDF}}</ref>

== 参见 ==
[[層級分析法|层次分析法]]
[[偏好 (經濟學)|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 ==
{{reflist}}
*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

[[Category:心理統計學]]