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Note on two dominance principles in decision theory

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Summary

Two partial ordering relations (called dominance principles and interpreted as preference relations) may be defined on the class of all real valued random variablesX: (I)X 1≻X 0 if there exists an expanding functionf such thatf(X 0) has the same distribution asX 1. (II)X 1≻X 0 ifF 1 (x)≤F 0 (x),F 1,F 0 being the distribution functions ofX 1,X 0. Both principles, though not equivalent in general, induce the same partial ordering on the class of random variables having a continuous distribution function.

Zusammenfassung

Man kann auf der Klasse aller ZufallsvariablenX zwei partielle Ordnungs-relationen definieren (genannt Dominanzprinzipien und interpretierbar als Präferenzrelationen): (I)X 1≻X 0, wenn es eine zunehmende Funktionf gibt, so daßf(X 0) dieselbe Verteilung wieX 1 besitzt. (II)X 1≻X 0, wennF 1 (x)≤F 0(x), wobeiF 1 undF 0 die Verteilungsfunktionen vonX 1 undX 0 sind. Beide Prinzipien induzieren dieselbe partielle Ordnung auf der Klasse der Zufalls-variablen mit stetigen Verteilungsfunktionen, sind aber allgemein nicht äquivalent.

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Authors and Affiliations

  1. Institut für ökonometrie der Universität des Saarlandes, 66 Saarbrücken 15

    H. Schneeweiss

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  1. H. Schneeweiss
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Revised issue of a paper delivered at the Joint European Meeting of the Econometric Society and The Institute of Management Sciences in Zürich 1964.

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Schneeweiss, H. Note on two dominance principles in decision theory. Unternehmensforschung Operations Research 12, 213–216 (1968). https://doi.org/10.1007/BF01918331

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  • DOI: https://doi.org/10.1007/BF01918331

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