An improvement to Jensen's inequality and its application to mating market clearing when paternity is uncertain

Research output: Contribution to journalArticle

Abstract

Jensen's inequality can be tightened in the context of discrete random variables. The suggested new inequality coincides with Jensen's inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen's. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that cannot be obtained when relying on Jensen's inequality.

Original languageEnglish
JournalMathematical Social Sciences
DOIs
Publication statusAccepted/In press - 2017

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Jensen's inequality
Welfare
market
Discrete random variable
Expected Value
Random variable
Social Welfare
Uncertainty
Integer
social welfare
welfare
Market
Market clearing
uncertainty
Context
Random variables

ASJC Scopus subject areas

  • Sociology and Political Science
  • Social Sciences(all)
  • Psychology(all)
  • Statistics, Probability and Uncertainty

Cite this

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title = "An improvement to Jensen's inequality and its application to mating market clearing when paternity is uncertain",
abstract = "Jensen's inequality can be tightened in the context of discrete random variables. The suggested new inequality coincides with Jensen's inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen's. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that cannot be obtained when relying on Jensen's inequality.",
author = "Dirk Bethmann",
year = "2017",
doi = "10.1016/j.mathsocsci.2017.08.004",
language = "English",
journal = "Mathematical Social Sciences",
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