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Measuring Ranks via the Complete Laws of Iterated Contraction

Authors: Wolfgang Spohn

Published in: Dagstuhl Seminar Proceedings, Volume 7351, Formal Models of Belief Change in Rational Agents (2007)

Abstract

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper gives a complete axiomatization of that behavior, i.e., a complete set of laws of iterated contraction. It does so by showing how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multi-plicative constant and thus how to measure ranks on a ratio scale.

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Wolfgang Spohn. Measuring Ranks via the Complete Laws of Iterated Contraction. In Formal Models of Belief Change in Rational Agents. Dagstuhl Seminar Proceedings, Volume 7351, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{spohn:DagSemProc.07351.14,
  author =	{Spohn, Wolfgang},
  title =	{{Measuring Ranks via the Complete Laws of Iterated Contraction}},
  booktitle =	{Formal Models of Belief Change in Rational Agents},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7351},
  editor =	{Giacomo Bonanno and James Delgrande and J\'{e}r\^{o}me Lang and Hans Rott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07351.14},
  URN =		{urn:nbn:de:0030-drops-12398},
  doi =		{10.4230/DagSemProc.07351.14},
  annote =	{Keywords: Ranking theory, iterated contraction, measurement theory}
}

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Measuring Ranks via the Complete Laws of Iterated Contraction

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