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The Laws of BeliefRanking Theory and Its Philosophical Applications$
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Wolfgang Spohn

Print publication date: 2012

Print ISBN-13: 9780199697502

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199697502.001.0001

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 The Measurement of Ranks

 The Measurement of Ranks

Chapter:
(p.162) 8 The Measurement of Ranks
Source:
The Laws of Belief
Author(s):

Wolfgang Spohn

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199697502.003.0008

Ranks are cardinal degrees of belief (that also represent belief). This calls for a theory of measurement of those numerical ranks. The chapter provides no less than three different methods of measurement. The basic theory is that of difference measurement. The main measurement method uniquely reconstructs a ranking function from its iterated contraction behavior on a ratio scale. Thereby, it offers a complete set of laws of iterated contraction, thus solving an old problem of belief revision theory. The chapter should be understood as providing additional justification of ranking theory. At the end, two possible further lines of justification, a Cox-type of justification and an analogy to the Dutch book argument, are presented and discussed.

Keywords:   measurement of ranks, difference measurement, iterated contraction, dutch book argument, cox-type of justification

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