Chapter

 The Measurement of Ranks

Wolfgang Spohn

in The Laws of Belief

Published in print March 2012 | ISBN: 9780199697502
Published online September 2012 | e-ISBN: 9780191739323 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199697502.003.0008
 The Measurement of Ranks

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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

Chapter.  12541 words. 

Subjects: Metaphysics

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