Baccelli, Jean (2023) Ordinal Utility Differences. Social Choice and Welfare.

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Abstract

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark---if any---of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Baccelli, Jean jean.baccelli@gmail.com 0000-0003-0275-0377
Keywords:	ordinal utility; ordinalism; quaternary relation; preference difference; preference intensity; strength of preference; utility difference; incompleteness; multi-utility representation; cardinal utility; cardinalism; IIA
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Probability/Statistics
Depositing User:	Jean Baccelli
Date Deposited:	02 Nov 2023 22:20
Last Modified:	02 Nov 2023 22:20
Item ID:	22727
Journal or Publication Title:	Social Choice and Welfare
DOI or Unique Handle:	10.1007/s00355-023-01488-w
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Probability/Statistics
Date:	8 September 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/22727

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