Editing Arrow's impossibility theorem (section)

==== {{Anchor|Meaning|Cardinal|Validity|Meaningfulness}}Meaningfulness of cardinal information ====
{{Main|Cardinal utility}}
Arrow's framework assumed individual and social preferences are [[Ordinal utility|orderings]] or [[Ranked voting|rankings]], i.e. statements about which outcomes are better or worse than others.<ref>{{Cite journal |last=Lützen |first=Jesper |date=2019-02-01 |title=How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem |url=https://www.sciencedirect.com/science/article/pii/S0315086018300508 |journal=Historia Mathematica |volume=46 |pages=56–87 |doi=10.1016/j.hm.2018.11.001 |issn=0315-0860}}</ref> Taking inspiration from the [[Behaviorism|strict behaviorism]] popular in psychology, some philosophers and economists rejected the idea of comparing internal human experiences of [[Cardinal utility|well-being]].<ref name="Racnchetti-2002">"Modern economic theory has insisted on the ordinal concept of utility; that is, only orderings can be observed, and therefore no measurement of utility independent of these orderings has any significance. In the field of consumer's demand theory the ordinalist position turned out to create no problems; cardinal utility had no explanatory power above and beyond ordinal. Leibniz' Principle of the [[identity of indiscernibles]] demanded then the excision of cardinal utility from our thought patterns." Arrow (1967), as quoted on [https://books.google.com/books?id=7ECXDjlCpB0C&pg=PA33 p.&nbsp;33] by {{citation |last=Racnchetti |first=Fabio |title=The Active Consumer: Novelty and Surprise in Consumer Choice |volume=20 |pages=21–45 |year=2002 |editor-last=Bianchi |editor-first=Marina |series=Routledge Frontiers of Political Economy |contribution=Choice without utility? Some reflections on the loose foundations of standard consumer theory |publisher=Routledge}}</ref><ref name="Pearce" /> Such philosophers claimed it was impossible to compare the strength of preferences across people who disagreed; [[Amartya Sen|Sen]] gives as an example that it would be impossible to know whether the [[Great Fire of Rome]] was good or bad, because despite killing thousands of Romans, it had the positive effect of letting [[Nero]] expand his palace.<ref name="The Possibility of Social Choice2">{{cite journal |last1=Sen |first1=Amartya |date=1999 |title=The Possibility of Social Choice |url=https://www.aeaweb.org/articles?id=10.1257/aer.89.3.349 |journal=American Economic Review |volume=89 |issue=3 |pages=349–378 |doi=10.1257/aer.89.3.349}}</ref>

Arrow originally agreed with these positions and rejected [[cardinal utility]], leading him to focus his theorem on preference rankings.<ref name="Racnchetti-2002" /><ref name="Arrow 1963234" /> However, he later stated that cardinal methods can provide additional useful information, and that his theorem is not applicable to them.

[[John Harsanyi]] noted Arrow's theorem could be considered a weaker version of his own theorem<ref>{{Cite journal |last=Harsanyi |first=John C. |date=1955 |title=Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility |journal=Journal of Political Economy |volume=63 |issue=4 |pages=309–321 |doi=10.1086/257678 |jstor=1827128 |s2cid=222434288}}</ref>{{Failed verification|reason=Paper seems to argue that if we can estimate others' utilities, then the decision function must be total utilitarianism - it doesn't say that Arrow's theorem is a corollary.|date=December 2024}} and other [[utility representation theorem]]s like the [[Von Neumann–Morgenstern utility theorem|VNM theorem]], which generally show that [[Coherence (philosophical gambling strategy)|rational behavior]] requires consistent [[Cardinal utility|cardinal utilities]].<ref name="VNM2">[[John von Neumann|Neumann, John von]] and [[Oskar Morgenstern|Morgenstern, Oskar]], ''[[Theory of Games and Economic Behavior]]''. Princeton, NJ. Princeton University Press, 1953.</ref>