Utility and Measurement (part 3a)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• For this vast and vague subject, even a course survey is not presented
• Sorry for Jeremy Bentham and ethical thinkers all time who take heterogeneity seriously, little treatment given for social contexts

Far Historical Landscape of Decision and Social Choice Theory

• There is impressive contrast between slow development of decision (voting) theory, which treats ordinal utility, or preference, and fast development of utility theory, which treats mainly cardinal utility
• Despite that we compare one with another everyday, and discrete and abstract argument of preference looks well intuitive, ordinal utility could not be well understood without complete foundation of measure theory, topology and set theory. Any interesting (or dismal) choice in reality faces on opposition and uncertainty, both requires utility calculus based on sets and measures, and defined utility make various such conditions comparable
• Bernoulli(1738, trans. 1954) considered St. Petersburg paradox and gave modern notion of risks and utility with uncertainty, left unconsidered before von Neumann-Morgenstern(2/e, 1947)
• (aside) Essentially also by von Neumann, together with some other mathematical abstractions, general topology were introduced to economics
• Condorcet(1785), known for voting paradox, was the first systematic treatise on decision theory, using order-theoretic argument built on probability theory. Simply it was too early for the human race in pre-Bourbaki age
• Essentially no disciplinary landmark before Arrow(1951, 1963)
• For detailed exposition, see Duncan Black(1958, 1998)
• Game theory give a way to describe operations to partial-ordering of consistent social preference. Discrete conception of preference and game made microeconomic arguments applicable to areas where no explicit or continuous quantity and price is given: these span for fundamentals of several disciplines in economic (off-market competition), social and political studies.

TODO

• write the latter half of part 3 (may treat development of utility theory and unnamed open sets inside indifference curves)