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BetacommandBot 11:23, 6 July 2007 (UTC)
Let me re-post here an interesting debate on the issue of cardinality. Please comment there. -- Forich ( talk) 22:34, 6 March 2009 (UTC)
How about this for the lead :
I think it suits the article but I'll put more time into it later to improve it and merge it with the current lead section. -- Forich ( talk) 20:17, 22 November 2009 (UTC)
quoting the Handbook of Game theory, i found very useful info on this:
I will expand the "shift toward ordinal utility" part with some of this. Any objections?-- Forich ( talk) 01:14, 27 November 2009 (UTC)
This is good for the early debate (needs some wikifying), but it doesn't cover expected utility and the debate over whether the von Neumann-Morgenstern utility function is cardinal in the sense discussed here (vN-M say no, others say yes). There's also a related debate in health economics where its common to use a zero condition - that is, the assumption that utility when you are not alive is zero. JQ ( talk) 22:13, 21 March 2010 (UTC)
"Suppose that the individual is faced with three alternatives and . Suppose also that in the absence of risk, the individual prefers to ; to ; and therefore to . Let and be two Lotteries such that
Suppose that the individual prefers to .
Let us now modifiy the values of and in , as eventually to arrive at the appropiate values () for which the individual is found to be indifferent between it and .
Expected utility theory tells us that:
If we now fix the arbitrary origin at (the utility index being =0 at ), and so choose our scale that the utility index at , we find:
Thus the utility function is found to be cardinal (it preserved the order of preference over except for an arbitrary choice of origin and scale). This is the same as representing these preferences by a class of utility functions related only by linear transformations.
Then you take another element and assign it a value higher/lower than depending on whether is preferred to/less preferred than . And you continue this way.
can be assumed to be a calculable money-prize in a controlled game of chance, unique up to one positive proportionality factor depending on the currency unit.
Source: Majumdar, Tapas. (1958). "Behaviourist cardinalism in utility theory". Economica, 25(97): 26-33.
Suzumura (1999, p. 204) says that there was "a harsh ordinalist criticism in the 1930s against the epistemological basis of the 'old' welfare economics created by Pigou...". The debate on the transition from cardinal to ordinal and its implications for welfare-economics theory deserves a mention in this entry. I'll see what I can do to insert something.-- Forich ( talk) 14:36, 12 June 2015 (UTC)
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