Talk:Cardinal utility

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BetacommandBot 11:23, 6 July 2007 (UTC)

Another discussion on Cardinal Utility
Let me re-post here an interesting debate on the issue of cardinality. Please comment there. --Forich (talk) 22:34, 6 March 2009 (UTC)

Proposal of lead section
How about this for the lead :


 * Almost 300 years ago, Daniel Bernoulli (1738) became the first person to conceive subjective wealth as something which could be treated in a mathematical fashion. During the second half of the nineteenth century, other people like Gossen (1854), Jevons (1871), Menger (1871), Walras (1874) and Marshall (1890) followed him. This was a period in economics where the concept of subjective value was treated as a synonym of moral worth and psychic satisfaction, making it a parallel theory to that of Utilitarianism. According to the ideas of this period, people could measure the utility they get from consuming goods and services. Utility was thought of as some kind of psychological entity, which could be measured, and could help explain certain patterns of consumer behaviour. Some economists of this era actually believed in the existence of this quantity, but others just found it useful for their theories of choice and demand. (source: Elsevier's Handbooks of economics)

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)

Shift towards Ordinal Utility part
quoting the Handbook of Game theory, i found very useful info on this:


 * The measurability issue waned under the ordinalist revolution of Edgeworth (1881), Fischer (1892), Pareto (1906) and Slutsky (1915), who mantained that utility represented only a person's preference order over commodity bundles or alternative riskless futures, so gradations in utility apart from its ordering are meaningless. A modest revival in measurable or 'cardinal' utility was generated by Frisch (1926), Lange (1934) and Alt (1936), who axiomatized notions of comparable preference differences. (source: Handbook of Game Theory)

I will expand the "shift toward ordinal utility" part with some of this. Any objections?--Forich (talk) 01:14, 27 November 2009 (UTC)

Uncertainty and expected utility
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)


 * vN-M utility functions are cardinal in the sense posted here in the article. That doesn't mean they measure utility. I could be wrong, but I think that the paper by Ellsberg in the references makes a word by word analysis of the work of vN-M. He claims that the authors meant cardinality but somehow that can only be inferred by reading certain footnotes in the right editions of their books. Otherwise, readers do not tend to interpret that vN-M were thinking of cardinality in the sense exposed here. I'll think of a way to incorporate that debate into the article when I find the time.--Forich (talk) 20:19, 22 March 2010 (UTC)


 * Found this excellente example in a paper by Tapas Majumdar:

"Suppose that the individual is faced with three alternatives $$x_{3}, x_{2}\!$$ and $$x_{1}\!$$. Suppose also that in the absence of risk, the individual prefers $$x_{3}\!$$ to $$x_{2}\!$$; $$x_{2}\!$$ to $$x_{1}\!$$; and therefore $$x_{3}\!$$ to $$x_{1}\!$$. Let $$L_{1}\!$$ and $$L_{2}\!$$ be two Lotteries such that

$$L_1 =(0.6, 0, 0.4)\!$$

$$L_2 =(0,1,0)\!$$

Suppose that the individual prefers $$L_{1}\!$$ to $$L_{2}\!$$.

Let us now modifiy the values of $$p_{1}\!$$ and $$p_{3}\!$$ in $$L_{1}\!$$, as eventually to arrive at the appropiate values ($$L_{1}'\!$$) for which the individual is found to be indifferent between it and $$L_{2}\!$$.

$$L_{1}' =(0.5, 0, 05)\!$$

Expected utility theory tells us that:

$$UE(L_{1}') = UE(L_2)\!$$

$$p_1.u(x_1)+p_2.u(x_{2})+p_3.u(x_{3})=p_1.u(x_1)+p_2.u(x_{2})+p_3.u(x_{3})\!$$

$$(0.5).u(x_1)+(0.5).u(x_{3})=p_2.u(x_{2})\!$$

If we now fix the arbitrary origin at $$x_{1}\!$$ (the utility index being =0 at $$x_{1}\!$$), and so choose our scale that the utility index at $$x_{2} = 1\!$$, we find:

$$(0.5).u(x_{1})=1\!$$

$$u(x_{1}) = 2\!$$

Thus the utility function is found to be cardinal (it preserved the order of preference over $$x_{i}\!$$ 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 $$x_{2}\!$$ and assign it a value higher/lower than $$u(x_{1})\!$$ depending on whether $$x_{2}\!$$ is preferred to/less preferred than $$x_{1}\!$$. And you continue this way.

$$X\!$$ 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.


 * I'll incorporate this same example into the entry soon.--Forich (talk) 17:20, 10 June 2010 (UTC)

Welfare
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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