Cyan comments on The Domain of Your Utility Function - Less Wrong

24 Post author: Peter_de_Blanc 23 June 2009 04:58AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (94)
Tags: decision_theory morality

Comments (94)

You are viewing a single comment's thread. Show more comments above.

Comment author: Cyan 24 June 2009 09:22:29PM 0 points [-]

I'm with you on "incomplete" (thanks for the catch!) but I'm not so sure about "violate continuity". Can you give an example of preferences that are transitive and complete but violate continuity and are therefore not encodable in a utility function?

Comment author: conchis 24 June 2009 11:45:26PM 0 points [-]

Lexicographic preferences are the standard example: they are complete and transitive but violate continuity, and are therefore not encodable in a standard utility function (i.e. if the utility function is required to be real-valued; I confess I don't know enough about surreals/hyperreals etc. to know whether they will allow a representation).

Comment author: Cyan 25 June 2009 12:42:16AM *  0 points [-]

I'd heard that mentioned before around these parts, but I didn't recall it because I don't really understand it. I think I must be making a false assumption, because I'm thinking of lexicographic ordering as the ordering of words in a dictionary, and the function that maps words to their ordinal position in the list ought to qualify. Maybe the assumption I'm missing is a countably infinite alphabet? English lacks that.

Comment author: conchis 25 June 2009 01:06:50AM 0 points [-]

The wikipedia entry on lexicographic preferences isn't great, but gives the basic flavour:

Lexicographic preferences (lexicographical order based on the order of amount of each good) describe comparative preferences where an economic agent infinitely prefers one good (X) to another (Y). Thus if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is. Only when there is a tie of Xs between bundles will the agent start comparing Ys.

Comment author: Cyan 25 June 2009 03:31:56AM *  0 points [-]

That entry says,

...the classical example of rational preferences that are not representable by a utility function, if amounts can be any non-negative real value.

So my intuition above was not correct -- an uncountably infinite alphabet is what's required.

Powered by Reddit Powered by Reddit