= 27d567bc2d48d9f40e9ccc20ea370b15)
tut comments on The Domain of Your Utility Function - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (94)
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).
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.
The wikipedia entry on lexicographic preferences isn't great, but gives the basic flavour:
That entry says,
So my intuition above was not correct -- an uncountably infinite alphabet is what's required.