A previous post introduced the theory of intertheoretic utility comparison. This post will give examples of how to do that comparison, by normalising individual utility functions.
The methods
All methods presented here obey the axioms of Relevant data, Continuity, Individual normalisation, and Symmetry. Later, we'll see which ones follow Utility reflection, Cloning indifference, Weak irrelevance, and Strong irrelevance.
Max, min, mean
The maximum of a utility function is , while the minimum is . The mean of .

The maxmin normalisation of is the such that the maximum of is and the minimum is .

The maxmean normalisation of is the such that the maximum of is and the mean is .
The maxmean normalisation has an interesting feature: it's precisely the amount of utility that an agent completely ignorant of its own utility, would pay to discover that utility (as a otherwise the agent would employ a random, 'mean', strategy).
For completeness, there is also:
 The meanmin normalisation of is the such that the mean of is and the minimum is .
Controlling the spread
The last two methods find ways of controlling the spread of possible utilities. For any utility , define the mean difference: . And define the variance: , where is the mean defined previously.
These lead naturally to:

The mean difference normalisation of is the such that has a mean difference of .

The variance normalisation of is the such that has a variance of .
Properties
The different normalisation methods obey the following axioms:
Property  Maxmin  Maxmean  Meanmin  Mean difference  Variance 

Utility reflection  YES  NO  NO  YES  YES 
Cloning indifference  YES  NO  NO  NO  NO 
Weak Irrelevance  YES  YES  YES  NO  YES 
Strong Irrelevance  YES  YES  YES  NO  NO 
As can be seen, maxmin normalisation, despite its crudeness, is the only one that obeys all the properties. If we have a measure on , then ignoring the cloning axiom becomes more reasonable. Strong irrelevance can in fact be seen as an antivariance; it's because of its second order aspect that it fails this.
This is very interesting  I hadn't thought about utility aggregation for a single agent before, but it seems clearly important now that it has been pointed out.
I'm thinking about this in the context of both the human brain as an amalgamation of subagents, and organizations as an amalgamation of individuals. Note that we can treat organizations as rationally maximizing some utility function in the same way we can treat individuals as doing so  but I think that for many or most voting or decision structures, we should be able to rule out the cla... (Read more)(Click to expand thread. ⌘/CTRL+F to Expand All)Cmd/Ctrl F to expand all comments on this post