Relative utilitarianism takes utilities as reported by agents, rescales them so that, for each agent, the alternatives have utility values between 0 and 1, and then chooses an alternative to maximize the (weighted) sum of the rescaled utilities. This forces an equality of sorts upon the agents as their utilities are all bounded on the same range. However, they can still express the degree to which they prefer A to B (relative to their preference of B over C) by making the gap between A and B larger (or smaller) than that between B and C.
Has anybody come across a mechanism like this except that, instead of rescaling reported utilities to a given range, we simply take the ordinal preferences expressed by the reported utilities and assign predetermined utility values (respecting the order).
That is, with relative utilitarianism:
$$ (10,4,2,0) \rightarrow (1,0.4,0.2,0) \text{ and } (100,9,1,0) \rightarrow (1,0.09,0.01,0)$$
What I want to do is the following:
$$ (10,4,2,0) \rightarrow (10,7,5,2) \text{ and } (100,9,1,0) \rightarrow (10,7,5,2)$$
The numbers in $(10,7,5,2)$ are irrelevant (they could be between 0 and 1) -- the point is just that they're the same across the two cases. Basically, I'm just extracting a preference order from the reported cardinal utilities and then slapping predetermined utility values on to them, respecting the order but not magnitudes in differences. Then, subsequently, I would choose an alternative to maximize the sum of utilities.
Two related questions:
- Have you seen this done anywhere, either explicitly or implicitly?
- Supposing you haven't, what would you call this?