Pardon the dust on this post; the LaTex display is acting up.
But, because E-utility functions are so ill-defined, there is, as best I can tell, not really any meaningful distinction between the two. For example, consider a utilitarian theory that assigns to each agent p a real-valued E-utility function U_p, and aggregates them by summing.
If you’re not making a prioritarian aggregate utility function by summing functions of individual utility functions, the mapping of a prioritarian function to a utility function doesn’t always work. Prioritarian utility functions, for instance, can do things like rank-order everyone’s utility functions and then sum each individual utility raised to the negative-power of the rank-order … or something*. They allow interactions between individual utility functions in the aggregate function that are not facilitated by the direct summing permitted in utilitarianism.
But then the utilitarian theory described by the U’_p, describes exactly the same theory as the prioritarian theory described by the U_p! The theory could equally well be described as “utilitarian” or “prioritarian”; for this reason, unless one puts further restrictions on E-utility functions, I do not consider there to be any meaningful difference between the two.
So from a mathematical perspective, it is possible to represent many prioritarian utility function as a conventional utilitarian utility function. However, from an intuitive perspective, they mean different things:
If you take a bunch of people’s individual utilities and aggregate them by summing the square roots, you’re implying: “we care about improving the welfare of worse-off people more than we care about improving the welfare of better-off people”
If you put the square-root into the utility functions, you’re implying “we believe that whatever-metric-is-going-in-the-square-root provides diminishing returns on inidividual welfare as it increases.”
This doesn’t practically affect decision-making of a moral agents but it does reflect different underlying philosophies—which affects the kinds of utility functions people might propose.
*[EDIT: what I was thinking of was something like \sum (a)^(-s_i) U_i where s_i is the rank-order of U_i in the sequence of all experiences individual utility functions. If a is below 1, this ensures that the welfare improvement of a finite number of low-welfare beings will be weighted more highly than the welfare improvement of any amount of higher welfare beings (for specific values of “low welfare” and “high welfare”). There’s a paper on this that I can’t find right now.∑a−siUi
If you’re not making a prioritarian aggregate utility function by summing functions of individual utility functions, the mapping of a prioritarian function to a utility function doesn’t always work. Prioritarian utility functions, for instance, can do things like rank-order everyone’s utility functions and then sum each individual utility raised to the negative-power of the rank-order … or something*. They allow interactions between individual utility functions in the aggregate function that are not facilitated by the direct summing permitted in utilitarianism.
This is a good point. I might want to go back and edit the original post to account for this.
So from a mathematical perspective, it is possible to represent many prioritarian utility function as a conventional utilitarian utility function. However, from an intuitive perspective, they mean different things:
This doesn’t practically affect decision-making of a moral agents but it does reflect different underlying philosophies—which affects the kinds of utility functions people might propose.
Sure, I’ll agree that they’re different in terms of ways of thinking about things, but I thought it was worth pointing out that in terms of what they actually propose they are largely indistinguishable without further constraints.
Pardon the dust on this post; the LaTex display is acting up.
If you’re not making a prioritarian aggregate utility function by summing functions of individual utility functions, the mapping of a prioritarian function to a utility function doesn’t always work. Prioritarian utility functions, for instance, can do things like rank-order everyone’s utility functions and then sum each individual utility raised to the negative-power of the rank-order … or something*. They allow interactions between individual utility functions in the aggregate function that are not facilitated by the direct summing permitted in utilitarianism.
So from a mathematical perspective, it is possible to represent many prioritarian utility function as a conventional utilitarian utility function. However, from an intuitive perspective, they mean different things:
If you take a bunch of people’s individual utilities and aggregate them by summing the square roots, you’re implying: “we care about improving the welfare of worse-off people more than we care about improving the welfare of better-off people”
If you put the square-root into the utility functions, you’re implying “we believe that whatever-metric-is-going-in-the-square-root provides diminishing returns on inidividual welfare as it increases.”
This doesn’t practically affect decision-making of a moral agents but it does reflect different underlying philosophies—which affects the kinds of utility functions people might propose.
*[EDIT: what I was thinking of was something like \sum (a)^(-s_i) U_i where s_i is the rank-order of U_i in the sequence of all experiences individual utility functions. If a is below 1, this ensures that the welfare improvement of a finite number of low-welfare beings will be weighted more highly than the welfare improvement of any amount of higher welfare beings (for specific values of “low welfare” and “high welfare”). There’s a paper on this that I can’t find right now.∑a−siUi
This is a good point. I might want to go back and edit the original post to account for this.
Sure, I’ll agree that they’re different in terms of ways of thinking about things, but I thought it was worth pointing out that in terms of what they actually propose they are largely indistinguishable without further constraints.