Equality and leveling down

A common popular criticism of valuing equality in and of itself is that one can achieve equality, say in utility, simply by bringing down everybody who is above the level of the least happy member of the community, which is plainly undesirable. I am ashamed to say that I've used this criticism myself in the past.

But the criticism only applies to a naive view where equality is considered in a binary way—you either have it or you don't, and there is a value in having it and a disvalue in not having it. But of course on any non-naive view, equality is valued along a continuum—a minor inequality has small disvalue, while a large inequality has large disvalue. If one takes this into account, it's easy to come up with ways of weighing the value of equality, or equivalently the disvalue of inequality, that are not subject to the above criticism.

For instance, suppose we have n persons, with utilities: u₁,...,u_n. Standard consequentialism calculates an overall value of u₁+...+u_n. But there are many ways of modifying this so that one (a) takes equality into account, and (b) avoids the popular criticism. Now, the intuition behind the popular criticism is, I think, based on the following intuition:

1. It is good if the utility of some is increased and the utility of none is decreased.

So what we need to do is to combine utilities in such a way that equality is valued, but (1) is maintained. Here is one very simple way of doing this. Just model the total good as u₁+...+u_n−c_n(|u₁−a|+...+|u_n−a|), where a is the arithmetic average (u₁+...+u_n)/n, and c_n is a constant such that 0<c_n<1/2. You get a different model, with different normative consequences, for different values of c_n. It's easy to check that increasing any one of the u_i increases the total good on this model[note 1] and so we have (1) and (b). It is never the case that on this valuation, decreasing the utility of some without increasing the utility of any will improve total good—thus, leveling down is not something to worry about. Moreover, equality is taken into account—a more equal distribution is, ceteris paribus, preferable even if it decreases u₁+...+u_n (but not preferable if it decreases each individual utility, or even some individual utilities without increasing others).

All that said, I think such numerical models are not something to take very seriously. Here's one reason. While we might think that there is an objective answer to the question: "What is the mass of the electron?", and that this might be some number, the idea that there should be an objective answer to the question: "What is the true value of c_n in the above total-good formula?" is very implausible to me. And all such additive formulae assume commensurability of goods between people, which I deny. But the models may still be useful, say for showing how an advocate of equality might avoid the leveling-down criticism.