Skirting the mere addition paradox

Stuart_Armstrong

Consider the following facts:

For any population of people of happiness h, you can add more people of happiness less than h, and still improve things.
For any population of people, you can spread people's happiness in a more egalitarian way, while keeping the same average happiness, and this makes things no worse.

This sounds a lot like the mere addition paradox, illustrated by the following diagram:

This is seems to lead directly to the repugnant conclusion - that there is a huge population of people who's lives are barely worth living, but that this outcome is better because of the large number of them (in practice this conclusion may have a little less bite than feared, at least for non-total utilitarians).

But that conclusion doesn't follow at all! Consider the following aggregation formula, where au is the average utility of the population and n is the total number of people in the population:

au(1-(1/2)ⁿ)

This obeys the two properties above, and yet does not lead to a repugnant conclusion. How so? Well, property 2 is immediate - since only the average utility appears, the reallocating utility in a more egalitarian way does not decrease the aggregation. For property 1, define f(n)=1-(1/2)ⁿ. This function f is strictly increasing, so if we add more members of the population, the product goes up - this allows us to diminish the average utility slightly (by decreasing the utility of the people we've added, say), and still end up with a higher aggregation.

How do we know that there is no repugnant conclusion? Well, f(n) is bounded above by 1. So let au and n be the average utility and size of a given population, and au' and n' those of a population better than this one. Hence au(f(n)) < au'(f(n')) < au'. So the average utility can never sink below au(f(n)): the average utility is bounded.

So some weaker versions of the mere addition argument do not imply the repugnant conclusion.

Consider the following facts:

For any population of people of happiness h, you can add more people of happiness less than h, and still improve things.
For any population of people, you can spread people's happiness in a more egalitarian way, while keeping the same average happiness, and this makes things no worse.

This sounds a lot like the mere addition paradox, illustrated by the following diagram:

But that conclusion doesn't follow at all! Consider the following aggregation formula, where au is the average utility of the population and n is the total number of people in the population:

au(1-(1/2)ⁿ)

So some weaker versions of the mere addition argument do not imply the repugnant conclusion.

It is also worth noting that average utilitarianism has also its share of problems: killing off anyone with below-maximum utility is an improvement.

If one averages across all time, the strong preference of people to not be killed would suffice to more than cancel the benefits of their non-participation in the future averages.

I don't know what you mean by "average across time". You typically discount across time.
Anyway, utilitarianism is a form of consequentialism in that it assigns moral preferences to world states rather than transitions. Being killed is a transition in any description at any meaningful level of abstraction, hence you can't assign an utility to it. If you do, then you have an essentially dentological ethics, not utilitarianism.

0Stuart_Armstrong12y

Rather than counting on other factors (people's preferences) to avoid outcomes we feel are bad, I think it would be better to encode the badness of these outcomes directly.

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Skirting the mere addition paradox

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Skirting the mere addition paradox

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