Skirting the mere addition paradox

Stuart_Armstrong

7 Skirting the mere addition paradox

by Stuart_Armstrong

18th Nov 2013

1 min read

7

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.

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7 Skirting the mere addition paradox

by Stuart_Armstrong

18th Nov 2013

1 min read

7

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.

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33Embracing the "sadistic" conclusion

7Population ethics and utility indifference

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V_V12y00

Indeed.

It is also worth noting that average utilitarianism has also its share of problems: killing off anyone with below-maximum utility is an improvement.
Stuart Armstrong's proposed aggregation function has essentially the same problem, since while it disincentivizes reducing the number of people, it doesn't disincentivizes it much at any significant population level.

BTW: all flavors of utilitarianism suffer from the fact that there is no known satisfactory way of comparing the utility of different people. Without interpersonal utility comparison, the point is moot.

Ghatanathoah12y10

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

No it isn't. This can be demonstrated fairly simply. Imagine a population consisting of 100 people. 99 of those people have great lives, 1 of those people has a mediocre one.

At the time you are considering doing the killing the person with the mediocre life, he has accumulated 25 utility. If you let him live he will accumulate 5 more utility. The 99 people with great lives will accumulate 100 utility o... (read more)

0ArisKatsaris12y

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.

2TheOtherDave12y

This is true insofar as it can be performed without creating significant disutility for their above-average-utility neighbors, and not otherwise. A community that would suffer greatly due to the deaths of half the people around them would not necessarily have its average utility increased by that operation. [...] True. Actually, it's worse than that... we don't even have a way to compare an individual's utility over time with any level of precision, though we talk casually as though we did. (If we had such an intertemporal utility comparison, then we could for example declare that the highest-utility state each individual has achieved in their lifetime is 1 unit of utility, and the lowest-utility state is 0 units, and interpolate linearly, recalibrating whenever an individual exceeds their previous maximum, and that would be one way of comparing interpersonal utilities at any given time. Of course, that might not be acceptable because it fails to account for the possibility that some individuals are just worth more than others, or for various other reasons, but it would at least be a place to start.) Without that, utilitarianism is at best no more than a qualitative way to address ethical questions.

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