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The Mere Addition Paradox

http://commons.wikimedia.org/wiki/File:MereAddition.svg

From Derek Parfit’s Reasons and Persons: World A contains a large group of people (say, 10 billion), all of whom have a high level of happiness. The width of the bar represents the size of the group, and its height represents their happiness.

World A+ contains twice as many people — the original group, plus a second group who are worse off. Assuming their lives are still happy, though, it appears that A+ is no worse than A. (Assume that the groups don’t know of one another, so there is no social injustice.)

In B-, the two groups are still distinct and of equal size, but all the inhabitants are somewhat happier than the average level in A+ — say, four-fifths the level in A.

Now combine the groups to produce B. This seems as good as B-, since we’ve only merged the two populations.

Intuitively, many people would feel that World B is worse than World A — all its inhabitants are less happy. But the logic seems to indicate that B is better — that “merely adding” people with tolerably happy lives makes the world a better place. Does it?