The Paradox
The paradox arises from consideration of four different possibilities. The following diagrams show different situations, with each bar representing a population. The group's size is represented by column width, and the group's happiness represented by column height. For simplicity, in each group of people represented, everyone in the group has exactly the same level of happiness, though Parfit did not consider this essential to the argument.
In situation A, everyone is happy.
In situation A+, there are the extra people. There is the same population as in A, and another population of the same size, which is less happy, but whose lives are nevertheless worth living. The two populations are entirely separate, that is, they cannot communicate and are not even aware of each other. Parfit gives the example of A+ being a possible state of the world before the Atlantic was crossed, and says that A, in that case, represents an alternative history in which the Americas had never been inhabited by any humans.
In situation B-, there are again two separate populations, of the same size as before, but now of equal happiness. The increase in happiness of the right-hand population is greater than the decrease in happiness of the left-hand population. Therefore, average happiness in B- is higher.
Finally in situation B, there is a single population whose size is the sum of the two populations in situation B-, and at the same level of happiness.
Read more about this topic: Mere Addition Paradox
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