Outline
1. Motivation
2. What is aggregation?
3. Aggregation and utilitarianism
4. Scanlonfs case for saving the greater number
5. The Tie-Breaking argument for saving the greater number
6. Two-Level Utilitarianism? : Harsanyifs Representation Theorem
7. Trivial example
8. Conclusion: No reason to rule out aggregation
Scanlonfs contractualism: An act is wrong just when and because it is ruled out by principles that no one could reasonably reject from individual standpoints.
Two remarks:
1. It would be reasonable to reject a principle for deciding what to do in the cases that did not give positive weight to each person's life.
2. It would also be reasonable to reject a principle that did not give each person's life the same importance. Scanlon (1998: 233).
The Tie-Breaking argument:
gThat argument [the tie-breaking argument] relied on the fact that if one of the members of the two-person group were absent then the positive reason for saving the one person would be balanced by an identical reason for saving the remaining member of the pair, thus creating a tie, which is broken by the claims of the other member of the pair, if there is one.h Scanlon (1998: 237).
Harsanyifs Representation Theorem
1. Individual rationality: The personal preferences of all individuals in society satisfy the Bayesian rationality postulates (the requirement of consistent preferences, a continuity axiom, the sure-thing principle, and the requirement that our preferences for lotteries should depend only on the possible prizes and on the specific random events deciding the actual prize.)
2. Rationality of moral preference: The social preference satisfy the Bayesian rationality.
3. Pareto: Suppose that at least on individual personally prefers alternative A to B, and no individual has an opposite personal preference. Then alternative A is preferred to B. (Compare Pareto with Scanlonfs first remark)
Representation Theorem: The social welfare function W must be of the mathematical form W=a1w1+a2w2+ ... +anwn with ai>0.