Appendices - Killing Happy Animals: Explorations in Utilitarian Ethics - page 162

Hare introduces the notion of pair-wise superiority . Option A is pair-wise
superior to option B when the following conditions hold:
(1) Supposing you actually take A, you would have brought about a less
preferable state of affairs by taking B.
(2) Supposing you actually take B, you would have brought about a
preferable state of affairs by taking A. 22
Hare proposes the following procedure:
Step 1: Choose an option.
Step 2: If there are pair-wise superior options choose one, otherwise
keep the option you have.
Step 3: Continue, until there are no pair-wise superior options. 23
An option is an attractor if, no matter how you apply this procedure (no
matter which option you start with, no matter which pair-wise superior
options you choose along the way) you will always get this option. 24
Hare assumes that if you are rational, and an option is a stable attractor,
you will take it. In Charlotte's case this means:
So, when Charlotte is in a position to push buttons B1, B2, B3, if she
has the preferences that she ought, morally to have (in particular her
preferences conform to Personal Dominance) and she is rational (in
particular she picks stable attractors) then she will press B3. 25
Charlotte, if she has the preferences she morally ought to have, and if
she is rational, will also choose B3 when the only options are B1 and B3.
The following principle about rationality can explain this:The practical
insignificance of irrelevant alternatives:
If, given the option of bringing about S 1 , S 2 , S 3 , you will willingly bring
about S 3 , then given the option of bringing about S 1 *, S 3 * (complete
states of affairs relevantly just like S 1 and S 3 , but in which the option
of bringing about S 2 is not available to you), you will willingly bring
about S 3 *. 26
Hare concludes that the 14-year-old girl in Parfit's example will prefer
to wait, if she is rational and has the preferences she morally ought to
have, just because the child she would have if she waited would be better
off than the child she would have if she conceived immediately.
At this point, I briefly want to discuss a criticism that has been brought
forward against Hare's argument. Graham claims that the second
version of Hare's argument fails. Graham argues that the Principle of