IN "SAVING PEOPLE AND FLIPPING COINS," Ben Bradley offers an intriguing counterexample to the principle of equal greatest chance (EGC). (1) The principle of equal greatest chance is designed to apply in contexts of moral equivalence. Let A and B be morally equivalent just in case there is no greater moral reason to save A than there is to save B and vice versa. (2) Suppose a lifeguard can save A and can save B, but she cannot save both A and B. Bradley's formulation of the principle states the following:
EGC. One must give each person the greatest possible chance of
survival consistent with everyone else having the same chance.
If the greatest equal chance of surviving that the lifeguard can give to each is .5, then EGC requires that the lifeguard give A and B each a .5 chance of surviving. (3) Perhaps she can discharge this obligation by flipping a fair coin and acting on the outcome "heads save A," "tails save B." (4)
The problems for EGC arise in cases where three morally equivalent agents require rescue. Suppose you are in a situation where you can save both A and B and you can save C, but you cannot save all A, B and C. Since A, B and C are morally equivalent, there are equally good moral reasons to save each A, B and C. If EGC is properly applicable in contexts of moral equivalence, then you should give each A, B and C the greatest equal chance of surviving. If the greatest equal chance of surviving that you can give to each is .5, then EGC requires that you give A, B and C each a .5 chance of surviving.
The recommendation that we ought to give each of A, B and C a .5 chance of surviving strikes many as counterintuitive. (5) If A, B and C were each on separate islands, or drowning in separate parts of some body of water, and the greatest equal chance of surviving we could give each were .5, it would seem perfectly reasonable to do so. (6) But in the case Bradley describes, we give each a .5 chance of surviving if and only if we give A and B together a .5 chance of surviving and we give C a .5 chance of surviving. (7) Fortunately, Bradley urges, this uncomfortable conclusion is avoidable. The principle of equal greatest chance is false. If Bradley is right, then we have made a very significant advance in assessing moral principles in contexts of moral equivalence. Bradley offers the following "decisive counterexample" to EGC entitled Bureaucracy and EGC. (8)
Imagine that the Joker has captured three hostages--Alice, Bob and Carol--and plans to randomly divide them into two groups, a larger group and a smaller group. The Joker informs Batman that he will kill all members of the group Batman does not select. Batman endorses EGC and indicates his decision to save the larger group by completing a form. Choosing the larger group gives each of Alice, Bob and Carol a two-thirds chance of surviving. Batman thereby gives each the greatest equal chance of surviving.
At noon, Batman checks the box indicating that the larger group
should be saved. The Joker proceeds to divide the hostages randomly
into two groups. Alice and Bob are in one group, Carol is in the
other. At 1:00, the Joker realizes he has lost the form. "I'm
sorry, Batman, but you'll have to fill out another form," he says.
If Batman is to follow EGC, at 1:00 he must flip a coin to decide
which box to check, since that gives each hostage an equal greatest
chance of survival.
This is a decisive counterexample against EGC. No plausible
principle entails that Batman should fill out the form differently
at 1:00. He knew at noon that this was one way things might turn
out. By 1:00 he has gained no new information that could be
relevant to his decision ... [T]he point is that it cannot be the
case that Batman should fill out the form differently at the two
But Bradley is mistaken in claiming that Batman has no relevant information at 1 p. …