When facing a choice between saving one person and saving many, some people have argued that fairness requires us to decide without aggregating numbers; rather we should decide by coin toss or some form of lottery, or alternatively we should straightforwardly save the greater number but justify this in a non-aggregating contractualist way. This paper expands the debate beyond well-known number cases to previously under-considered probability cases, in which not (only) the numbers of people, but (also) the probabilities of success for saving people vary. It is shown that, in these latter cases, both the coin toss and the lottery lead to what is called an awkward conclusion, which makes probabilities count in a problematic way. Attempts to avoid this conclusion are shown to lead into difficulties as well. Finally, it is shown that while the greater number method cannot be justified on contractualist grounds for probability cases, it may be replaced by another decision method which is so justified. This decision method is extensionally equivalent to maximising expected value and seems to be the least problematic way of dealing with probability cases in a non-aggregating manner.
Aggregation Coin toss Fairness Lottery Number cases Probability cases