Robert must behave like somebody assigning some consistent dollar value to saving a human life.
Note that this number provides only a lower bound on Robert’s revealed preference regarding the trade-off and that it will vary with the size of the budget.
One could imagine an alternative scenario where there is a fluctuating bankroll (perhaps with a fixed rate of increase — maybe even a rate proportional to its current size) and possible interventions are drawn sequentially from some unknown distribution. In this scenario Robert can’t just use the greedy algorithm until he runs out of budget (modulo possible knapsack considerations), but would have to model the distribution of interventions and consider strategies such as “save no lives now, invest the money, and save many more lives later”.
Note that this number provides only a lower bound on Robert’s revealed preference regarding the trade-off and that it will vary with the size of the budget.
One could imagine an alternative scenario where there is a fluctuating bankroll (perhaps with a fixed rate of increase — maybe even a rate proportional to its current size) and possible interventions are drawn sequentially from some unknown distribution. In this scenario Robert can’t just use the greedy algorithm until he runs out of budget (modulo possible knapsack considerations), but would have to model the distribution of interventions and consider strategies such as “save no lives now, invest the money, and save many more lives later”.
Saving lives now may be worth more than saving lives later.