## A Bayesian approach to the trolley problem? (mini-thought experiment)

Note: This is a follow-up to our Nov. 14 post titled “A Bayesian defense of the Hadley rule.”

In our 2014 paper Trolley Problems, we wrote (footnotes omitted): “Consider the [standard] version of the trolley problem [pictured below]. There are seven parties to this conflict. On the one side of this moral equation is the person at the switch, who must make the difficult decision whether to leave the trolley on the main track where five workers will be harmed or divert it to a side track where only one worker will be harmed. On the other side of this moral balance are a total of six workers who are all potentially at risk from the runaway trolley, depending on whether the switch is pulled. But because of the veil of ignorance, none of the players knows their role ahead of time. Given this counterfactual world, imagine what would occur if these seven unfortunate souls could call a Coasean time-out to take part in a Coasean auction behind a veil of ignorance. In truth, since this a second-order thought experiment, the outcome of such a hypothetical auction is not obvious, unless a probabilistic approach to the trolley problem is taken.”

In place of a hypothetical Coasean auction, however, what if we imagined a “diabolical trolley lottery” instead? In the original position, there is a 0.714 probability that you will be one of the five workers trapped on the main track (5 ÷ 7), a 0.143 probability that you will be the worker on the side track (1 ÷ 7), and a 0.143 probability that you will be the person at the switch (1 ÷ 7). Accordingly, we can now imagine a negative lottery corresponding with these same probabilities and ask, How much would we pay to avoid having to play this diabolical lottery? Or in the alternative, would we prefer to pay nothing and take our chances? After all, in the original position there is a high probability (71.4%) that we will be one of the five workers trapped on the main track, and likewise, isn’t there a high (but unknown) probability that the person at the switch is a Humean consequentialist who will divert the trolley to the side track to save the five lives?