Adam, thank you for this. In my work it is always important to remember and apply this principel you outlined that "justice isn’t about broad statistics; it’s about specific evidence. If we were to let baseline probabilities dictate verdicts, we’d risk punishing the likely without evidence – instead of proving who was guilty"
> The Blue Bus paradox is a useful, if counter-intuitive, reminder that justice isn’t about broad statistics; it’s about specific evidence. If we were to let baseline probabilities dictate verdicts, we’d risk punishing the likely without evidence – instead of proving who was guilty.
This is a very handwavy and unsatisfactory resolution to the 'paradox'. Surely someone is almost as guilty if one has 50.0% probability they are guilty as if one has 50.1%. And if we imagine enough alternative ways, how would we ever get to the magic 50.1%? And what if a group of actors collaborate to diffuse uncertainty so you know with 100% confidence that one of them did it, but there's 3 or 4 of them and so you never get to the mystical 50.1%? Or what if it's some extremely bad outcome, or global? Think about the implications of this doctrine for, say, lead pollution or global warming.
Law & Economics provides a much more satisfactory answer: you should not punish simply based on priors like base rates because they are not incentive-compatible. If you punish a company for all the sins of blue buses simply because they own the majority, you incentivize them to not care about safety ('don't worry about running over pedestrians, we get sued either way'), you incentivize them to engage in wasteful and harmful actions like repainting buses arbitrary colors to try to diffuse responsibility, and you incentivize plaintiffs to be ignorant or lie in order to go after convenient targets. ('Gosh officer, I just didn't see the license plates on that blue bus. It must've been the big rich blue bus company which will be worried about PR, not the scandal-ridden little one in bankruptcy. Guess I'll have to sue the first one for damages, since it was probably them.') But if you require evidence, then the bus company has good reason to invest in safety (because they will be sued when they are unsafe, and not when other bus companies are unsafe), and the required level of proof calibrated to who can reduce harms how much and so on and so forth.
Of course, the parallel problem exists in considering all possible explanations of a phenomenon. If we ignore relative plausibility, then there will be an infinite number of explanations and everything becomes intractably uncertain.
This points to the underlying necessity of a priori theory and standards of credibility for evaluating theory. Ultimately, this is the problem Carnap struggled to solve.
All collection of evidence is based on a priori theory as is all experimental design. In that sense, the Blue Bus problem is a bit misleading. It restricts our ex ante information to a set of facts too small to achieve an adequate level of confidence.
Ideas like "beyond reasonable doubt" that typically rely on very fallible human opinion become the substitute. This is as true of journal reviewing as it is of courtroom argument. In the end, truth is decided by judges, juries, and academic reviewers.
So in this case, blue bus service should be liable for 75% and the others for a collective 25%.
This seems silly for a lawsuit decided in court, where we expect a binary up or down verdict. But it is more applicable for broad cases like insurance or liability for a polluted body of water where cost can be statistically and proportionately allocated.
At the risk of unintentionally offending anyone (no intent, really) I wonder whether this example might be linked to the matter of looking at a process result and determining it's flaws (real or imagined). For example, looking at racial or gender population distribution in universities or corporate positions and determine that it proves a racial or gender bias.
Adam, thank you for this. In my work it is always important to remember and apply this principel you outlined that "justice isn’t about broad statistics; it’s about specific evidence. If we were to let baseline probabilities dictate verdicts, we’d risk punishing the likely without evidence – instead of proving who was guilty"
> The Blue Bus paradox is a useful, if counter-intuitive, reminder that justice isn’t about broad statistics; it’s about specific evidence. If we were to let baseline probabilities dictate verdicts, we’d risk punishing the likely without evidence – instead of proving who was guilty.
This is a very handwavy and unsatisfactory resolution to the 'paradox'. Surely someone is almost as guilty if one has 50.0% probability they are guilty as if one has 50.1%. And if we imagine enough alternative ways, how would we ever get to the magic 50.1%? And what if a group of actors collaborate to diffuse uncertainty so you know with 100% confidence that one of them did it, but there's 3 or 4 of them and so you never get to the mystical 50.1%? Or what if it's some extremely bad outcome, or global? Think about the implications of this doctrine for, say, lead pollution or global warming.
Law & Economics provides a much more satisfactory answer: you should not punish simply based on priors like base rates because they are not incentive-compatible. If you punish a company for all the sins of blue buses simply because they own the majority, you incentivize them to not care about safety ('don't worry about running over pedestrians, we get sued either way'), you incentivize them to engage in wasteful and harmful actions like repainting buses arbitrary colors to try to diffuse responsibility, and you incentivize plaintiffs to be ignorant or lie in order to go after convenient targets. ('Gosh officer, I just didn't see the license plates on that blue bus. It must've been the big rich blue bus company which will be worried about PR, not the scandal-ridden little one in bankruptcy. Guess I'll have to sue the first one for damages, since it was probably them.') But if you require evidence, then the bus company has good reason to invest in safety (because they will be sued when they are unsafe, and not when other bus companies are unsafe), and the required level of proof calibrated to who can reduce harms how much and so on and so forth.
Of course, the parallel problem exists in considering all possible explanations of a phenomenon. If we ignore relative plausibility, then there will be an infinite number of explanations and everything becomes intractably uncertain.
This points to the underlying necessity of a priori theory and standards of credibility for evaluating theory. Ultimately, this is the problem Carnap struggled to solve.
All collection of evidence is based on a priori theory as is all experimental design. In that sense, the Blue Bus problem is a bit misleading. It restricts our ex ante information to a set of facts too small to achieve an adequate level of confidence.
Ideas like "beyond reasonable doubt" that typically rely on very fallible human opinion become the substitute. This is as true of journal reviewing as it is of courtroom argument. In the end, truth is decided by judges, juries, and academic reviewers.
Another way of saying it: "preponderance of the evidence" does not equate to "preponderance of the probabilities".
So in this case, blue bus service should be liable for 75% and the others for a collective 25%.
This seems silly for a lawsuit decided in court, where we expect a binary up or down verdict. But it is more applicable for broad cases like insurance or liability for a polluted body of water where cost can be statistically and proportionately allocated.
At the risk of unintentionally offending anyone (no intent, really) I wonder whether this example might be linked to the matter of looking at a process result and determining it's flaws (real or imagined). For example, looking at racial or gender population distribution in universities or corporate positions and determine that it proves a racial or gender bias.
Ian I think Adam mentioned that there was only 449 paid hence 501 didnot pay.