The relevant comparison will be between the likelihood of arrest and trial for an innocent person of group X and a guilty person of group X, not between the rates of likelihood of conviction for random individuals of group X and Y, respectively.
In the Sally Clark case, prior probabilities are derived from statistics relating to the incidence of SIDS in the general population, in comparison to infant murder. Let us imagine that there were different statistics for group X mothers/babies and group Y mothers/babies. It might then be the case that the incidence of SIDS was lower, and murder higher, in group X than group Y. Therefore, a group Y mother with two dead infants and indecisive evidence from the alleged crime scenes might perhaps be acquitted (e.g. probability of guilt 40%) whereas the group X mother in exactly the same situation is convicted (e.g. probability of guilt 90%).
What we are questioning in this case is whether mothers are more likely to murder their babies twice, or have their babies die innocently twice for no apparent medical reason. But we are using statistics recording the incidence of one infant dying from “SIDS” or one infant being murdered. So we are legitimately using statistics about the likelihood of a random mother in either group either murdering her infant or having it die from SIDS, in a case of double infant murder or double SIDS.
This is one example in which what you implied is untrue; we have good reason to use statistics in our prior relating to the general population rather than people in court accused of this particular offence (since mothers with one SIDS infant death are not necessarily suspected of murder and arrested) and one example is enough to prove the point that use of Bayesian priors in court may have the unfortunate consequence of allowing differential convinction rates purely based on sex, ethicity or social group membership.
But in any case, even if the relevant comparison is “the likelihood of arrest and trial for an innocent person of group X and a guilty person of group X”, there is no particular reason why this should be the same across all possible groups. Therefore this (social and political) problem is likely to emerge in all sorts of criminal cases, if Bayesian priors were to become more widely used in court.
How would you describe how an ideal jury should perform its task?
That’s far too broad a question to expect someone to answer in a comment thread. All I’m saying is that, even setting aside the issue of ethicity/sex discrimination, the idea of convicting someone primarily on a statistical basis makes me uncomfortable and does not resonate with my values of fairness. I also believe that most other people would feel the same way (for example the judge in the Sally Clark case evidently agrees).
Since we try and punish criminals purely for our own reasons—not because the God of criminal cases wants us to—there’s no reason why we have to convict based on totally unbiased Bayesian calculations of guilt. If we feel that this conflicts with our other values (apart from the desire to see guilty people punished, and prevent future crimes by them), then perhaps there should be other considerations informing verdicts in criminal trials. And there might well be pragmatic reasons not to do so in any case, since the way in which the criminal justice system works in a country is not causally isolated from the behaviour of its citizens. If people think that the courts are evil, this probably isn’t going to improve any man’s quality of life even if he likes the idea of convicting based primarily on Bayesian priors.
I don’t think there’s an easy answer to this conundrum—but I’m arguing that it is a conundrum that cannot be dismissed with a wave of the hand.
In the Sally Clark case, prior probabilities are derived from statistics relating to the incidence of SIDS in the general population, in comparison to infant murder. Let us imagine that there were different statistics for group X mothers/babies and group Y mothers/babies. It might then be the case that the incidence of SIDS was lower, and murder higher, in group X than group Y. Therefore, a group Y mother with two dead infants and indecisive evidence from the alleged crime scenes might perhaps be acquitted (e.g. probability of guilt 40%) whereas the group X mother in exactly the same situation is convicted (e.g. probability of guilt 90%).
What we are questioning in this case is whether mothers are more likely to murder their babies twice, or have their babies die innocently twice for no apparent medical reason. But we are using statistics recording the incidence of one infant dying from “SIDS” or one infant being murdered. So we are legitimately using statistics about the likelihood of a random mother in either group either murdering her infant or having it die from SIDS, in a case of double infant murder or double SIDS.
This is one example in which what you implied is untrue; we have good reason to use statistics in our prior relating to the general population rather than people in court accused of this particular offence (since mothers with one SIDS infant death are not necessarily suspected of murder and arrested) and one example is enough to prove the point that use of Bayesian priors in court may have the unfortunate consequence of allowing differential convinction rates purely based on sex, ethicity or social group membership.
But in any case, even if the relevant comparison is “the likelihood of arrest and trial for an innocent person of group X and a guilty person of group X”, there is no particular reason why this should be the same across all possible groups. Therefore this (social and political) problem is likely to emerge in all sorts of criminal cases, if Bayesian priors were to become more widely used in court.
That’s far too broad a question to expect someone to answer in a comment thread. All I’m saying is that, even setting aside the issue of ethicity/sex discrimination, the idea of convicting someone primarily on a statistical basis makes me uncomfortable and does not resonate with my values of fairness. I also believe that most other people would feel the same way (for example the judge in the Sally Clark case evidently agrees).
Since we try and punish criminals purely for our own reasons—not because the God of criminal cases wants us to—there’s no reason why we have to convict based on totally unbiased Bayesian calculations of guilt. If we feel that this conflicts with our other values (apart from the desire to see guilty people punished, and prevent future crimes by them), then perhaps there should be other considerations informing verdicts in criminal trials. And there might well be pragmatic reasons not to do so in any case, since the way in which the criminal justice system works in a country is not causally isolated from the behaviour of its citizens. If people think that the courts are evil, this probably isn’t going to improve any man’s quality of life even if he likes the idea of convicting based primarily on Bayesian priors.
I don’t think there’s an easy answer to this conundrum—but I’m arguing that it is a conundrum that cannot be dismissed with a wave of the hand.