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The discussion on the impact on false positive / false negatives would be more fair if you also discussed the negative impacts implementing bayesian punishment would have. For example, if you start giving small punishments for crimes with low credence of guilt, that would not be punished in the current system, this will add its lot of false positive.
I would not be confident it would be a good idea to implement this in our current justice systems. It may have a negative impact on people's faith in justice (is it deserved ? yeah ! is it good ? not sure) and my view of the justice system is that it's an essential part of society which is quite fragile as it relies in part on the lie that the justice system is fair and that it's decision is the truth. Plus, more generally, I don't think judges would handle the credences correctly, it's quite a difficult task to transform an heteregoneous and large set of proofs, among which testimonials, into a credence.
Thanks for the post ! I have tried doing EMDR by myself following these instructions after struggling to find a reliable EMDR therapist and it's definitely a new addendum to my therapeutic toolbox. It's great to process difficult events that happened in the past and the subsequent feelings.
In the link you refer to, there is a phase at the beginning where the therapist teaches self-care techniques to handle strong emotions (or they ensure that the patient already has such tools). This was lost in your post and I think it is important in order to avoid retraumatization and bad experiences. I felt confident trying the technique because I know how to soothe myself if needed and be present with my feelings, but I am pretty sure it would have been a scary or even maybe a painful experience otherwise.