Ah, I see. To draw an analogy: if you boil water, there is not a big upward jump in temperature at the point where the water turns to steam. Likewise here: the prison population is like temperature. I would not particularly expect a large upward jump in the population, right around the time of the phase change.
If there were a large upward jump in population during some time, then that would be a more-than-usually-likely time to cross phase-change thresholds, just as a large jump in temperature is likely to cross phase-change thresholds. But the converse does not apply: a phase change can occur even when the underlying parameter is changing slowly. So while this is Bayesian evidence against the model on net, it is quite weak.
(I do think the big jump in prison population in the 80′s is indicative of a phase change in a different system somewhere upstream of imprisonment, but I think that’s largely a separate phenomenon from that discussed in the post. Continuing the analogy: if we see a sharp jump in temperature, that’s probably indicative of something sharply changing in the system, but not necessarily water boiling.)
Anyway, I did just go back and re-check the relevant chapter of Legal Systems Very Different From Ours, and I do think my summary was wrong on the timeline: it says that there has been a dramatic increase in gangs and gang members “since the 60′s”, with the “Code era” covering roughly the first half of the twentieth century. So I will definitely edit that. Thanks again for the check!
(Note that the timeline from the book is a bit more consistent with what you expected, though I still maintain that we shouldn’t put particularly high prior on a big population jump around the time of the phase change. Weak evidence, either way.)
Ah, I see. To draw an analogy: if you boil water, there is not a big upward jump in temperature at the point where the water turns to steam. Likewise here: the prison population is like temperature. I would not particularly expect a large upward jump in the population, right around the time of the phase change.
If there were a large upward jump in population during some time, then that would be a more-than-usually-likely time to cross phase-change thresholds, just as a large jump in temperature is likely to cross phase-change thresholds. But the converse does not apply: a phase change can occur even when the underlying parameter is changing slowly. So while this is Bayesian evidence against the model on net, it is quite weak.
(I do think the big jump in prison population in the 80′s is indicative of a phase change in a different system somewhere upstream of imprisonment, but I think that’s largely a separate phenomenon from that discussed in the post. Continuing the analogy: if we see a sharp jump in temperature, that’s probably indicative of something sharply changing in the system, but not necessarily water boiling.)
Anyway, I did just go back and re-check the relevant chapter of Legal Systems Very Different From Ours, and I do think my summary was wrong on the timeline: it says that there has been a dramatic increase in gangs and gang members “since the 60′s”, with the “Code era” covering roughly the first half of the twentieth century. So I will definitely edit that. Thanks again for the check!
(Note that the timeline from the book is a bit more consistent with what you expected, though I still maintain that we shouldn’t put particularly high prior on a big population jump around the time of the phase change. Weak evidence, either way.)