Unfortunately, Bayesian probability theory doesn’t exactly tell us how to remedy the situation; in that way it fails Demski’s criterion that a theory of rationality is meant to provide advice about how to be more rational.
This isn’t a complete answer to how best to deal with incoherent beliefs, but it’s perhaps the start of one—and you can still tell your incoherent friends to use Bayes’ rule to become more coherent!
I read the paper, but it seems the slides go into much more depth on increasing coherence via Bayes rule. It appears that coherence can be increased by redistributing “unused” probability mass in an appropriate way, and a Bayes-like update is one possible method?
There is some work on this. In “Measures of incoherence: How not to Gamble If You Must,” Schervish, Seidenfeld, and Kadane (2002) provide a measure of incoherence and show that, for an incoherent agent, updating via Bayes will reduce their incoherence.
This isn’t a complete answer to how best to deal with incoherent beliefs, but it’s perhaps the start of one—and you can still tell your incoherent friends to use Bayes’ rule to become more coherent!
Very interesting! I have been enjoying reading up on Seidenfeld’s work.
I read the paper, but it seems the slides go into much more depth on increasing coherence via Bayes rule. It appears that coherence can be increased by redistributing “unused” probability mass in an appropriate way, and a Bayes-like update is one possible method?