The Lindley paradox can teach us some deep lessons about the conduction of our everyday business: one cannot (and in fact should not!) expect to win over an argument when one is confronting a person with much stronger convictions, even if that person is wrong!! Furthermore when we witness such an encounter, one cannot (and in fact should not!) always attribute this outcome to other reasons e.g. deference to authority, lack of determination or even outright bullying. Even in the absence of these factors a rational exchange between two individuals of widely different convictions would lead to the one with the stronger ones coming out of the debate a winner. This is not particularly troublesome if the person is right, but it turns out to be problematic when that person is outright wrong.
So what can one do to avoid the paradox in everyday life? First of all, one should try and sharpen one’s opinions before encounters (meetings, clinical rounds or business planning sessions) so that the person with strong conviction will not be met by a person who is diffusely indecisive. Secondly, one should try to gauge the range of other people’s beliefs and degrees of conviction likely to encounter and given them an unbiased consideration; if none of them appears to be right then one should try and have each party bring out the incompatibility of the experience/data with their strong conviction during the conversation. In this monologue within the dialogue one tries to recapitulate Sherlock Holmes’s modus operandi:
“… when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”
In other words, one should give people a chance to see how untenable their position is instead of trying to explore a number of far-fetched possibilities.
These two strategies is just common sense advice that one may have heard during one’s formative and/or professional years: be focused, try to think about the problem, if unsure try and explore others positions without being exposed. Interestingly enough they correspond to mathematical insights by academic statisticians working to understand the Lindley paradox confirming once again the role of Probability as Logic!