The dependence of evidence on prior confidence

Whether p is evidence for q will often depend on one’s background beliefs. This is a well-known phenomenon.

But here’s an interesting fact that I hadn’t noticed before: sometimes whether p is evidence for q depends on how confident one is in q.

The example is simple: let p be the proposition that all other reasonable people have confidence level around r in q. If r is significantly bigger than one’s current confidence level, then p tends to be evidence for q. If r is significantly smaller than one’s current confidence level, then p tends to be evidence against q.