theoretically, you might both even have exactly the same evidence, but gathered in a different order. The question is one of differing interpretations, not raw data as such.

I happen to be studying conflicts in a completely different domain, in which I claim the solution is to ensure the events shape identical result no matter in which order they are applied. I briefly wondered whether my result could be useful in other domains, and I thought of lesswrong: perhaps we should advocate update strategies which don't depend on the order in which the evidence is encountered.

And then your post came up! Nice timing.