They don’t start with the same priors or preferences, but unless they have a good reason to trust their own more than the other person’s, they’d use both.
For example, imagine you were in some treasure hunt. Everyone has a different, imperfect map. This could result in you all looking in different places, but if you stop and think about it (and it’s not a competition) you’ll just share maps. The fact that one map happened to be in your hands doesn’t make it better.
They don’t start with the same priors or preferences, but unless they have a good reason to trust their own more than the other person’s, they’d use both.
For example, imagine you were in some treasure hunt. Everyone has a different, imperfect map. This could result in you all looking in different places, but if you stop and think about it (and it’s not a competition) you’ll just share maps. The fact that one map happened to be in your hands doesn’t make it better.