I picked my example so that the proper influence of the prior would be clear. You are absolutely right that there are many cases where different people with equivalent information have different beliefs. But being faced with complications like this makes correct reasoning more important, and not less.
When you try to sweep the proper influence of the prior under the carpet, people will manipulate their statistics to draw the conclusions that they want. Worse still, if each is using subjective techniques that they believe are objective, the unexamined assumption will lead to them talking past each other.
By contrast with correct reasoning you can show each why they continue to believe what they believe while showing them how the other side is not going to have their opinions changed. In my experience this opens up a bigger possibility of useful dialog and changed opinions.
When you try to sweep the proper influence of the prior under the carpet, people will manipulate their statistics to draw the conclusions that they want. Worse still, if each is using subjective techniques that they believe are objective, the unexamined assumption will lead to them talking past each other.
By contrast with correct reasoning you can show each why they continue to believe what they believe while showing them how the other side is not going to have their opinions changed. In my experience this opens up a bigger possibility of useful dialog and changed opinions.