What would you have to be shown, or what evidence would it take for you to change your position on this rule?
A: Examples of a better way to phrase the question.
A: That for some category or type of person the question won't make sense, in which case it's better to ask a different question--or perhaps not to engage in conversation.
You might start by asking for what evidence--experience, observations, or stories--have framed their approach before asking for them to speculate about new evidence that would cause them to change their decision.
I have used your approach and found it effective in dealing with managers: is there any new data or information we could gather that would affect your decision? If the answer is "no" then you know that you are dealing with a political situation (small "p" as in organizational politics) not a problem solving one.
A lot of the time people don't have a good response to the second question because they have never actually even considered the possibility that they could ever hold the opposing view on something, or what holding that view would entail.
That said, swearing by a particular "course of action" and thinking it superior to other approaches is a "value" in my opinion.
My apologies if I imputed motives in your question that were not there.
I am curious: what would you do if you were facing a high stakes situation where another person's decision was going to have a material impact on your life? How would you go about trying to change their decision?
Regarding your question: Depends on how much impact on my life it would have, and what exactly the decision is. I have no prepared strategies to change people's minds apart from presenting reasonable arguments and maybe slightly bullshitting my way through it at times. There was never a need for more than that.
In the extreme the response would be lies and even violence, if nothing else works, I suppose. Again, it depends on what the situation and "material impact" on my life is.