100% agree with the principle that buying peace of mind can be a good deal whether the peace of mind is quantitatively justified or not, and the broader principle that we shouldn’t be disdainful of emotions. But while emotions aren’t entirely rational, they’re not entirely irrational either. I expect that learning and applying the method in this post will help the user feel peace of mind at a level of insurance that’s somewhat closer to optimal than they would have otherwise.
It’s also probably useful to learn the quantiatively optimal strategy so you can be consciously aware of what premium you’re paying for peace of mind, and make thoughtful decisions about how much it’s worth to you. I said that buying peace of mind can be a good deal, but I’ll bet there are people who—if they could see exactly how big the risk-aversion premium they’re paying is—would decide that they’d rather deal with more anxiety and pocket the cash.
I’d go with “I don’t think this conversation is helping us ________” (eg, come up with solutions, figure out what to do next, understand why we really disagree). It opens the door to suggest meta-level changes to how you’re interacting without 1) accusing them, 2) suggesting that they’re the only one who should change, or 3) inviting arguments about their intentions or internal state. It might also help reorient the conversation from a small-scale win/lose frame towards a broader shared goal of accomplishing something. Finally, it allows you to suggest specific changes to make the conversation more truth-seeking while also addressing whatever may be motivating them to not be truth-seeking (eg, fearing that if they “lose” then their needs won’t get met, perceiving you as trying to pull status on them, trying to preserve their image for an external audience).
If you’re having a debate that’s mostly for an external audience, then maybe you should just call out that the liar is lying. If you’re trying to work with them, then it’s probably better to try to figure out what aspect of the conversation is motivating them to lie and trying to incentivise telling the truth instead. If you can’t do that then it doesn’t really matter what’s going on in their head; you’re not going to have a productive conversation anyway.