So, when I pester them for a rational reason, why do they keep giving an answer that is irrational for this situation?
Because human beings often first have a reaction based on an evolved, unconscious heuristic, and only later form a conscious rationalization about it, which can end up looking irrational if you ask the right questions (e.g. the standard reactions to the incest thought experiment there). So, yes, they were probably unaware of the heuristic they were actually using.
I'd suppose that the heuristic is along the lines of the following: Say there's an agreed-upon fair procedure for deciding who gets something, and then someone changes that procedure, and someone other than you ends up benefiting. Then it's unfair, and what's yours has probably been taken.
Given that rigorous probability theory didn't emerge until the later stages of human civilization, there's not much room for an additional heuristic saying "unless it doesn't change the odds" to have evolved; indeed, all of the agreed-upon random ways of selecting things (that I've ever heard of) work by obvious symmetry of chances rather than by abstract equality of odds†, and most of the times someone intentionally changed the process, they were probably in fact hoping to cheat the odds.
† Thought experiment: we have to decide a binary disagreement by chance, and instead of flipping a coin or playing Rock-Paper-Scissors, I suggest we do the following: First, you roll a 6-sided die, and if it's a 1 or 2 you win. Otherwise, I roll a 12-sided die, and if it's 1 through 9 I win, and if it's 10 through 12 you win.
Now compute the odds (50-50, unless I made a dumb mistake), and then actually try it (in real life) with non-negligible stakes. I predict that you'll feel slightly more uneasy about the experience than you would be flipping a coin.
I'd suppose that the heuristic is along the lines of the following: Say there's an agreed-upon fair procedure for deciding who gets something, and then someone changes that procedure, and someone other than you ends up benefiting. Then it's unfair, and what's yours has probably been taken.
Everything else you've said makes sense, but I think the heuristic here is way off. Firstly, they object before the results have been produced, so the benefit is unknown. Second, the assumption of an agreed upon procedure is only really valid in the poker example. Othe...
We've had these for a year, I'm sure we all know what to do by now.
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