I think there is a potential third reason, which is that the question to switch cups may be perceived as a trick of the experimenter: you feel certain that you got it and know which cup is right, and since you assume that the experimenter is aware of this as well, they now try to lure you into switching just to save their skin. Refusing to switch is basically done in the spirit of trying to evade this alleged trap, and the experimenter’s question may further emphasise that your initial guess was correct.
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> [...] So why not switch? Experimenters point to two reasons. First is the endowment effect [...]. The second reason is [...] to minimize regret.
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I agree completely. It doesn't even require you to believe you have the right answer, or that the experimenter knows this. All it has to be is some niggling feeling that there is some trickery going on here. Something along the lines of, "why are they contriving to make me choose and then immediately trying to 'make me' change my decision with no other information or incentives offered?" Then, in the next iterations when more money is offered, the suspicion changes to, "why are they trying to make me change my decision by offering me more money?"
If, as the researchers propose, people experience more regret by changing their decision with "no additional information," they will experience significantly more regret still if they feel as though they have been tricked into giving up on their instinctive choice.
I put no information in quotes because even though the article puts it this way, there actually is some additional information: that the researchers want participants to have the option to change their choice, but only to be aware of that after making their first choice. Although cryptic, this does give some additional information into the real nature of their experiment, and to a random study participant certainly could be suggestive of some trickery going on.