Indeed it is weird to theorize why somebody should switch if they trusted the process to be random. There's no reason to. And if I'm not sure about the process, indeed I may want to stick with my choice. I was wondering how a study would control for this. One could make a group where the price was shared with the person doing the shuffling. If people in that group were more inclined to switch, it would indicate that they don't trust the process to be random.