In the naive model of the self, where "you" make a decision, and then your body executes that decision, and it's the same "you" every time. And it's true that this is a very simple model, and if we didn't have any other evidence, that's what we would probably go with.

But that model that doesn't explain the Peak-end rule very well -- how is it that a certain experience is worse while experienced, but better when remembered? Similarly, it's hard to explain hyperbolic discounting in terms of a continuous self. And how would self-talk be effective (and it is) if the self were indivisible -- whom would you be trying to convince? Finally, how can we make a decision before becoming conscious of it?.

A better mode of the self would say that there's not one thing that you can call your "self" -- instead, your mind is basically bodged together from a bunch of random parts. So when we say that there are different experiencing vs remembering selves, what we're really saying is that reasoning about your preferences as though you only had one set of preferences, doesn't work. At the time, you really prefer to avoid the additional bit of small pain at the end. But when you remember the experience, you really do remember it as being better than you otherwise would. So what do "you" prefer? There's no single sensible answer to that.