Suppose someone — who, for reasons that will become apparent, Quinn calls the self-torturer — has a special electric device attached to him. The device has 1001 settings: 0, 1, 2, 3, …, 1000 and works as follows: moving up a setting raises, by a tiny increment, the amount of electric current applied to the self-torturer's body. The increments in current are so small that the self-torturer cannot tell the difference between adjacent settings. He can, however, tell the difference between settings that are far apart. And, in fact, there are settings at which the self-torturer would experience excruciating pain. Once a week, the self-torturer can compare all the different settings. He must then go back to the setting he was at and decide if he wants to move up a setting. If he does so, he gets $10,000, but he can never permanently return to a lower setting. Like most of us, the self-torturer would like to increase his fortune but also cares about feeling well. Since the self-torturer cannot feel any difference in comfort between adjacent settings but gets $10,000 at each advance, he prefers, for any two consecutive settings s and s+1, stopping at s+1 to stopping at s. But, since he does not want to live in excruciating pain, even for a great fortune, he also prefers stopping at a low setting, such as 0, over stopping at a high setting, such as 1000.
This is generally framed as a puzzle for rational choice: what setting should the self-torturer rationally select? But I think it is illuminating to first consider the question of objective value: which outcome would in fact be best for the agent?
The described scenario is one in which indiscriminability is intransitive. This implies that indiscriminability is not sufficient to establish phenomenal identity (since identity must be transitive). It cannot be that setting 0 feels the same as 1 which is the same as 2 ... 1000, if setting 0 does not feel the same as 1000. So it may well be that setting 1 is actually more painful than 0, and to that extent worse for the agent to experience, even if he cannot tell that this is so.
So, supposing that pain and wealth are perfectly commensurable, there will be some setting s that is objectively best for the agent -- i.e., representing the ideal tradeoff between pain and wealth -- even though superficial introspection would lead the agent to consider s+1 a better option (offering more wealth and seemingly no more pain). So far so good: there's nothing particularly puzzling about the idea that non-omniscient agents may fail to recognize the best option.
But once we've secured the result that there is some fact of the matter as to which stopping point would be best, this also dissolves the 'puzzle' about rational choice. It is just like any other case of decision-making under uncertainty. The agent shouldn't determinately prefer each s+1 to the previous s, since he knows that at some point along the way there will be an s that is the optimal choice, even though the next s+1 will superficially seem like a better option to him.
In short: the puzzle is dissolved by recognizing that the agent shouldn't take pairwise indiscriminability to necessarily show that two experiences are phenomenally just as good. The puzzle arises because we're tempted to think that if you can't distinguish two experiences then they must feel the same way. But if one's ability to distinguish between experiences isn't transitive, then the tempting principle must be false. (The temptation is amplified by the ambiguity of 'seeming'. We might say that two experiences 'seem' the same when (i) the agent judges them alike, i.e. cannot tell them apart, or (ii) when they are phenomenally identical, i.e. have the same phenomenal feel. These two criteria come apart in the case under consideration!)
* My thoughts here arose in the course of class discussion, and are especially indebted to John Hawthorne.