Preferential gaps, by contrast, are insensitive to some sweetenings and sourings. Consider another example. A is a lottery that gives the agent a Fabergé egg for sure. B is a lottery that returns to the agent their long-lost wedding album. The agent does not strictly prefer A to B and does not strictly prefer B to A. How do we determine whether the agent is indifferent or whether they have a preferential gap? Again, we sweeten one of the lotteries. A+ is a lottery that gives the agent a Fabergé egg plus a dollar-bill for sure. In this case, the agent might not strictly prefer A+ to B. That extra dollar-bill might not suffice to break the tie. If that is so, the agent has a preferential gap between A and B. If the agent has a preferential gap, then slightly souring A to get A- might also fail to break the tie, as might slightly sweetening and souring B to get B+ and B- respectively.
This seems obviously wrong. The reason that adding 1 dollar doesn’t make choosing between a Faberge egg and and a lost wedding album easier is because of ambiguity: The utility you’d gain from those 2 options is really hard to precisely predict, so the margin of error is large enough that giving 1 extra dollar doesn’t matter. Like it technically matters a little, but so little that our brains would have a hard time distinguishing the difference from 0.
In contrast money doesn’t work like this because people can easily see that 1,000,001 dollars is more than 1,000,000: Even though it might be very hard to distinguish the utility you subjectively get from both.
Thus I’d argue that if you had perfect information and were still indifferent between a Faberge egg and a lost wedding album; then 1$ would actually be enough to flip your decision in one direction.
So I just don’t see any coherent way in which preference gaps and indifference gaps are meaningfully distinct.
Yeah so you might think ‘Given perfect information, no agent would have a preferential gap between any two options.’ But this is quite a strong claim! And there are other plausible examples of preferential gaps even in the presence of perfect information, e.g. very different ice cream flavors:
Consider a trio of ice cream flavors: buttery and luxurious pistachio, bright and refreshing mint, and that same mint flavor further enlivened by chocolate chips. You might lack a preference between pistachio and mint, lack a preference between pistachio and mint choc chip, and yet prefer mint choc chip to mint.
Note also that if we adopt a behavioral definition of preference, the existence of preferential gaps is pretty much undeniable. On other definitions, their existence is deniable but still very plausible.
This seems obviously wrong. The reason that adding 1 dollar doesn’t make choosing between a Faberge egg and and a lost wedding album easier is because of ambiguity: The utility you’d gain from those 2 options is really hard to precisely predict, so the margin of error is large enough that giving 1 extra dollar doesn’t matter. Like it technically matters a little, but so little that our brains would have a hard time distinguishing the difference from 0.
In contrast money doesn’t work like this because people can easily see that 1,000,001 dollars is more than 1,000,000: Even though it might be very hard to distinguish the utility you subjectively get from both.
Thus I’d argue that if you had perfect information and were still indifferent between a Faberge egg and a lost wedding album; then 1$ would actually be enough to flip your decision in one direction.
So I just don’t see any coherent way in which preference gaps and indifference gaps are meaningfully distinct.
Yeah so you might think ‘Given perfect information, no agent would have a preferential gap between any two options.’ But this is quite a strong claim! And there are other plausible examples of preferential gaps even in the presence of perfect information, e.g. very different ice cream flavors:
Note also that if we adopt a behavioral definition of preference, the existence of preferential gaps is pretty much undeniable. On other definitions, their existence is deniable but still very plausible.