Could someone explain the reasoning behind answer A being the correct choice in Question 4? My analysis was to assume that, since 30 migraines a year is still pretty terrible (for the same reason that the difference in utility between 0 and 1 migraines per year is larger than the difference between 10 and 11), I should treat the question as asking “Which option offers more migraines avoided per unit money?”
And when I did the numbers in my head I thought it was obvious that the answer should be B. What exactly am I missing that led the upper tiers of LWers to select option A?
You’re answering the wrong question. “Which of these fixes more migraines per dollar” is a fast and frugal heuristic, but it doesn’t answer the question of which you should purchase.
(If the first three wheels of your new car cost $10 each, but the fourth cost $100, you’d still want to shell out for the fourth, even though it gives you less wheel per dollar.)
In this case, the question you should be asking is, “is it worth another $250 a year to prevent another 20 migraines?”, which is overwhelmingly worth it at even a lower-class time-money tradeoff rate. (The inability to do anything for several hours costs them more than $12.50 in outcomes- not to mention the agony.)
I think it’s a pretty questionable assumption that the utility difference between 0 and 1 migraines a year is significantly greater than that between 10 and 11. Both are infrequent enough not to be a major disruptor of work, and also infrequent enough that the subject is used to the great majority of their time being non-migraine time.
Headaches avoided per unit money isn’t a very good metric; by that measure, a hypothetical medicine D which prevents one headache per year, and costs a dollar, would be superior to medicines A-C. But medicine D leaves the patient nearly as badly off as they were to start with. A patient satisfied with medicine D would probably be satisfied with no medicine at all.
The metric I used to judge between A and B was to question whether, once the patient has already paid $100 to reduce their number of headaches from 100 to 50, they would still be willing to buy a further reduction of 60 hours of headaches at a rate of about 4.16 dollars per headache-hour. My answer was indeterminate, depending on assumptions about income, but I chose “yes” because I would have to assume very strict money constraints before the difference between A and B stops looking like a good deal.
The costs that get payed per prevented migraine in option B are irrelevant. The value of a prevented migraine isn’t determined by the price that you pay to prevent a migraine.
The difference between option A and option B is that A prevents 20 additional migraines a cost of 250$. This means $12.50 per migraine.
What kind of migraine are we talking about? A duration of 3 hours and involve intense pain, nausea, dizziness, and hyper-sensitivity to bright lights and loud noises.
$4.16 per hour of suffering migraine is lower than minimum wage. Normal minimum wage happens at a time that you can shedule in advance.
You can’t shedule your migraines in advance. They are likely to happen during the times where you have the most stress.
Being occupied with the migraine however isn’t the only thing. Intensive pain also matters. You don’t want people suffering intensive pain without good reason.
Letting someone else suffer intensive pain is morally torture if you are a utilitarian.
There is no right or wrong answer to Decision 1, but if you choose A on Decision 1 then you should also choose A on Decisions 2 & 3 (since A & B are the same options, and C & D are clearly not better options). Similarly, if you choose B on Decision 1, you should choose B on Decisions 2 & 3. So responses to all 3 questions should be the same.
But it turns out that people who get Decision 2 are more likely to choose B than if they’d gotten Decision 1, because the presence of C (which is easily comparable to B, and clearly worse) makes B look better. And people who get Decision 3 are more likely to choose A than if they’d gotten Decision 1, because the presence of D (which is easily comparable to A, and clearly worse) makes A look better. This is called the decoy effect (or the attraction effect, or asymmetric dominance).
The ideal way to test this would be to divide people into three groups, and give each group one of these 3 decisions. But, failing that (with everyone taking the same survey), we can also just give everyone Decision 2 and guess that, if one subset of people is more likely than another to choose B, then they are more susceptible to the decoy effect. (Or, we could just give everyone Decision 3 and guess that, if a subset of people is more likely to choose A, then they are more susceptible to the decoy effect.) It’s not a perfect design, but it is evidence.
(It’s also possible that the difference arose because people were using the reasoning that Nick_Tarleton describes in his comment, in which case the question was tapping into something different than what it was designed to test.)
Look at it on the margin: A costs $250 more than B, and prevents 20 migraines. That could be a good deal.
There’s no reason to look at the ratio for each treatment. Note that doing so would recommend B over A even if A cost 35 cents and B cost 10 cents; that can’t be right.
Could someone explain the reasoning behind answer A being the correct choice in Question 4? My analysis was to assume that, since 30 migraines a year is still pretty terrible (for the same reason that the difference in utility between 0 and 1 migraines per year is larger than the difference between 10 and 11), I should treat the question as asking “Which option offers more migraines avoided per unit money?”
And when I did the numbers in my head I thought it was obvious that the answer should be B. What exactly am I missing that led the upper tiers of LWers to select option A?
You’re answering the wrong question. “Which of these fixes more migraines per dollar” is a fast and frugal heuristic, but it doesn’t answer the question of which you should purchase.
(If the first three wheels of your new car cost $10 each, but the fourth cost $100, you’d still want to shell out for the fourth, even though it gives you less wheel per dollar.)
In this case, the question you should be asking is, “is it worth another $250 a year to prevent another 20 migraines?”, which is overwhelmingly worth it at even a lower-class time-money tradeoff rate. (The inability to do anything for several hours costs them more than $12.50 in outcomes- not to mention the agony.)
I think it’s a pretty questionable assumption that the utility difference between 0 and 1 migraines a year is significantly greater than that between 10 and 11. Both are infrequent enough not to be a major disruptor of work, and also infrequent enough that the subject is used to the great majority of their time being non-migraine time.
Headaches avoided per unit money isn’t a very good metric; by that measure, a hypothetical medicine D which prevents one headache per year, and costs a dollar, would be superior to medicines A-C. But medicine D leaves the patient nearly as badly off as they were to start with. A patient satisfied with medicine D would probably be satisfied with no medicine at all.
The metric I used to judge between A and B was to question whether, once the patient has already paid $100 to reduce their number of headaches from 100 to 50, they would still be willing to buy a further reduction of 60 hours of headaches at a rate of about 4.16 dollars per headache-hour. My answer was indeterminate, depending on assumptions about income, but I chose “yes” because I would have to assume very strict money constraints before the difference between A and B stops looking like a good deal.
The costs that get payed per prevented migraine in option B are irrelevant. The value of a prevented migraine isn’t determined by the price that you pay to prevent a migraine.
The difference between option A and option B is that A prevents 20 additional migraines a cost of 250$. This means $12.50 per migraine. What kind of migraine are we talking about? A duration of 3 hours and involve intense pain, nausea, dizziness, and hyper-sensitivity to bright lights and loud noises.
$4.16 per hour of suffering migraine is lower than minimum wage. Normal minimum wage happens at a time that you can shedule in advance. You can’t shedule your migraines in advance. They are likely to happen during the times where you have the most stress.
Being occupied with the migraine however isn’t the only thing. Intensive pain also matters. You don’t want people suffering intensive pain without good reason. Letting someone else suffer intensive pain is morally torture if you are a utilitarian.
The logic behind the question is that there is no correct answer, but Option B is more likely to be reflective of the decoy effect.
Consider these 3 decisions:
Decision 1: Option A: $350 / 70 migraines avoided Option B: $100 / 50 migraines avoided
Decision 2: Option A: $350 / 70 migraines avoided Option B: $100 / 50 migraines avoided Option C: $100 / 40 migraines avoided
Decision 3: Option A: $350 / 70 migraines avoided Option B: $100 / 50 migraines avoided Option D: $500 / 70 migraines avoided
There is no right or wrong answer to Decision 1, but if you choose A on Decision 1 then you should also choose A on Decisions 2 & 3 (since A & B are the same options, and C & D are clearly not better options). Similarly, if you choose B on Decision 1, you should choose B on Decisions 2 & 3. So responses to all 3 questions should be the same.
But it turns out that people who get Decision 2 are more likely to choose B than if they’d gotten Decision 1, because the presence of C (which is easily comparable to B, and clearly worse) makes B look better. And people who get Decision 3 are more likely to choose A than if they’d gotten Decision 1, because the presence of D (which is easily comparable to A, and clearly worse) makes A look better. This is called the decoy effect (or the attraction effect, or asymmetric dominance).
The ideal way to test this would be to divide people into three groups, and give each group one of these 3 decisions. But, failing that (with everyone taking the same survey), we can also just give everyone Decision 2 and guess that, if one subset of people is more likely than another to choose B, then they are more susceptible to the decoy effect. (Or, we could just give everyone Decision 3 and guess that, if a subset of people is more likely to choose A, then they are more susceptible to the decoy effect.) It’s not a perfect design, but it is evidence.
(It’s also possible that the difference arose because people were using the reasoning that Nick_Tarleton describes in his comment, in which case the question was tapping into something different than what it was designed to test.)
Look at it on the margin: A costs $250 more than B, and prevents 20 migraines. That could be a good deal.
There’s no reason to look at the ratio for each treatment. Note that doing so would recommend B over A even if A cost 35 cents and B cost 10 cents; that can’t be right.