it is unhelpful to “critique” the theory by insisting that some other mechanism that also has the same effect must account for all of the effect.
This is a very common conversation in science. Some of it is conducted improperly, which is annoying, but I would hardly categorize the whole thing as unhelpful. In particular, the “improper” critiques usually consist of hypothesizing more and more elaborate hidden mechanisms with no evidence to support them as alternatives.
But we know hyperbolic discounting exists. We know that people are insensitive to the smallness of small probabilities.
When the other mechanism is nailed down by other evidence (hyperbolic discounting (for crack), or neglect of the tinyness of tiny odds (for lottery tickets)) and the new mechanism is not known, then A->B, C->B, C steals the evidence that C provides for A. You need to provide new D with A->D, C!->B. Where the implication from C to B is imperfect then B goes on providing some trickle of evidence to A but if the implications are equally strong then the trickle does not distinguish between A and C as opposed to other hypotheses and the prior odds win out.
In particular, the notion that ticket buyers really are making an expected utility calculation says that decreasing the odds of a lottery win by a factor of 10 (while perhaps multiplying the number of tickets sold by 10 and keeping the price constant, so that the number of lottery winners reported in the media is constant), will decrease the price they are willing to pay for a given lottery ticket by a factor of 10. Are you willing to make that prediction? I’d expect ticket sales to remain pretty much the same.
If lottery tickets were bought after paying off debts and after loss of government benefits, no one who was in debt, or who was receiving government benefits, could buy lottery tickets. Unless I misunderstand.
A->B, C->B, C steals the evidence that C provides for A. You need to provide new D with A->D, C!->B. Where the implication from C to B is imperfect then B goes on providing some trickle of evidence to A but if the implications are equally strong then the trickle does not distinguish between A and C as opposed to other hypotheses and the prior odds win out.
I tried to explain in my previous comment why I think this is the wrong way of looking at it. You’re speaking as if B is a proposition with a truth-value that has a single cause. However, I think my explanation was not quite right either.
The weakest, most obviously true reply is that this is not a Boolean net; B does not have a single cause; and A ⇒ B and C ⇒ B can both be having an effect. It’s even possible, in the real-valued non-Boolean world, to have (remember this is not Boolean; this is more like a metabolic network) A > 0, C > 0, A ⇒ B, C ⇒ B, B < 0.
A reply that is a little stronger ( = has more consequences), and a little less clearly correct, is that your argument for C ⇒ B is not as good as my argument for A ⇒ B, so who’s stealing whose evidence?
The strongest, least-clear reply is that we have priors in favor of both A ⇒ B and C ⇒ B. Because they’re both just-so stories, and we have no quantitative expectations of how much of an increase in B either would provide; and, unlike when B is a truth-value, there’s no upper limit on how large B can get; A or C can’t steal much evidence from each other without some quantitative prediction. All the info you have is that A and C would both make B > 0, and B > 0. If C accounts for x points of B, and B = x + y, then this knowledge can increase the probability of A. C, C ⇒ B diminishes the probability of A in the absence of knowledge about the value of B and the value of B explained by C, but by so little compared to the priors, that presenting it as an argument against an argument from principles is misleading.
In particular, the notion that ticket buyers really are making an expected utility calculation says that decreasing the odds of a lottery win by a factor of 10 (while perhaps multiplying the number of tickets sold by 10 and keeping the price constant, so that the number of lottery winners reported in the media is constant), will decrease the price they are willing to pay for a given lottery ticket by a factor of 10. Are you willing to make that prediction? I’d expect ticket sales to remain pretty much the same.
That’s an interesting point.
If, as I said in my post, it is possible for all situations in which utility < 0 to be considered equivalent because one can commit suicide, then you would predict that ticket sales would remain nearly the same.
I don’t claim that they are all making a good utility calculation. But who does? I claim that more of their behavior is attributable to utility calculations than is commonly believed.
Please amplify on “#1 is wrong”.
This is a very common conversation in science. Some of it is conducted improperly, which is annoying, but I would hardly categorize the whole thing as unhelpful. In particular, the “improper” critiques usually consist of hypothesizing more and more elaborate hidden mechanisms with no evidence to support them as alternatives.
But we know hyperbolic discounting exists. We know that people are insensitive to the smallness of small probabilities.
When the other mechanism is nailed down by other evidence (hyperbolic discounting (for crack), or neglect of the tinyness of tiny odds (for lottery tickets)) and the new mechanism is not known, then A->B, C->B, C steals the evidence that C provides for A. You need to provide new D with A->D, C!->B. Where the implication from C to B is imperfect then B goes on providing some trickle of evidence to A but if the implications are equally strong then the trickle does not distinguish between A and C as opposed to other hypotheses and the prior odds win out.
In particular, the notion that ticket buyers really are making an expected utility calculation says that decreasing the odds of a lottery win by a factor of 10 (while perhaps multiplying the number of tickets sold by 10 and keeping the price constant, so that the number of lottery winners reported in the media is constant), will decrease the price they are willing to pay for a given lottery ticket by a factor of 10. Are you willing to make that prediction? I’d expect ticket sales to remain pretty much the same.
If lottery tickets were bought after paying off debts and after loss of government benefits, no one who was in debt, or who was receiving government benefits, could buy lottery tickets. Unless I misunderstand.
I tried to explain in my previous comment why I think this is the wrong way of looking at it. You’re speaking as if B is a proposition with a truth-value that has a single cause. However, I think my explanation was not quite right either.
The weakest, most obviously true reply is that this is not a Boolean net; B does not have a single cause; and A ⇒ B and C ⇒ B can both be having an effect. It’s even possible, in the real-valued non-Boolean world, to have (remember this is not Boolean; this is more like a metabolic network) A > 0, C > 0, A ⇒ B, C ⇒ B, B < 0.
A reply that is a little stronger ( = has more consequences), and a little less clearly correct, is that your argument for C ⇒ B is not as good as my argument for A ⇒ B, so who’s stealing whose evidence?
The strongest, least-clear reply is that we have priors in favor of both A ⇒ B and C ⇒ B. Because they’re both just-so stories, and we have no quantitative expectations of how much of an increase in B either would provide; and, unlike when B is a truth-value, there’s no upper limit on how large B can get; A or C can’t steal much evidence from each other without some quantitative prediction. All the info you have is that A and C would both make B > 0, and B > 0. If C accounts for x points of B, and B = x + y, then this knowledge can increase the probability of A. C, C ⇒ B diminishes the probability of A in the absence of knowledge about the value of B and the value of B explained by C, but by so little compared to the priors, that presenting it as an argument against an argument from principles is misleading.
That’s an interesting point.
If, as I said in my post, it is possible for all situations in which utility < 0 to be considered equivalent because one can commit suicide, then you would predict that ticket sales would remain nearly the same.
I don’t claim that they are all making a good utility calculation. But who does? I claim that more of their behavior is attributable to utility calculations than is commonly believed.
On this theory the “rational poor” should not spend money on anything except lottery tickets, then commit suicide.