1) Lottery tickets are bought using income that is after tax, after debt, and after loss of government benefits.
2) Many people buy more than one lottery ticket; they spend hundreds of dollars per year or more.
3) There was a period during which poor folks had reason to legitimately distrust banks and played the illegal numbers game as a sort of stochastic savings mechanism, up to 600-to-1 payouts on 1000-to-1 odds, which meant they did get large units of cash occasionally. Post-FDIC this is no longer a realistic motive and the odds on the government lotteries are worse.
4) Yes, your life can suck, yes, the lottery can seem like the only way out. But this is not a reasoned decision based on having literally no better life-improving use for hundreds of after-tax dollars. It is based on the lure and temptation of easy money to a mind that can’t multiply.
5) Those who buy tickets will not win the lottery. If you think the chance is worth talking about, you’ve fallen prey to the fallacy yourself. In ordinary conversation odds of one in a hundred million of being wrong would correspond to a Godlike level of calibrated confidence. Therefore I say simply, “You WILL NOT win the lottery!” with far more confidence than I say that the Sun will rise tomorrow (since something could always… happen… overnight). On a statistical basis, before selective reporting, lottery winners are nonexistent—you would never encounter one if you lived in the ancestral environment and had no newspapers. The lottery is simply a lie.
Point #1 is wrong. Point #2 is consistent with my idea. Point #4 is not a point, but a conclusion presented as a point. Point #5 requires reformulating rationalism around something other than expected utility in order for it to be right.
Point #3 is interesting.
If one person (me, for instance), observes a phenomenon, and then proposes a theory that partly explains that phenomenon, and gives reasons why the assumptions required are valid, and shows that the proposed mechanism has the proposed results given the assumptions; and gives a testable hypothesis and shows that his theory passes at least that test,
Then 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.
Can we all please be very careful about making arguments of the form (A=>B, C ⇒ B, C) ⇒ not(A) ?
(You can use such an argument to say that if A=>B, C ⇒ B, then C diminishes the evidence for A. That is most useful when B has a binary truth-value. When B is assigned not a truth-value, but a number indicating how often B goes on in the real world; and you have no quantitative knowledge of how much of the observed B C accounts for; then A=>B, C ⇒ B, C just diminishes the expected proportion of the observed B that is accounted for by A. You can’t leap to the conclusion not(A).)
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.
About point 5: I’ve encountered this idea quite often. And I agree, but only if “win the lottery” means winning the big prize.
I’ve never seen the consideration* that, in addition to the one (or, statistically, fewer than one) “jackpot”, there are in most lotteries relatively large numbers of consolation prizes.
(*: this doesn’t mean that it’s absent; it may be included in the general calculations, but I’ve never seen the point being made explicit.)
In terms of expected dollars this part doesn’t change much (it’s still sub-unitary, since lotteries don’t generally go bankrupt), but in terms of expected utility as discussed in the post, and in particular with respects with your fifth point, it seems very significant. On the monetary side, even payoffs of a few hundred dollars may have highly “distorted” utilities for some persons. And on the epistemological side, probabilities of one in a few thousand (even more for lower payoffs) are much more relevant than one in a hundred million.
That doesn’t mean that lottery players actually do the math—or base their decisions on more than intuition—but at such relatively lower levels of uncertainty it’s not as obvious that the concept is completely invalid. Also, I expect there would be many takers for any winner-takes-all lottery, too, but I’d be surprised if the number wasn’t significantly lower, all else being equal.
1) Lottery tickets are bought using income that is after tax, after debt, and after loss of government benefits.
2) Many people buy more than one lottery ticket; they spend hundreds of dollars per year or more.
3) There was a period during which poor folks had reason to legitimately distrust banks and played the illegal numbers game as a sort of stochastic savings mechanism, up to 600-to-1 payouts on 1000-to-1 odds, which meant they did get large units of cash occasionally. Post-FDIC this is no longer a realistic motive and the odds on the government lotteries are worse.
4) Yes, your life can suck, yes, the lottery can seem like the only way out. But this is not a reasoned decision based on having literally no better life-improving use for hundreds of after-tax dollars. It is based on the lure and temptation of easy money to a mind that can’t multiply.
5) Those who buy tickets will not win the lottery. If you think the chance is worth talking about, you’ve fallen prey to the fallacy yourself. In ordinary conversation odds of one in a hundred million of being wrong would correspond to a Godlike level of calibrated confidence. Therefore I say simply, “You WILL NOT win the lottery!” with far more confidence than I say that the Sun will rise tomorrow (since something could always… happen… overnight). On a statistical basis, before selective reporting, lottery winners are nonexistent—you would never encounter one if you lived in the ancestral environment and had no newspapers. The lottery is simply a lie.
Point #1 is wrong. Point #2 is consistent with my idea. Point #4 is not a point, but a conclusion presented as a point. Point #5 requires reformulating rationalism around something other than expected utility in order for it to be right.
Point #3 is interesting.
If one person (me, for instance), observes a phenomenon, and then proposes a theory that partly explains that phenomenon, and gives reasons why the assumptions required are valid, and shows that the proposed mechanism has the proposed results given the assumptions; and gives a testable hypothesis and shows that his theory passes at least that test,
Then 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.
Can we all please be very careful about making arguments of the form (A=>B, C ⇒ B, C) ⇒ not(A) ?
(You can use such an argument to say that if A=>B, C ⇒ B, then C diminishes the evidence for A. That is most useful when B has a binary truth-value. When B is assigned not a truth-value, but a number indicating how often B goes on in the real world; and you have no quantitative knowledge of how much of the observed B C accounts for; then A=>B, C ⇒ B, C just diminishes the expected proportion of the observed B that is accounted for by A. You can’t leap to the conclusion not(A).)
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.
About point 5: I’ve encountered this idea quite often. And I agree, but only if “win the lottery” means winning the big prize.
I’ve never seen the consideration* that, in addition to the one (or, statistically, fewer than one) “jackpot”, there are in most lotteries relatively large numbers of consolation prizes.
(*: this doesn’t mean that it’s absent; it may be included in the general calculations, but I’ve never seen the point being made explicit.)
In terms of expected dollars this part doesn’t change much (it’s still sub-unitary, since lotteries don’t generally go bankrupt), but in terms of expected utility as discussed in the post, and in particular with respects with your fifth point, it seems very significant. On the monetary side, even payoffs of a few hundred dollars may have highly “distorted” utilities for some persons. And on the epistemological side, probabilities of one in a few thousand (even more for lower payoffs) are much more relevant than one in a hundred million.
That doesn’t mean that lottery players actually do the math—or base their decisions on more than intuition—but at such relatively lower levels of uncertainty it’s not as obvious that the concept is completely invalid. Also, I expect there would be many takers for any winner-takes-all lottery, too, but I’d be surprised if the number wasn’t significantly lower, all else being equal.