Ignoring the frame, EU theory with log utility suggest a cutoff of about 2700. At that wealth, the first bet raises wealth by a factor of ~20, the second by a factor of ~400 and log 400 is roughly 2 log 20 [base doesn't matter]. So below that wealth you should go for the sure thing, above it take the risk
IF you switch from WTA to WTP you get a plausible class of questios. for moderate intail wealth, a bit over 50k, would you risk nearly all of it for a 50 per cent chance of a million pounds. This kind of choice faces lots of aspiring entrepreneurs who have (or think they have) an idea that can make them rich.
This problem is more acute, or perhaps just more relevant, in the case of the funders of the entrepreneurs. It also explains some of the differences between the economies of the US and Europe. In the US, funders are much more likely to make the "rational" bet of a small chance of a 50x return while in Europe the funders already basically control economic decision making and thus are much more likely to make the "intuitive" choice that a 15% return still keeps them on top.
Having been a part of this world for a while, I gradually came to realize that US startup investments/valuations are only partly explained by economics (or obvious economics). The real driver is social influence in an environment where all the players have so much money that in a sense money isn't money anymore (and tend to be so dizzyingly smart that "smartest" isn't really a thing either). So how do you pick an in crowd? It starts to look a lot like the contemporary art market; the calculations and risk assessments and so forth are merely the autisty-engineer equivalent of the art world's wafty "social critique" and "bold violations of formal expectations" and so forth. You want to be the guy who bought Basquiat early.
None of these are good investments by any reasonable economic criteria. It's just that some of them will get you invited to a three-day retreat with Larry Ellison and a dozen of his closest friends.
It's also why taking pronouncements about "the death of Silicon Valley" at face value is a serious mistake. Either the statement-maker doesn't understand the real game, or they're the equivalent of a painter that couldn't make it in New York.
The value of the trollyverse is in demonstrating how thoroughly internally-contradictory each person's set of moral intuitions are. I agree that, like ~all hypotheticals, they're ~useless at telling us anything interesting about how we should react to real-world situations, but that's not the point of a hypothetical - the value is in exploring our responses to them, not in applying them to reality.
Susquehanna International Group famously likes to hire people who are good at games, and their new trainees spend some hours actually playing games against one another. (Several of the strongest US backgammon players worked there in the 90s.)
A friend of mine interviewed there many years ago, and they asked him several versions of this question, trying to find his pain point. Then they went way past it (bigger numbers). He eventually said, "Well, I'd call up my friends at Susquehanna and offer to sell them some of my action."
I particularly like the story (via Matt Levine) about them asking as an interview question "if one of our traders offered you 51% odds on a coin toss, would you take it?", where the answer they're looking for is of the general shape "no, because if one of your traders was offering me that trade, he's presumably figured out how to rig the toss" (which is a valuable lesson in evaluating trades in that sort of environment).
"Nobody is ever going to put you in any situation where you’re stopped in the street as a stranger and offered either tens of thousands of pounds for nothing, or a risk free gamble worth half a million."
Yeah. The problem stated is just a more intellectual version of "Here are four common desserts. Which one has to go?"
I'm seeing this theme a lot, which I value more and more, "...a failure of the model to describe reality."
I had a finance career that morphed from measuring profit to forecasting. I saw models fail all the time, but didn't have words for the failure mode, other than assumption mistakes.
The description of economic models in "The Unaccountability Machine" that throw away a lot of data make them workable was clarifying.
Now, rightly or wrongly, I see parallels in our current "LLM's will lead to AGI soon" race.
There's a lot of missing data in that model. To me, it's the Sidney Harris cartoon: "A miracle occurs" to provide the missing data.
‘His favourite example is that of Harry Markowitz, who won a Nobel prize in economics for creating a formula to produce maximum gain from an investment portfolio, in a sophisticated mathematical weighting of gain and risk. When it came to investing for his own retirement, however, Markowitz didn’t bother with that his formula – which Gigerenzer proved to be certainly effective only over a 500-year period – he simply divided his investment equally among a given number of assets. He used the heuristic of “not putting all his eggs in one basket” because he knew that would probably be good enough.’
Thank you for providing a rational underpinning for the proper respect for the pattern matching that got humans to where we are.
What’s so irritating to me is that the example is a terrible application of rationality. It assumes that rational actors only care about average returns and are indifferent to the range and variance of returns.
This is a shocking form of innumeracy from the “rational” camp, as the insight about variance is the foundation of all basic investing advice.
You have $50,000 to invest. You can buy an index fund and you are quite certain that at the end of x years it will be worth $100,000. You can also invest in a biotech startup working on an important drug, but because it is not public you have to invest the whole $50,000. You are certain there is a 50 percent chance the drug will work and in x years the stock will be worth $2 million, and 50 percent chance it won’t work and be worthless.
Very few of these rationalists have a big enough portfolio to take that second bet. Not caring about covariance and variance only makes sense in the fantasy world of being given the lottery ticket, artificially taking covariance to zero.
not super related to your point but imo it is rational (in natural usage) to think "we would all be better off if everyone did this, therefore I will do this" when that is irrational as defined by theory (such as, I dunno, voting).
what you say about lotteries etc. not being very relevant reminds if the distinction between small worlds and large worlds - this Gintis review of a Binmore book describes it: https://www.umass.edu/preferen/gintis/BinmoreRational.pdf
I'm not sure appealing to what humans are evolved to do is a move you want to make. After all, humans evolved in very different circumstances than the ones we live in today and heuristics that worked for them won't necessarily work for us. Of course, you know this. "Does the decision-making apparatus humans got from evolution conform to objectively justified canons of rationality?" is still a real question, and thought experiments are going to be part of answering it (even if this particular one may not be all that helpful).
Ha, I came here to say this and I'm not surprised you beat me to saying it better! "Numeracy" is different from "common sense", and it is helpful to encourage people in a society that contains important examples of both to be aware of both and know when to use which!
Yes, indeed, as you say. There is no single “rational” answer which applies to every person. The answer depends also on the circumstances of the individual, their risk preference, and the like. Trying to determine a single answer for everyone is pointless.
Urr, yes. But economics is not a branch of psychology. It is a study of aggregate behavior. In some contexts aggregate behavior is perforce rational, since certain behavioral patterns displace others. Compare Toyota to Yugo. Uncle Miltie may have smoked a bit too much "as if rational", but he has a point.
or, as I like to say, "all probabilities are conditional probabilities"
Irrational, adj: "behaving in a way which doesn't match my model's predictions"; implicitly, the problem is with reality rather than with the model.
Well said.
It also bugs me that implicit in "Expected Value" is basically "repeated game" analysis.
(i.e. the form of this gotcha is actually that "if you do this a bunch of times, the person taking the risk comes out ahead")
Only this isn't (as stated) a repeated game.
Ignoring the frame, EU theory with log utility suggest a cutoff of about 2700. At that wealth, the first bet raises wealth by a factor of ~20, the second by a factor of ~400 and log 400 is roughly 2 log 20 [base doesn't matter]. So below that wealth you should go for the sure thing, above it take the risk
IF you switch from WTA to WTP you get a plausible class of questios. for moderate intail wealth, a bit over 50k, would you risk nearly all of it for a 50 per cent chance of a million pounds. This kind of choice faces lots of aspiring entrepreneurs who have (or think they have) an idea that can make them rich.
This problem is more acute, or perhaps just more relevant, in the case of the funders of the entrepreneurs. It also explains some of the differences between the economies of the US and Europe. In the US, funders are much more likely to make the "rational" bet of a small chance of a 50x return while in Europe the funders already basically control economic decision making and thus are much more likely to make the "intuitive" choice that a 15% return still keeps them on top.
Having been a part of this world for a while, I gradually came to realize that US startup investments/valuations are only partly explained by economics (or obvious economics). The real driver is social influence in an environment where all the players have so much money that in a sense money isn't money anymore (and tend to be so dizzyingly smart that "smartest" isn't really a thing either). So how do you pick an in crowd? It starts to look a lot like the contemporary art market; the calculations and risk assessments and so forth are merely the autisty-engineer equivalent of the art world's wafty "social critique" and "bold violations of formal expectations" and so forth. You want to be the guy who bought Basquiat early.
None of these are good investments by any reasonable economic criteria. It's just that some of them will get you invited to a three-day retreat with Larry Ellison and a dozen of his closest friends.
It's also why taking pronouncements about "the death of Silicon Valley" at face value is a serious mistake. Either the statement-maker doesn't understand the real game, or they're the equivalent of a painter that couldn't make it in New York.
Quite right. Which is why artificial "trolley problems" in ethics aren't very helpful in illuminating questions about moral choice
The value of the trollyverse is in demonstrating how thoroughly internally-contradictory each person's set of moral intuitions are. I agree that, like ~all hypotheticals, they're ~useless at telling us anything interesting about how we should react to real-world situations, but that's not the point of a hypothetical - the value is in exploring our responses to them, not in applying them to reality.
was just thinking the same thing!
Susquehanna International Group famously likes to hire people who are good at games, and their new trainees spend some hours actually playing games against one another. (Several of the strongest US backgammon players worked there in the 90s.)
A friend of mine interviewed there many years ago, and they asked him several versions of this question, trying to find his pain point. Then they went way past it (bigger numbers). He eventually said, "Well, I'd call up my friends at Susquehanna and offer to sell them some of my action."
He got the job.
I particularly like the story (via Matt Levine) about them asking as an interview question "if one of our traders offered you 51% odds on a coin toss, would you take it?", where the answer they're looking for is of the general shape "no, because if one of your traders was offering me that trade, he's presumably figured out how to rig the toss" (which is a valuable lesson in evaluating trades in that sort of environment).
"Nobody is ever going to put you in any situation where you’re stopped in the street as a stranger and offered either tens of thousands of pounds for nothing, or a risk free gamble worth half a million."
Yeah. The problem stated is just a more intellectual version of "Here are four common desserts. Which one has to go?"
I'm seeing this theme a lot, which I value more and more, "...a failure of the model to describe reality."
I had a finance career that morphed from measuring profit to forecasting. I saw models fail all the time, but didn't have words for the failure mode, other than assumption mistakes.
The description of economic models in "The Unaccountability Machine" that throw away a lot of data make them workable was clarifying.
Now, rightly or wrongly, I see parallels in our current "LLM's will lead to AGI soon" race.
There's a lot of missing data in that model. To me, it's the Sidney Harris cartoon: "A miracle occurs" to provide the missing data.
This is Gigerenzer vs Kahneman all over again https://www.theguardian.com/science/2014/jun/01/nudge-economics-freakonomics-daniel-kahneman-debunked
‘His favourite example is that of Harry Markowitz, who won a Nobel prize in economics for creating a formula to produce maximum gain from an investment portfolio, in a sophisticated mathematical weighting of gain and risk. When it came to investing for his own retirement, however, Markowitz didn’t bother with that his formula – which Gigerenzer proved to be certainly effective only over a 500-year period – he simply divided his investment equally among a given number of assets. He used the heuristic of “not putting all his eggs in one basket” because he knew that would probably be good enough.’
Thank you for providing a rational underpinning for the proper respect for the pattern matching that got humans to where we are.
What’s so irritating to me is that the example is a terrible application of rationality. It assumes that rational actors only care about average returns and are indifferent to the range and variance of returns.
This is a shocking form of innumeracy from the “rational” camp, as the insight about variance is the foundation of all basic investing advice.
You have $50,000 to invest. You can buy an index fund and you are quite certain that at the end of x years it will be worth $100,000. You can also invest in a biotech startup working on an important drug, but because it is not public you have to invest the whole $50,000. You are certain there is a 50 percent chance the drug will work and in x years the stock will be worth $2 million, and 50 percent chance it won’t work and be worthless.
Very few of these rationalists have a big enough portfolio to take that second bet. Not caring about covariance and variance only makes sense in the fantasy world of being given the lottery ticket, artificially taking covariance to zero.
not super related to your point but imo it is rational (in natural usage) to think "we would all be better off if everyone did this, therefore I will do this" when that is irrational as defined by theory (such as, I dunno, voting).
what you say about lotteries etc. not being very relevant reminds if the distinction between small worlds and large worlds - this Gintis review of a Binmore book describes it: https://www.umass.edu/preferen/gintis/BinmoreRational.pdf
I'm not sure appealing to what humans are evolved to do is a move you want to make. After all, humans evolved in very different circumstances than the ones we live in today and heuristics that worked for them won't necessarily work for us. Of course, you know this. "Does the decision-making apparatus humans got from evolution conform to objectively justified canons of rationality?" is still a real question, and thought experiments are going to be part of answering it (even if this particular one may not be all that helpful).
Ha, I came here to say this and I'm not surprised you beat me to saying it better! "Numeracy" is different from "common sense", and it is helpful to encourage people in a society that contains important examples of both to be aware of both and know when to use which!
A cuckoo escaped Nurse Ratched, and laid an egg in a model's nest.
Much or most of the behavioral economics biases are based on these kind of hypothetical I-fooled-you problems.
Yes, indeed, as you say. There is no single “rational” answer which applies to every person. The answer depends also on the circumstances of the individual, their risk preference, and the like. Trying to determine a single answer for everyone is pointless.
Urr, yes. But economics is not a branch of psychology. It is a study of aggregate behavior. In some contexts aggregate behavior is perforce rational, since certain behavioral patterns displace others. Compare Toyota to Yugo. Uncle Miltie may have smoked a bit too much "as if rational", but he has a point.