Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?
Given that people are often irrational (e.g., they buy lottery tickets), would you make more money this way?
14 comments
I think you're interpreting people's irrationality in the wrong way. People are often irrationally risk averse: most people would much rather pay $X with probability 1 than $2X with probability 1/2 and $0 elsewhere. The reason lottery tickets sell is because utility functions are nonlinear. After buying a $1 lotto ticket, they're still poor; they don't miss the dollar. But if they win, suddenly they are rich, which is qualitatively different from being poor. Thus, the calculation is a small but nonzero chance of being rich, vs. the certainty of being poor. Most people don't do the math to figure out just how small.
There's a reason why people indulge "If I won the lottery..." fantasies.
There's a reason why people indulge "If I won the lottery..." fantasies.
Actually people are thought to be risk seeking when it comes to losses instead of gains.
http://www.jstor.org/pss/1914185
Unlike most people in this discussion, I like the idea and think it might work under certain circumstances (probably goods with low prices and high price inelasticity).
http://www.jstor.org/pss/1914185
Unlike most people in this discussion, I like the idea and think it might work under certain circumstances (probably goods with low prices and high price inelasticity).
Utility functions are nonlinear with decreasing slope. When you don't have enough money to buy everything you want, you buy the most important things first. A 50% chance of gaining 2x dollars is a worse deal than a 100% chance of gaining x dollars, with the difference in utility becoming more significant percentage-wise for larger x.
This rant used to conclude with "therefore, buying lottery tickets is irrational; period", but someone on Less Wrong recently brought up a valid exception: it can be rational if you're currently deeply in debt. Utility functions are actually sigma-shaped: they flatten as you get more deeply negative as well. Being two trillion in debt isn't very much worse than being one trillion in debt. So when you're in debt, your utility function can get steeper before it gets shallower.
This rant used to conclude with "therefore, buying lottery tickets is irrational; period", but someone on Less Wrong recently brought up a valid exception: it can be rational if you're currently deeply in debt. Utility functions are actually sigma-shaped: they flatten as you get more deeply negative as well. Being two trillion in debt isn't very much worse than being one trillion in debt. So when you're in debt, your utility function can get steeper before it gets shallower.
I think it's a lot more complicated than the diminishing-marginal-returns model taught in econ courses. For example, there's a pretty sharp discontinuity at "can move to a better neighborhood". There's another one at "can afford a vacation home", and another one at "can send kids to college". And then there's a big one at "never has to work again." When an event bumps you from one category into the next one up, it can often be rational to take a small chance at that rather unlikely event than to worry about a few dollars that don't make a material difference in your lifestyle anyway.
Actually, this is a big problem with conventional economics: it assumes that all variables are conventional. So income taxes don't affect people's willingness to work nearly as much as theory predicts, because their choice is usually between "Have a job" and "Don't have a job" and not "Do $30K of work per year" and "Do $40k of work per year". Unemployment exists because a business can't just drop wages to the equilibrium level, but rather workers make the choice between "I'm being paid fairly" and "I'm not being paid fairly" and act appropriately. Market niches are not instantly filled because entrepreneurship often has a binary outcome of "Get rich" and "Fail", and not a continuous distribution of outcomes.
Actually, this is a big problem with conventional economics: it assumes that all variables are conventional. So income taxes don't affect people's willingness to work nearly as much as theory predicts, because their choice is usually between "Have a job" and "Don't have a job" and not "Do $30K of work per year" and "Do $40k of work per year". Unemployment exists because a business can't just drop wages to the equilibrium level, but rather workers make the choice between "I'm being paid fairly" and "I'm not being paid fairly" and act appropriately. Market niches are not instantly filled because entrepreneurship often has a binary outcome of "Get rich" and "Fail", and not a continuous distribution of outcomes.
"all variables are conventional"
s/conventional/continuous/. I can't type at night.
s/conventional/continuous/. I can't type at night.
If they don't like this scheme, you could allow them to pay $X with prob 1.
More generally, you could let them specify the pay probability p or price $Y >= $X. Given p, have them pay $X/p. Given $Y, make them pay with probability $X/$Y.
More generally, you could let them specify the pay probability p or price $Y >= $X. Given p, have them pay $X/p. Given $Y, make them pay with probability $X/$Y.
Actually, people play the lottery because they can't do math.
I'm not so sure about that. In California (and in several other places I've lived) the odds of winning are written out on the back of the ticket. Sure, a lot of people believe in not-systems like studying past numbers or drawing numbers from their dreams or casting spells; but deep down I think most people understand 'odds of winning = 1 in 57 million'.
Lottery addicts certainly can't do math since they waste a lot of money on tickets. But a good many other people just buy one a week or just occasionally, eg when there's a particularly large jackpot on offer. This isn't so irrational; a regular player will make a few bucks back over the year on small prizes, and the risk/reward ratio improves for a big jackpot even though the odds don't.
It's worth recalling that while the odds on any individual ticket are awful, enough people are playing that people do win big prizes on a semi-regular basis. For small-spend players who can afford it, and may think of it as semi-charitable given the uses to which lottery profits are put, is it really any more irrational than certain kinds of insurance?
Lottery addicts certainly can't do math since they waste a lot of money on tickets. But a good many other people just buy one a week or just occasionally, eg when there's a particularly large jackpot on offer. This isn't so irrational; a regular player will make a few bucks back over the year on small prizes, and the risk/reward ratio improves for a big jackpot even though the odds don't.
It's worth recalling that while the odds on any individual ticket are awful, enough people are playing that people do win big prizes on a semi-regular basis. For small-spend players who can afford it, and may think of it as semi-charitable given the uses to which lottery profits are put, is it really any more irrational than certain kinds of insurance?
Same goes for renting movies. And it's worse, because there's about zero chance of winning money renting a movie. :)
Some people get a kick out of the whole buy a ticket, wait for the numbers, get excited dreaming thing.
For some folks, it's entertainment.
Some people get a kick out of the whole buy a ticket, wait for the numbers, get excited dreaming thing.
For some folks, it's entertainment.
Q: How do you increase your odds of winning Lotto by 0.0000001%?
A: Buy a ticket
A: Buy a ticket
As omegazero pointed out, there might be a selection bias if you don't do it right -- people will back out if they see they are in the unlucky group of folks who will get charged $2X.
If you make people commit before revealing the amount, the issue is trust: how do customers know that the odds are actually 1/2 that they'll pay $0? How do they know you aren't just charging everyone $2X? You'd have to use some verifiably random bit, which gets complicated. People will smell a scam.
(Speaking of which: are there any commonly used publicly verifiable random numbers, like a die roll, but outside of any party's control? I presume there must be a need for them in a number of situations.)
If you make people commit before revealing the amount, the issue is trust: how do customers know that the odds are actually 1/2 that they'll pay $0? How do they know you aren't just charging everyone $2X? You'd have to use some verifiably random bit, which gets complicated. People will smell a scam.
(Speaking of which: are there any commonly used publicly verifiable random numbers, like a die roll, but outside of any party's control? I presume there must be a need for them in a number of situations.)
I'm sorry if this response is off-topic, but your last question piqued my curiosity so I would like to answer it.
There is an authoritative source of random numbers. In 1955, The RAND Corporation (a Cold War-era think tank) published a wonderful book entitled "A Million Random Digits with 100,000 Normal Deviates". Amazon.com has a copy of it, including some amusing reviews: http://www.amazon.com/Million-Random-Digits-Normal-Deviates/... .
For a good source of truly random numbers accessible from an API, I personally use http://random.org . They use atmospheric noise to create random numbers, which ultimately boils down to the true randomness that is Quantum Mechanics. It's not suitable for high-security applications -- I could do some network trickery and redirect your API request to my server that always returns 1.0 -- but it's better than the PRNGs on modern computers.
There is an authoritative source of random numbers. In 1955, The RAND Corporation (a Cold War-era think tank) published a wonderful book entitled "A Million Random Digits with 100,000 Normal Deviates". Amazon.com has a copy of it, including some amusing reviews: http://www.amazon.com/Million-Random-Digits-Normal-Deviates/... .
For a good source of truly random numbers accessible from an API, I personally use http://random.org . They use atmospheric noise to create random numbers, which ultimately boils down to the true randomness that is Quantum Mechanics. It's not suitable for high-security applications -- I could do some network trickery and redirect your API request to my server that always returns 1.0 -- but it's better than the PRNGs on modern computers.
Thanks for the informative reply, gmazzola. Could someone who doesn't trust random.org verify that the numbers are indeed random and impossible to rig? What I have in mind is a number that (1) nobody has influence over, (2) can be measured objectively, (3) is observable to everybody, and (4) is impossible to predict.
For example, I could tell my friend that I'll do his laundry for a month if Barack Obama's speech tomorrow contains an even number of words, and he'll do my laundry otherwise. This would appear to be truly random, but what if I secretly am friends with Barack Obama and can rig it in advance?
Is there some easy, practical way of producing a number whose randomness a large number of mutually distrustful parties can agree on? (I am thinking of something like asking each party to produce a number, and then publicly summing everyone's numbers together.)
For example, I could tell my friend that I'll do his laundry for a month if Barack Obama's speech tomorrow contains an even number of words, and he'll do my laundry otherwise. This would appear to be truly random, but what if I secretly am friends with Barack Obama and can rig it in advance?
Is there some easy, practical way of producing a number whose randomness a large number of mutually distrustful parties can agree on? (I am thinking of something like asking each party to produce a number, and then publicly summing everyone's numbers together.)
Sadly, this is outside my area of expertise. I will nonetheless attempt to answer your question, but please take my words with a grain of salt.
Before we even begin delving into true RNGs, it is worthwhile to consider if we're over-engineering the problem. Is a PRNG "good enough" for the task at hand? In most cases, it is. A well-seeded PRNG, such as the ones present in modern-day Operating Systems, are suitable for most tasks not involving National Security.
However, if you have a genuine need for a true RNG, a computer algorithm certainly won't be generating it. Computers are by nature deterministic, and thus are very poor at behaving unpredictably. Thus, like with all good problems, we are forced to enter the realm of physics.
The fundamental problem is, who will be observing the source of randomness? To my knowledge, there isn't a physical source of randomness that is observable to everybody. (I did some quick googling to confirm my suspicions, but if you're planning on using my words to do anything useful, please confirm my statement!). Thus, as I see it, you have several options:
1) Your idea, where all parties derive a true random number from physics and publically sum everyone's numbers together. Your qualifiers (2) through (4) hold, but (1) is difficult. In this case, a certain number of rogue nodes will be able to manipulate the computation. I remember a Professor of mine, who does research in this field, stating the minimum number of truthful nodes needed in a distributed computation is (2/3)n + 1, but again confirm this number for yourself.
My point here is, using the public-summing method, you are faced with the difficult problem of determining if a node is attempting to manipulate the system. While a provable solution has been found, after decades of research across the globe, my Professor still is working on the problem, thus demonstrating it is not an easy task.
2) Have a single computer (say, random.org) that is observing a true RNG, and publicizes the result for all to see. Of course you'd use asymmetric crypto so that all parties can prove that they've received the correct number.
Again, your qualifiers (2) through (4) pass, but (1) presents a different problem. We're back to where we started: do you trust random.org?
However, it's an easier task to make an authority trustable than a peer in a distributed computation. We trust Verisign to be a certificate authority, because we believe their security practices are half-decent, and they can be audited. (Every year all CA's are independently audited by WebTrust.org using pretty strict criteria.)
The same could be done for random.org: why not require certification and frequent auditing of their RNG equipment?
The other nice thing about RNGs is that you can audit them yourself, given enough time and expertise. When viewed correctly, poor RNGs will have distinct patterns visible to the eye (example: http://www.cs.hku.hk/cisc/projects/va/index.htm ).
The crux of my argument is: I don't know of a true RNG, that upon observation by multiple parties, all will receive the same random number. My instinct and my research says that none exist, but I would love to be proven wrong. Crypto experts, correct me!
If you'd like more information, Wikipedia is always invaluable: http://en.wikipedia.org/wiki/Hardware_random_number_generato...
Before we even begin delving into true RNGs, it is worthwhile to consider if we're over-engineering the problem. Is a PRNG "good enough" for the task at hand? In most cases, it is. A well-seeded PRNG, such as the ones present in modern-day Operating Systems, are suitable for most tasks not involving National Security.
However, if you have a genuine need for a true RNG, a computer algorithm certainly won't be generating it. Computers are by nature deterministic, and thus are very poor at behaving unpredictably. Thus, like with all good problems, we are forced to enter the realm of physics.
The fundamental problem is, who will be observing the source of randomness? To my knowledge, there isn't a physical source of randomness that is observable to everybody. (I did some quick googling to confirm my suspicions, but if you're planning on using my words to do anything useful, please confirm my statement!). Thus, as I see it, you have several options:
1) Your idea, where all parties derive a true random number from physics and publically sum everyone's numbers together. Your qualifiers (2) through (4) hold, but (1) is difficult. In this case, a certain number of rogue nodes will be able to manipulate the computation. I remember a Professor of mine, who does research in this field, stating the minimum number of truthful nodes needed in a distributed computation is (2/3)n + 1, but again confirm this number for yourself.
My point here is, using the public-summing method, you are faced with the difficult problem of determining if a node is attempting to manipulate the system. While a provable solution has been found, after decades of research across the globe, my Professor still is working on the problem, thus demonstrating it is not an easy task.
2) Have a single computer (say, random.org) that is observing a true RNG, and publicizes the result for all to see. Of course you'd use asymmetric crypto so that all parties can prove that they've received the correct number.
Again, your qualifiers (2) through (4) pass, but (1) presents a different problem. We're back to where we started: do you trust random.org?
However, it's an easier task to make an authority trustable than a peer in a distributed computation. We trust Verisign to be a certificate authority, because we believe their security practices are half-decent, and they can be audited. (Every year all CA's are independently audited by WebTrust.org using pretty strict criteria.)
The same could be done for random.org: why not require certification and frequent auditing of their RNG equipment?
The other nice thing about RNGs is that you can audit them yourself, given enough time and expertise. When viewed correctly, poor RNGs will have distinct patterns visible to the eye (example: http://www.cs.hku.hk/cisc/projects/va/index.htm ).
The crux of my argument is: I don't know of a true RNG, that upon observation by multiple parties, all will receive the same random number. My instinct and my research says that none exist, but I would love to be proven wrong. Crypto experts, correct me!
If you'd like more information, Wikipedia is always invaluable: http://en.wikipedia.org/wiki/Hardware_random_number_generato...
That is really a fantastic answer, Greg! Thanks for the valuable information.
You are right. The reviews are worth the trip over to Amazon. I suspect some Amazon programmers are having a little fun with randomness.
> (Speaking of which: are there any commonly used publicly verifiable random numbers, like a die roll, but outside of any party's control? I presume there must be a need for them in a number of situations.)
Just use next week's state lottery's numbers and similar things. That is fairly impartial and hard to influence. Though that might be too few bits and too much latency for your liking.
Just use next week's state lottery's numbers and similar things. That is fairly impartial and hard to influence. Though that might be too few bits and too much latency for your liking.
[deleted]
heard of the game "evens or odds"? Each party can choose their own trusted random number generator to decide to play "even" or "odd"
People will "irrationally" learn that your product is valueless (after all, you give it away for free) and you will attract pathological customers (the kind who would put up with this pricing model, which screams scam).
To sell your good a consumer must be both willing and able to pay. Under this system that would be the 2X price since he doesn't know which price he will actually get (if he knew ahead of time, or could back out of the deal after learning the price, you'd always be giving them away).
There's always going to be less people you can afford 2X than X.
There's always going to be less people you can afford 2X than X.
A clever idea but I worry what happens to the people that miss out. They are either aware they've paid $2X (if you tell them) or they are aware that they've been "ripped off" (you are prepared to give it away for $0 so you must have at least 50% markup. Kind of like jewellery stores putting half price sales on $10-20k diamond rings). Either way you are associating negative feelings immediately and a sense of buyer's regret.
On a practical note, what stops them getting a refund and repurchasing until they get it for free.
On a practical note, what stops them getting a refund and repurchasing until they get it for free.
On a practical note, what stops them getting a refund and repurchasing until they get it for free.
Your other observation is good, too, but I think this sentence gets to the heart of the problem. The double-or-nothing transaction is irreversible, which is what makes it a bad one.
People like commercial transactions that can be reversed. Ideally, both parties should walk away feeling like they got a fine deal, but that if the deal goes sour at any point in the near future (because a part was broken; because the customer had second thoughts) they would be both be willing to "undo" it without much harm done.
Your other observation is good, too, but I think this sentence gets to the heart of the problem. The double-or-nothing transaction is irreversible, which is what makes it a bad one.
People like commercial transactions that can be reversed. Ideally, both parties should walk away feeling like they got a fine deal, but that if the deal goes sour at any point in the near future (because a part was broken; because the customer had second thoughts) they would be both be willing to "undo" it without much harm done.
maybe you can make it reversible by refunding it on the same terms, i.e the buyer has the right to return the good to the seller, and the seller pays 2X or 0 with prob 1/2 to the buyer.
Maybe, but a) there may be statutory rights issue, b) this just seems likely to annoy people and c) you might run the risk of actually having to comply with gambling laws if you take money from people and offer them a chance of doubling it.
No. A lottery ticket is a way to buy a fantasy: if you're a housekeeper who doesn't speak much English and already has two kids, you know you'll never be rich -- but for $1, you can spend a couple hours thinking it's a possibility.
To take advantage of this, you might charge 1.1X with a 10% chance of getting 10X worth of similar goods. But that wouldn't be too exciting, either.
To take advantage of this, you might charge 1.1X with a 10% chance of getting 10X worth of similar goods. But that wouldn't be too exciting, either.
I like the lottery ticket analogy some people have made, but here is my twist.
My service costs $X per month. So if you like it, you'll want to pay $X. ... But for a just this month, there is a 1/10 chance your $X will get you the service for the entire year!! ... and if you don't "win", you still get what you paid for.
I think this might encourage people who are on the edge to sign up now, and still feel good no matter what the outcome, plus they might tell their friends about it.
-- David Jones
My service costs $X per month. So if you like it, you'll want to pay $X. ... But for a just this month, there is a 1/10 chance your $X will get you the service for the entire year!! ... and if you don't "win", you still get what you paid for.
I think this might encourage people who are on the edge to sign up now, and still feel good no matter what the outcome, plus they might tell their friends about it.
-- David Jones
Just a note: we don't sign our posts/comments here. Your username does that for you.
http://news.ycombinator.com/item?id=198817
http://news.ycombinator.com/item?id=198817
This may just be me having a bad day, but I do sense a little arrogance in your response. It does not hurt anyone if you add your name at the end of a comment.
It hurts everyone. It uses up screen space and reading time and has absolutely zero value.
That version's been done, eg. Jordan's Furniture's "If the Red Sox win the pennant, all furniture is free!" promotion. And it works pretty well. I'd imagine that the publicity Jordan's got from that was well worth the money their insurance company paid out.
For it to be a lottery ticket analogy, you'd pay half the cost for a 50% change of actually getting the goods
A more common variation of this idea is "Win your purchase free!", with the odds of winning being fairly low, but the price remaining the same.
Car dealerships seem to like this one, and Visa ran a similar contest here in Canada recently (called "Win What You Buy").
The success of this kind of promotion is most likely proportional to the price of your product.
Car dealerships seem to like this one, and Visa ran a similar contest here in Canada recently (called "Win What You Buy").
The success of this kind of promotion is most likely proportional to the price of your product.
Sounds like the Neo-Futurists' pricing scheme: """Tickets are $9 + the roll of a single six-sided die ($10 - $15, depending on your luck!)"""
http://www.neofuturists.org/index.php?option=com_content&...
http://en.wikipedia.org/wiki/Global_Gillette does it, right?
From experience in running various marketing campaigns, the magic 'number' is 1 in 10. Charging $X with the option of paying $1.1X (or just over, even) for a 0.1 probability of getting the money straight back will get the most people buying into the scheme. That'll be around 1 in 10 people too. Force the extra payment and around half of them will walk away there and then(1). Bump the price up to $1.1X without mentioning it, only that there's a 1 in 10 chance of getting it free and you'll see the overall take-up go up anywhere from 25% to 100%.
Long story short: Make your new price $1.1X without fanfare, offer a 1 in 10 chance of getting it for free and you all win. They get their chance at a freebie at a cost they don't notice, you get your promotion vibe bumping up sales.
(1)I know that that's obvious, and it was dumb to run it - but we ran it anyway for the sake of completeness.
Long story short: Make your new price $1.1X without fanfare, offer a 1 in 10 chance of getting it for free and you all win. They get their chance at a freebie at a cost they don't notice, you get your promotion vibe bumping up sales.
(1)I know that that's obvious, and it was dumb to run it - but we ran it anyway for the sake of completeness.
The expected value is the same:
(0.5 * 2X) + (0.5 * 0) = X = (X * 1.0)
but perhaps you would be able to attract more customers. I doubt it. While it's certainly true that everybody loves a freebie, no one likes to pay twice for something.
Why not charge X with probability (1-p) and charge zero with probability p? The expected value would be reduced to (1-p) but perhaps you would attract people looking for freebies. More customers is always a good thing, right?
(0.5 * 2X) + (0.5 * 0) = X = (X * 1.0)
but perhaps you would be able to attract more customers. I doubt it. While it's certainly true that everybody loves a freebie, no one likes to pay twice for something.
Why not charge X with probability (1-p) and charge zero with probability p? The expected value would be reduced to (1-p) but perhaps you would attract people looking for freebies. More customers is always a good thing, right?
There is a way that you can do this. You charge $X and simply state that every Yth customer gets it free.
Problem solved.
Problem solved.
No. Buying a product/paying for a service isn't the same as gambling, and without a potential high payoff (3 million dollars or whatever) you aren't triggering the same neurochemicals.