4 ms·

This reminds me of a TV show here in Brazil: They stop someone at the street to ask 4 questions. If the person knows the answer, he has to find someone else on

This reminds me of a TV show here in Brazil: They stop someone at the street to ask 4 questions. If the person knows the answer, he has to find someone else on the street who also does; if he doesn't know, find someone who doesn't know. Everytime both he and the person he finds either answer correctly or not, the participant gets R$ 250. Then, after the participant wins R$ 1000, he's offered the chance to find one person on the street who can answer 2 of 4 (trivial) questions correctly to win R$ 2000, or leave with R$ 1000. The funny thing is that, even when the participants manage to find 4 others who answer all the questions correctly, they refuse the chance to double their money out of fear - even when they proved themselves that the people on the street know the answers! It's mind-boggling how risk-adverse we are.

pekk 14y ago
You don't live forever, and many things can only be done a few times, so the infinite-run expected payoff is not entirely relevant to realistic decision making.
derefr 14y ago
That's not simple risk-aversion, that's the decreasing marginal utility of gains versus risk. If you need $1000 for something urgently, then $1000 at 100% probability is much more important than $2000 at 50%.
- hcarvalhoalves 14y ago
  I guess you're right. By my math, the probability of one given person knowing two answers out of four to win another R$ 1000 is way higher than the probability of four people answering exactly like the participant required to win the first R$ 1000. So it feels intuitive to take the final chance, specially given how much data/options the participant has (knows all the questions and correct answers already, and can choose any geek on the street). But I'm being purely rational - R$ 1000 on the hand is certainly worth more than a possible R$ 2000. Maybe if the final prize were R$ 10.000 or more people would chose differently?
  - derefr 14y ago
    Also note: if the participant and their partners got all four questions wrong (but got them wrong together), the particpant still "wins", and moves on to the second round. But in this case, they have no evidence that the people on the street can be trusted to answer questions. If this scenario is common, it could be throwing off your expectations.
    - hcarvalhoalves 14y ago
      Not sure if my math is right, but cope with me... To win the first prize, four independent events should happen: the participant has to answer (either right or wrong), and a random person in the street has to answer the same way. Let an event "QnPmAo" mean "Question n, Person m, Answer o", where n=4, and o can be 1 (right) or 0 (wrong). The probability of winning the first prize would be: P(Win) = (P(Q1P1A1 ∩ Q1P2A1) + P(Q1P1A0 ∩ Q1P2A0)) * (P(Q2P1A1 ∩ Q2P3A0) + P(Q2P1A1 ∩ Q1P3A0)) * ... and so on, for all four questions. To win the second prize, only two independent events are need: a participant knowing any two out of four questions. The probability would be: P(Win) = P(Q1 ∩ Q2) + P(Q2 ∩ Q3) + P(Q3 ∩ Q4) + P(Q1 ∩ Q4) From a statistical viewpoint, the second scenario seems always more likely than the first, assuming the knowledge of the population about trivial questions follows a normal distribution. If during the first round all four participants know the answers, the odds of a fifth participant knowing at least two are high. Still, from the episodes I watched, people seem to refuse the second challenge regardless of the outcome of the first round - in other words, they don't seem to make a rational decision. Hope someone less rough than me in statistics can shed some light if there's a mistake!
      - derefr 14y ago
        > assuming the knowledge of the population about trivial questions follows a normal distribution This is the assumption I question. Knowledge tends to cluster geographically--people in the same area get the same cable channels, on which are aired the same re-runs of Jeopardy on the same nights.
- technotony 14y ago
  In behavioral economics this is known as loss aversion: http://en.wikipedia.org/wiki/Loss_aversion http://en.wikipedia.org/wiki/Loss_aversion In a nutshell it's this: They now have $1000 in the bank, and worry more about losing that than winning an additional $1000.
  - 001sky 14y ago
    There is a social-status related concept in psychology as well. it is implicitly assumed that hierarchy, seniority, and weatlth are linear functions of time. going backward is a (rare) and thus high information datapoint. it is therefore, actively avoided. TLDR the consequences of actions are more complex.
tempestn 14y ago
That reminds me of a little experiment I did on omegle.com (text chat site). I asked random people this question: "Say you win a lottery, and as your prize you can either have $1M, or a (true) random amount between zero and $5M. Which would you choose?" Perhaps unsurprisingly, everyone picked the guaranteed million. What did surprise me was that changing the $5M to $50M still resulted in around 90% taking the $1M, and at no amount could I get a majority of people to choose the random option. At a guaranteed $1M versus zero to $100B, it was split about 50/50. Apparently even a one thousandth of a percent chance of earning less than $1M is enough for many people to "play it safe". Either that or 50% of people don't understand basic math. ;)
- guard-of-terra 14y ago
  The value of (large sums of) money is logarithmic. Don't know which base, it varies. So it's all pretty logical. I would have chosen random to 5$, but then again I hope I know the tricks how to make money value linear.
  - xenophanes 14y ago
    It's not logical. You can sell the 0-5m random option for more than 1m (more than 2m!). Or you can buy some sort of insurance where someone pays you if you get a low roll, but you pay them if you get a high roll. Taking 40% as much money (on average) is some really expensive risk mitigation. There are much, much better deals available. For the larger amounts of money, the risk mitigation comes at a much higher price and is even more silly.
    - rictic 14y ago
      I agree with your reasoning, but I don't think it's a strong objection to the above. You're assuming that they have the time and legal ability to mitigate the risk. The question, as asked, seems to suggest that the imagined payout would be immediate, with no opportunity to mitigate.
    - tempestn 14y ago
      Exactly. I mean, I assume people operated under the assumption that the risk was non-transferrable, so I can see the logic in taking $1M over 0-5. You're giving up some expected value in order to reduce risk. Especially when you take into account the diminishing marginal value of money, especially around the low to mid millions, it makes some sense. What doesn't, as you say, is considering a random amount between zero and 100 billion dollars in any way risky compared to $1M. You're probably more likely to take the $1M then to be struck by lighting than you are to take the random option and end up with less. (And even THEN, ending up with $900k isn't the end of the world, so the odds are even lower of a really unfortunate outcome.) So you're giving up an absolutely massive expected value in order to avoid a truly miniscule risk. This is risk-aversion at its most ridiculous IMO.

pekk 14y ago

You don't live forever, and many things can only be done a few times, so the infinite-run expected payoff is not entirely relevant to realistic decision making.

derefr 14y ago

That's not simple risk-aversion, that's the decreasing marginal utility of gains versus risk. If you need $1000 for something urgently, then $1000 at 100% probability is much more important than $2000 at 50%.

hcarvalhoalves 14y ago
I guess you're right. By my math, the probability of one given person knowing two answers out of four to win another R$ 1000 is way higher than the probability of four people answering exactly like the participant required to win the first R$ 1000. So it feels intuitive to take the final chance, specially given how much data/options the participant has (knows all the questions and correct answers already, and can choose any geek on the street). But I'm being purely rational - R$ 1000 on the hand is certainly worth more than a possible R$ 2000. Maybe if the final prize were R$ 10.000 or more people would chose differently?
- derefr 14y ago
  Also note: if the participant and their partners got all four questions wrong (but got them wrong together), the particpant still "wins", and moves on to the second round. But in this case, they have no evidence that the people on the street can be trusted to answer questions. If this scenario is common, it could be throwing off your expectations.
  - hcarvalhoalves 14y ago
    Not sure if my math is right, but cope with me... To win the first prize, four independent events should happen: the participant has to answer (either right or wrong), and a random person in the street has to answer the same way. Let an event "QnPmAo" mean "Question n, Person m, Answer o", where n=4, and o can be 1 (right) or 0 (wrong). The probability of winning the first prize would be: P(Win) = (P(Q1P1A1 ∩ Q1P2A1) + P(Q1P1A0 ∩ Q1P2A0)) * (P(Q2P1A1 ∩ Q2P3A0) + P(Q2P1A1 ∩ Q1P3A0)) * ... and so on, for all four questions. To win the second prize, only two independent events are need: a participant knowing any two out of four questions. The probability would be: P(Win) = P(Q1 ∩ Q2) + P(Q2 ∩ Q3) + P(Q3 ∩ Q4) + P(Q1 ∩ Q4) From a statistical viewpoint, the second scenario seems always more likely than the first, assuming the knowledge of the population about trivial questions follows a normal distribution. If during the first round all four participants know the answers, the odds of a fifth participant knowing at least two are high. Still, from the episodes I watched, people seem to refuse the second challenge regardless of the outcome of the first round - in other words, they don't seem to make a rational decision. Hope someone less rough than me in statistics can shed some light if there's a mistake!
    - derefr 14y ago
      > assuming the knowledge of the population about trivial questions follows a normal distribution This is the assumption I question. Knowledge tends to cluster geographically--people in the same area get the same cable channels, on which are aired the same re-runs of Jeopardy on the same nights.
technotony 14y ago
In behavioral economics this is known as loss aversion: http://en.wikipedia.org/wiki/Loss_aversion http://en.wikipedia.org/wiki/Loss_aversion In a nutshell it's this: They now have $1000 in the bank, and worry more about losing that than winning an additional $1000.
- 001sky 14y ago
  There is a social-status related concept in psychology as well. it is implicitly assumed that hierarchy, seniority, and weatlth are linear functions of time. going backward is a (rare) and thus high information datapoint. it is therefore, actively avoided. TLDR the consequences of actions are more complex.

tempestn 14y ago

That reminds me of a little experiment I did on omegle.com (text chat site). I asked random people this question: "Say you win a lottery, and as your prize you can either have $1M, or a (true) random amount between zero and $5M. Which would you choose?" Perhaps unsurprisingly, everyone picked the guaranteed million. What did surprise me was that changing the $5M to $50M still resulted in around 90% taking the $1M, and at no amount could I get a majority of people to choose the random option. At a guaranteed $1M versus zero to $100B, it was split about 50/50. Apparently even a one thousandth of a percent chance of earning less than $1M is enough for many people to "play it safe". Either that or 50% of people don't understand basic math. ;)

guard-of-terra 14y ago
The value of (large sums of) money is logarithmic. Don't know which base, it varies. So it's all pretty logical. I would have chosen random to 5$, but then again I hope I know the tricks how to make money value linear.
- xenophanes 14y ago
  It's not logical. You can sell the 0-5m random option for more than 1m (more than 2m!). Or you can buy some sort of insurance where someone pays you if you get a low roll, but you pay them if you get a high roll. Taking 40% as much money (on average) is some really expensive risk mitigation. There are much, much better deals available. For the larger amounts of money, the risk mitigation comes at a much higher price and is even more silly.
  - rictic 14y ago
    I agree with your reasoning, but I don't think it's a strong objection to the above. You're assuming that they have the time and legal ability to mitigate the risk. The question, as asked, seems to suggest that the imagined payout would be immediate, with no opportunity to mitigate.
  - tempestn 14y ago
    Exactly. I mean, I assume people operated under the assumption that the risk was non-transferrable, so I can see the logic in taking $1M over 0-5. You're giving up some expected value in order to reduce risk. Especially when you take into account the diminishing marginal value of money, especially around the low to mid millions, it makes some sense. What doesn't, as you say, is considering a random amount between zero and 100 billion dollars in any way risky compared to $1M. You're probably more likely to take the $1M then to be struck by lighting than you are to take the random option and end up with less. (And even THEN, ending up with $900k isn't the end of the world, so the odds are even lower of a really unfortunate outcome.) So you're giving up an absolutely massive expected value in order to avoid a truly miniscule risk. This is risk-aversion at its most ridiculous IMO.