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I'm reading the book Priceless by William Poundstone which discusses the work of Kahneman and Tversky (among others) in great detail as it relates to the psycho

by dools 14y ago

I'm reading the book Priceless by William Poundstone which discusses the work of Kahneman and Tversky (among others) in great detail as it relates to the psychology of pricing (excellent read, btw). This is O.T from what the article is saying but mildly O.T (meaning on-topic) and I'd love to hear HN's opinion on this. One of the problems presented in Priceless is: Would you rather $3,000 as a sure thing, or an 80% chance of $4,000 and a 20% chance of nothing versus: Would you rather a $3,000 loss as a sure thing, or an 80% chance of losing $4,000 and a 20% chance of losing nothing. The erroneous path that most people take, in the eyes of these researchers, is that they set their base reference point at the sure thing, ie. they say "well the $3,000 is a sure thing so I can assume I have it". If you do that, then your answers are different: In the first instance you keep the $3,000 (because it becomes an 80% chance of winning $1,000 versus a 20% chance of losing $3,000). In the second instance you go to court (because it's an 80% chance of losing $1,000 versus a 20% chance of winning $3,000). However if you don't "rebase" your reference point, then you would make the same decision in both cases - that is you would take the 80% of $4,000 bet because it's "worth" $3,200. As much as I realise what they're saying and they say it's statistically incorrect to do this, it really seems to me the most sensible way to make the decisions (which is, I guess, exactly what they're saying right? I'm human, ergo fallible to this kind of illusion). The thing that kills me is this: if this is a one time thing, I'd rather be sure of the $3,000. If I'm buying and selling these bets all day, then sure I should take the $4,000 at 80% because even if I lose this round, the next time I take the bet will make up for it (ie. law of large numbers). But what this problem doesn't address is how often I get this opportunity? Depending on my circumstances, $3,000 could be a life changing opportunity, ie. if I "win" $3,000 or $4,000, my circumstances are essentially the same so I should always go for the sure thing. If I lose $3,000 or $4,000 I'm equally screwed, so I should take the risk and try and win in court. What am I missing?

kristopolous 14y ago
I'm trying to follow. So you are saying that with the following scenario: 1. +3000 at P100 or +4000 at P80 2. -3000 at P100 or -4000 at P80 Depending on the context, the answer is basically universally different if you say "1 then 2" as opposed to "just 1" or "just 2"?
- dools 14y ago
  The issue is that the answers are (yes basically) universally different regardless of whether both options are provided, but that statistically speaking they are identical. The foible of humanity that makes the answers different is that we first "rebase" our expectations to the 100% chance, rather than considering our current position to be the baseline.
  - kristopolous 14y ago
    Yes, statistically they are identical. However, the fact that people consider the significance of the objects and the context of the decision isn't a fault of human intellect. Really, stating otherwise is a fault of human analysis. It's a game theory problem I think (likely a variation of the stag hunt: http://en.wikipedia.org/wiki/Stag_hunt http://en.wikipedia.org/wiki/Stag_hunt). It's a paradox only because Armchair mathematical intuition fails to explain it.
    - roel_v 14y ago
      No because the stag hunt family of problems are about trust in other people, the situation in the OP is not. It's about risk aversion. Whether or not that is a 'fault of human intellect' is a matter of definition and up for debate, it's not as clear-cut as you make it out to be.
      - kristopolous 14y ago
        Ok thanks. I am no specialist in this by any means. But I do know enough to be cautious when dealing with these types of problems. Glad you clarified.
btmorex 14y ago
The issue is that the first $1000 gained is worth more than the second $1000. Similarly, the first $1000 lost hurts more than the second $1000. On the gain side, the different values should be self evident. I think we can all intuitively understand why making $100000 instead of $50000 is bigger deal than $150000 instead of $100000. So let's assign utility to the numbers: first $1000 = 1 second $1000 = .8 third = .6 fourth = .4 Option #1 gives us 2.4 whereas option #2 gives us 2.24. I'd argue that we can similarly rank the losses the same: first $1000 lost = -1 second = -.8 etc. which gives us -2.4 vs --2.24 meaning we should obviously take the option #2. Now the interesting question is why we can assign similar yet negative values for the losses. I'll give two examples that might show why this is true. First, consider living paycheck to paycheck. I only have $500 of buffer. In this case, while losing $2000 instead of $1000 is worse, it's not worse by a lot because either way I can't afford rent and I'm evicted. As a second example, consider bankruptcy. If we take losses to high values, eventually each additional loss doesn't subtract anything from my "happiness". I've already hit the bankruptcy point and nothing worse can happen. These are of course the two extremes, but I think it's easy to complete the spectrum and show that for any $x the first loss of $x hurts more than the second loss of $x.

by dools 14y ago

kristopolous 14y ago

I'm trying to follow. So you are saying that with the following scenario: 1. +3000 at P100 or +4000 at P80 2. -3000 at P100 or -4000 at P80 Depending on the context, the answer is basically universally different if you say "1 then 2" as opposed to "just 1" or "just 2"?

dools 14y ago
The issue is that the answers are (yes basically) universally different regardless of whether both options are provided, but that statistically speaking they are identical. The foible of humanity that makes the answers different is that we first "rebase" our expectations to the 100% chance, rather than considering our current position to be the baseline.
- kristopolous 14y ago
  Yes, statistically they are identical. However, the fact that people consider the significance of the objects and the context of the decision isn't a fault of human intellect. Really, stating otherwise is a fault of human analysis. It's a game theory problem I think (likely a variation of the stag hunt: http://en.wikipedia.org/wiki/Stag_hunt http://en.wikipedia.org/wiki/Stag_hunt). It's a paradox only because Armchair mathematical intuition fails to explain it.
  - roel_v 14y ago
    No because the stag hunt family of problems are about trust in other people, the situation in the OP is not. It's about risk aversion. Whether or not that is a 'fault of human intellect' is a matter of definition and up for debate, it's not as clear-cut as you make it out to be.
    - kristopolous 14y ago
      Ok thanks. I am no specialist in this by any means. But I do know enough to be cautious when dealing with these types of problems. Glad you clarified.

btmorex 14y ago

The issue is that the first $1000 gained is worth more than the second $1000. Similarly, the first $1000 lost hurts more than the second $1000. On the gain side, the different values should be self evident. I think we can all intuitively understand why making $100000 instead of $50000 is bigger deal than $150000 instead of $100000. So let's assign utility to the numbers: first $1000 = 1 second $1000 = .8 third = .6 fourth = .4 Option #1 gives us 2.4 whereas option #2 gives us 2.24. I'd argue that we can similarly rank the losses the same: first $1000 lost = -1 second = -.8 etc. which gives us -2.4 vs --2.24 meaning we should obviously take the option #2. Now the interesting question is why we can assign similar yet negative values for the losses. I'll give two examples that might show why this is true. First, consider living paycheck to paycheck. I only have $500 of buffer. In this case, while losing $2000 instead of $1000 is worse, it's not worse by a lot because either way I can't afford rent and I'm evicted. As a second example, consider bankruptcy. If we take losses to high values, eventually each additional loss doesn't subtract anything from my "happiness". I've already hit the bankruptcy point and nothing worse can happen. These are of course the two extremes, but I think it's easy to complete the spectrum and show that for any $x the first loss of $x hurts more than the second loss of $x.