I initially chose 1A and 2B, but after reading the analysis of those decisions, I agree that they are inconsistent in a way that implies that one choice was irrational (in the context of this silly little game). So I did some introspection to figure out where I went wrong. Here’s what I found:
1) I may have misjudged how small 1⁄34 is, and this only became apparent when the question was phased as it is in example 2.
2) I think I assumed an implicit costs in these gambles. The first cost is a delay in learning the outcome of these gambles; the second is the implicit need to work to earn this money. I think that these assumptions are reasonable because there is essentially no realistic condition in which I would instantly see the results of a decision that might earn me $27,000; there would probably be a delay of several months (if working) or years (if investing) between making the decision and learning whether I got the money or not. This prolonged uncertainty has a negative utility, since I am unable to make firm plans for the money during that interval. This negative utility would apply to all options except 1A. Furthermore, earning $24,000 would realistically require several months of work on my part. However, a project that had a 1⁄3 chance of paying out $24,000 might only take a month. The implicit difference in opportunity cost between scenario 1 and scenario 2 has implications for the marginal utility of money in each scenario (making me more risk-averse in scenario 1, which implicitly has a higher opportunity cost).
These implicit costs are not specified in this game, so it is technically “irrational” to incorporate them into my decision-making. However, in any realistic scenario, such costs will exist (regardless of what the salesman says), so it is good that I/we intuitively include them in my/our decision-making.
I initially chose 1A and 2B, but after reading the analysis of those decisions, I agree that they are inconsistent in a way that implies that one choice was irrational (in the context of this silly little game). So I did some introspection to figure out where I went wrong. Here’s what I found:
1) I may have misjudged how small 1⁄34 is, and this only became apparent when the question was phased as it is in example 2.
2) I think I assumed an implicit costs in these gambles. The first cost is a delay in learning the outcome of these gambles; the second is the implicit need to work to earn this money. I think that these assumptions are reasonable because there is essentially no realistic condition in which I would instantly see the results of a decision that might earn me $27,000; there would probably be a delay of several months (if working) or years (if investing) between making the decision and learning whether I got the money or not. This prolonged uncertainty has a negative utility, since I am unable to make firm plans for the money during that interval. This negative utility would apply to all options except 1A. Furthermore, earning $24,000 would realistically require several months of work on my part. However, a project that had a 1⁄3 chance of paying out $24,000 might only take a month. The implicit difference in opportunity cost between scenario 1 and scenario 2 has implications for the marginal utility of money in each scenario (making me more risk-averse in scenario 1, which implicitly has a higher opportunity cost).
These implicit costs are not specified in this game, so it is technically “irrational” to incorporate them into my decision-making. However, in any realistic scenario, such costs will exist (regardless of what the salesman says), so it is good that I/we intuitively include them in my/our decision-making.