If there was a voting among those 5 people to decide which strategy to be adopted, which one do you think would be adopted? What are the factors contributing to that decision making process?
By pure statistical game of chance and assuming everyone wants to maximize their money, in the first case, the expected amount is $20 and in the second case also, it is (1/5)*$80 + (4/5)*$5 = $20 because there is a 20% chance of getting $80 & 80% chance of getting $5. The expected amounts being same, in the second case there is a remote chance of getting $80 and so based on rational behavior probably people will pick the second strategy.
However, to get into more statistical measures to help making a rational decision, it is good to note that in the first case, standard deviation is zero and the in the second it is 30 meaning higher risk or higher uncertainty associated with it.
By borrowing the following line from wikipedia, "The overall concept of risk is that as it increases, the expected return on the asset will increase as a result of the risk premium earned – in other words, investors should expect a higher return on an investment when said investment carries a higher level of risk, or uncertainty of that return."
One can argue in this example that the expected return did not increase then why should one take the risk of taking the second strategy? Rather if someone is rational they should adhere to the first strategy where there is no risk and fixed return. So, as behavioral economists assume that individuals behave rationally to maximize their utility function may not be a very sound assumption.
Can it be generalized to say, the first strategy is boring and it is socialism(in some form) and the second one is capitalism with it's inherent excitement of making big or losing big, I believe the latter being more prevalent these days of economic turbulence.
