Personal Risk, Self-Esteem and the St. Petersburg Lottery

There used to be an unsolved problem in economics:  if there were a lottery that consisted of a coin toss, and the pot doubled every day starting from a penny, how much should you pay for a ticket?  (St. Petersburg Russia in fact had such a lottery at once time, hence the name.)  It's not so straightforward.  If there's a lottery where you have a 1% chance of winning a thousand dollars, you should be willing to pay about 10.  But what about this one? 

Standard economic theory used to say that we should be willing to pay a huge, if not infinite amount to buy a ticket, but few people are.  The solution has to do with the fact that the richer you are, the more you're willing to pay for a ticket.  That is to say, once you take into account how much it "hurts" someone to part with a certain sum, then you have your solution.  And it  hurts Bill Gates less to part with $100 than it does you or me; the same sum lost translates to fewer "points off" his utility.  Consequently, we shouldn't be surprised that it's the people who have a lot to begin with who are more willing to venture it to get more.  The perverse effect of this is that the more you have, the more you risk, and the more still you end up making in the end if your bets are rational.

What does this have to do with self-esteem?  Humans are status-driven creatures, which is to say our status is also strongly connected to our utility.  So are there marginal status effects?  Is there a status-equivalent to the St. Petersburg lottery?  Imagine someone who is extremely self-confident, for whatever reason (more on these reasons later).  He has a large reserve of status, at least in his own view of himself.  As with Bill Gates, he will get fewer points off his utility for the same status-losing failure or transgression than the rest of us might.  Therefore, these very self-confident people are more willing to risk status, in order ultimately to gain status.  There are several reasons for confidence that make sense of certain behaviors:


- A confident individual might be "justified" in their view of their status in the sense of a social or professional track record that is publicly recognized, and be willing to go out on otherwise socially unacceptable or status-threatening ventures to achieve more.  The wealthy and successful engaging in ventures that can fail in public are an example of this.

- The individual might be isolated from a peer-group's judgment; he might be a foreigner, or around people in a different socioeconomic class.  A failure seen by you, a mere native, is less skin off their back than if seen by someone from back home or from their good schools.  This might account for the strange burst of assertiveness, innovation and even comfort that people feel when working overseas.

- The individual might just be innately very self-assured.  He's not motivated by status and doesn't much care what others think.  In other words, the status-to-utility conversion factor is small.


These provide testable predictions and if correct, could result in improved innovation.