Trom
November 19, 2009, 4:09pm
41
iamthewalrus_3:
The marginal utility of money is not constant. In particular, there is tremendous emergent value in hitting a certain threshold of money that is life-changing.
It’s the same reason that purchasing insurance (paying a small downside to eliminate a small risk of a large downside) is rational, even though the expected value is negative. Playing the lottery is paying a small downside to add a small chance of a large upside. The small downside can be easily absorbed into one’s current economic state, while the potential large swings are paradigm-shifting.
Looked at another way, it’s because we’re risk-averse and dealing with a small enough sample size (lifespan) that significant deviation from the mean is likely.
Would I take a 51% chance to bet a dollar and win 2? Sure, I guess, but I’d be bored by it.
Would I take a 51% chance to bet $100,000 and win $200,000? Hell no. It would wipe me out if I lose.
Would I take a 0.00000051% chance to bet a dollar and win $2 million? That sounds like fun.
All three bets have the same expected value (per dollar bet). But they absolutely don’t have the same expected utility. It turns out that the utility of the last bet has a lot more to do with the $2 million payoff than it does with the chance of winning. You can make the odds much worse, and people will still happily (and rationally!) play the last bet, just because $2 million is so much, and $1 is so little.
Thanks for the explanation. I see where you’re coming from. Though, in your example, I would argue that all of those bets, on their face, are rational bets (They have a positive EV). Only when we factor in the bettors’ financial situations might they become irrational.
It would be interesting to expand on this topic while considering cumulative prospect theory .
The main observation of CPT (and its predecessor Prospect Theory) is that people tend to think of possible outcomes usually relative to a certain reference point (often the status quo) rather than to the final status, a phenomenon which is called framing effect. Moreover, they have different risk attitudes towards gains (i.e. outcomes above the reference point) and losses (i.e. outcomes below the reference point) and care generally more about potential losses than potential gains (loss aversion). **Finally, people tend to overweight extreme, but unlikely events, but underweight “average” events. **The last point is a difference to Prospect Theory which assumes that people overweight unlikely events, independently of their relative outcomes.
Bolding mine.
Wouldn’t the end result of your logic result in a situation where poorer people would give their money to rich people running a large payout lottery with a small edge, and both parties could claim to be acting rationally?