Sunday, April 17, 2011

Prince William and Kate – Let the Market Decide

Apparently, Brits will bet on anything. I was just watching the BBC and there was a short clip on questions Brits were asking and what bookies were placing in terms of odds of various events happening at the wedding: Kate’s car breaking down, Prince Harry dropping the ring etc.

This got me to thinking about mathematically predicting the future. Not just in physical models (for instance forecasting weather) which is difficult enough, but also in these sort of abstract ideas. After all, how do you predict what is Prince Harry’s chance of dropping the ring? Let’s say you could even come up with a very convincing model that would give you one good guess.

Another method would be to let the invisible hand of the gambling market decide. Assuming you could get enough interested people to bid in the “market” on an individual question, having more or less people bid for or against any particular question can give you an indication as to whether the odds offered are too “generous” and allow you to recalibrate the odds directionally until you arrive at a relatively stable number.

For example, when asked: “What’s the chance of the Queen wearing a blue hat?” initially it’s even odds. However, people start doing their homework, statistical multi-factor regressions, etc and discover that she actually tends to wear a blue hat quite often (especially at royal weddings) and people starting overwhelmingly taking bets that she will wear a blue hat. If the bookie is paying attention, they will start moving the odds, maybe now offering 2:1 odds that she will wear a blue hat. People start fine tuning their model and continue to make bets until the odds rest at 3:1 (the current odds of the Queen wearing a blue hat). The bookie takes bets on either side taking the spread.

The invisible hand of the gambling market has determined the probability of the Queen wearing a blue hat. While we aren’t even sure what models were used, assuming intelligent people using real money have staked a “best guess” at what the appropriate value for the probability of the Queen wearing a blue hat is, we are given another robust answer.

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Another method would be to let the invisible hand of the gambling market decide. Assuming you could get enough interested people to bid in the “market” on an individual question, having more or less people bid for or against any particular question can give you an indication as to whether the odds offered are too “generous” and allow you to re-calibrate the odds directional until you arrive at a relatively stable number.