The set of potential multicolored variations of Swans is infinite (purple, brown, grey, blue, green, etc). We can not prove any one of them do not exist. But every day that proceeds where we don’t see these swans gives us a higher probability they do not exist. It never equals 1, but it’s darn close.
The problem with the Black Swan parable is not that it’s untrue, but rather unimportant. The set of things we have no evidence of is infinite. To then pounce across an unexpected observation (eg, a Black Swan, that Kevin Federline is a relatively good parent, last week’s liquidity run on mortgage lenders), and say, “aha! You were all wrong!” merely sets up a staw man, that everything we reasonably don’t anticipate and plan for is assumed to have had a probability of zero.
In reality, when you want to pay money for extreme events you overpay, that is, the implied probability is overweighted because sellers can’t insure against these events. London bookmakers offer only 250-1 odds against a perpetual motion machine being discovered, 100-1 that aliens won’t be proven. In option markets you have a volatility smile so that extreme events get higher and higher implied volatilities as you move away from the mean, meaning their probability is not assumed Gaussian.
The bottom line is that “absence of evidence is not evidence of absence” merely uses hindsight to attack a caricature of beliefs, and seems to suggests something practically important. In practice, people lose money on lottery tickets (or hurricane insurance, or buing a 3-delta put), so exploiting this is a fool’s game.
per the Black Swan:
The set of potential multicolored variations of Swans is infinite (purple, brown, grey, blue, green, etc). We can not prove any one of them do not exist. But every day that proceeds where we don’t see these swans gives us a higher probability they do not exist. It never equals 1, but it’s darn close.
The problem with the Black Swan parable is not that it’s untrue, but rather unimportant. The set of things we have no evidence of is infinite. To then pounce across an unexpected observation (eg, a Black Swan, that Kevin Federline is a relatively good parent, last week’s liquidity run on mortgage lenders), and say, “aha! You were all wrong!” merely sets up a staw man, that everything we reasonably don’t anticipate and plan for is assumed to have had a probability of zero.
In reality, when you want to pay money for extreme events you overpay, that is, the implied probability is overweighted because sellers can’t insure against these events. London bookmakers offer only 250-1 odds against a perpetual motion machine being discovered, 100-1 that aliens won’t be proven. In option markets you have a volatility smile so that extreme events get higher and higher implied volatilities as you move away from the mean, meaning their probability is not assumed Gaussian.
The bottom line is that “absence of evidence is not evidence of absence” merely uses hindsight to attack a caricature of beliefs, and seems to suggests something practically important. In practice, people lose money on lottery tickets (or hurricane insurance, or buing a 3-delta put), so exploiting this is a fool’s game.