> I don't think there's a constraint on "Nate Silver has a probability model" that mathematically guarantees "Nate Silver's probability model" is correct
If I'm understanding the article correctly, it's not talking about models being "correct," it's just talking about the probabilities of all the outcomes adding up to 100%, which means you can't place a bet that guarantees you make money regardless of the outcome.
In other words, offering a bet that was based on the claim that there is a 99% chance of rain today in the Atacama Desert, and a 1% chance of no rain there, is arbitrage-free. It's still clearly a poor probability model for one of the driest places on Earth, but it's arbitrage-free.
If I'm understanding the article correctly, it's not talking about models being "correct," it's just talking about the probabilities of all the outcomes adding up to 100%, which means you can't place a bet that guarantees you make money regardless of the outcome.
In other words, offering a bet that was based on the claim that there is a 99% chance of rain today in the Atacama Desert, and a 1% chance of no rain there, is arbitrage-free. It's still clearly a poor probability model for one of the driest places on Earth, but it's arbitrage-free.