Really, I think it would be just fine to specify win probabilities to the nearest 10%, which will register shifts of 0.4% in expected vote share. Probabilities to the nearest 10%: if it’s good enough for the National Weather Service, it’s good enough for me.
He quotes a comment that disagrees:
I disagree with Andrew that 65.7% is too precise. One reason is that intrade prices are quoted to 3 digit precision — viz., ranging from $0.00 to $10.00, with bid-ask spreads as low as 1 cent. So, for example, if I believed Nate’s formula was more accurate than Intrade, and the current quote was $6.56 bid, $6.57 ask, I would like Nate to provide more precision in order to determine whether or not to buy ‘Barack Obama to be re-elected on 2012′. Even with today’s low interest rates, I would still need Nate to forecast at least a 65.74% probability in order to believe purchasing ’Obama 2012′ at $6.57 would outperform a 0.90% money market rate over the next 18 days.
This is absurd to anyone who has traded election markets seriously. You do not trade a 0.1% edge on a market like this.
If Alice said “I need to provide a point estimate, so I think it’s 36.49284727693% likely”, we would all recognize it as absurd. So we’re just haggling over the price. In general, outside of areas where you have enough data to calibrate well, nearest 5% is all that’s meaningful.
This is separate from the probability range Bob offers, which should only be done when you specify what you mean.
I agree with Andrew Gelman that in many cases we should report probabilities with fewer significant digits.
https://statmodeling.stat.columbia.edu/2012/10/22/is-it-meaningful-to-talk-about-a-probability-of-65-7-that-obama-will-win-the-election/
He quotes a comment that disagrees:
This is absurd to anyone who has traded election markets seriously. You do not trade a 0.1% edge on a market like this.
If Alice said “I need to provide a point estimate, so I think it’s 36.49284727693% likely”, we would all recognize it as absurd. So we’re just haggling over the price. In general, outside of areas where you have enough data to calibrate well, nearest 5% is all that’s meaningful.
This is separate from the probability range Bob offers, which should only be done when you specify what you mean.