“if I tell you an event has a 0% chance of occurring, I cannot change my mind and tell you tomorrow it now has a 50% chance of occurring. Otherwise I shouldn’t have told you it has a 0% chance in the first place”
I think this is the key to Taleb’s argument, and it’s pretty damning for Mr Siver.
If there’s high uncertainty, you can’t say whether someone’s probability to win is low. The uncertainty widens the probability.
For example,
Say I told you there’s a 2% chance it will rain Monday next year in New York
- This would _have_ to be a bogus prediction. So much could happen until then. I have _high_ uncertainty. There’s no way that uncertainty is accounted for with 2%
The prediction should have more data to it about variance, but it isn't necessarily wrong.
We have good data about rain, I am sure we could find out what percentage of the time it rains in New York on a given day during that time of the year. There might be high variance, but that doesn't mean it is wrong to say there is a 2% chance it rains on a particular Monday.
This is how insurance works, how sports betting works, how option pricing works. Just because something has high variance doesn't mean we can't give probabilities that work out over a large number of samples.
Imagine someone offered you this as a bet. They’ll pay you 3 dollars if it rains Monday next year. Otherwise you pay them 90 dollars.
Now, it’s pretty intuitively clear that at a year interval, there’s way too much uncertainty to take this bet. If you accounted for it, you would approach something like the average chance of raining on any particular day in November in New York.
You are right that with enough data, you would be able to price this correctly.
Taleb’s point is that Nate is not doing that, by demonstration: since Nate’s models oscillated so much, it demonstrates that he did not account for it.
First, your odds don't make sense. It wouldn't be 30x more likely to rain than not on a particular day. However, this is a detail and not that important.
Second, though, is that people make highly uncertain bets all the time, and the price for those bets DOES fluctuate wildly over time.
For example, you can currently place bets at a number of sports books for the winner of next year's NBA finals. There is a TON of uncertainty (we don't even know who is going to be on teams, free agency and the draft haven't happened yet... not to mention injuries, player improvement, etc)
That uncertainty is priced into the bet, and people will take both sides of that bet.
As the year progresses and things happen, that price will fluctuate as we get more information and we get closer to the finals. The favorite might change, and a 200 to 1 might end up being a 10 to 1 by the time the finals gets here.
It isn't that the odds were WRONG at the earlier time, they just had less information. It doesn't mean the odds makers didn't understand what the state of the world was, or that they didn't take into account the uncertainty of what could happen.
I am not quite following you... the "price" of a bet is synonymous with the odds (i.e. they are two different ways of expressing the same information). For example, the money line price of something that has a 90% chance of winning would be `-900`... meaning you have to bet $900 to win $100.
No one has odds that say the Warriors (or any team) has a 90% chance of winning the NBA title. In fact, the current favorite (the Lakers) are listed at +350 (meaning you will win $450 on a $100 bet).
I am not sure what you mean by the 90% chance thing...
> For example, the money line price of something that has a 90% chance of winning would be `-900`... meaning you have to bet $900 to win $100.
This is what Nate saying, when he says Biden has a 90% chance of winning.
You intuit correctly that it would be ridiculous for anyone to offer odds like that for the NBA title one year out.
Why do you think it would be ridiculous? Likely because you intuit that there's too much uncertainty for a chance to be 90% for any team to win the NBA title.
Taleb's reasoning is similar, but for the election. 90% Biden win implies way too much certainty.
> Say I told you there’s a 2% chance it will rain Monday next year in New York - This would _have_ to be a bogus prediction.
Yet betting odds exist, because we can predict things far into the future accounting for variance and risk by looking at history. If it's never rained on 2% of Monday's in NYC then a 2% prediction would make sense.
From the article:
> Premise 1: If you give a probability, you must be willing to wager on it
The best way to settle this is have Talib bet on Trump to win at 50% odds (or whatever he thinks is appropriate) every day up until the election and Silver to bet using his odds (currently around 10%). May the more accurate prediction prevail. Too late for this election, but there will be plenty more elections in the future.
Most betting markets are at 66%. That I believe is for who is sworn in in January.
Silver's forecast is slightly different. It's for who will win if all votes are counted and no courts intervene.
Given that Biden's lead in states exceeding 270 electoral votes is above the polling margin of error and even above an unexpected 2016 sized error, and that Trump would need a clean sweep of all 7 swing states, 90% isn't crazy considering Trump is an incumbent with a low 40% approval rating.
The extra 23% the betting markets are giving Trump are probably because of the courts and some 2016 "anything could happen" bias. The Supreme Court is conservative as are some of the attorney generals in the swing states. In 2000 that proved decisive and is probably an easier path to victory for Trump than winning a clean vote.
In 2016 Trump had a forecasted 30% chance to win. He lost the popular vote by 3M, but won 3 decisive swing states by a combined 80k votes. The betting markets assist to be giving him about the same 30% chance as 2016 even though the polling, approval rating, undecideds, etc. are all decidedly worse for him this time around.
Yeah, except both of them are modeling how people will vote, and people change their minds.
Saying that one should’ve held a constant chance of a candidate winning no matter what the polls do is frankly insane. This stance basically requires that you pretend that the outcome is determined and that voters opinions either don’t matter or don’t change. It’s utter nonsense, especially since we know that in 2016 undecided voters broke late for Trump. If your model doesn’t react to that, what are you even modeling?
Taleb’s point is not that your prediction should not change.
His point is that if it does change, and frequently at that, the purported 90% chance at t(n) is bogus. That prediction needed to account for the volatility
I think this is the key to Taleb’s argument, and it’s pretty damning for Mr Siver.
If there’s high uncertainty, you can’t say whether someone’s probability to win is low. The uncertainty widens the probability.
For example, Say I told you there’s a 2% chance it will rain Monday next year in New York - This would _have_ to be a bogus prediction. So much could happen until then. I have _high_ uncertainty. There’s no way that uncertainty is accounted for with 2%