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It would be nice to have a site like electionbettingodds.com but with intervals rather than point preditions. Given the betting odds it's possible to calculate

It would be nice to have a site like electionbettingodds.com but with intervals rather than point preditions. Given the betting odds it's possible to calculate upper and lower bounds on the probabilities. Ideally you would take into account the fees and the opportunity cost of having your money locked in the bet. The bounds would be the range in which it wouldn't be possible to make an expected profit by betting either way. The advantage would be that instead of an absurd point estimate like "Michelle Obama has a 6.90% of winning the election" you'd get something like "the probability of Michelle Obama winning the election is between 7.0% and 0.01%". Which makes it clear that while the upper bound can't be driven to 0, the lower bound is perfectly sensible.

Xcelerate 3y ago
> instead of an absurd point estimate like "Michelle Obama has a 6.90% of winning the election" A probability distribution is defined over a set of outcomes. If “Michelle Obama winning” is one independent, categorical outcome, then there is one probability associated with that outcome. > you'd get something like "the probability of Michelle Obama winning the election is between 7.0% and 0.01%" Stacking another layer of probability on top of probability distributions still results in only one final distribution for prediction purposes. I think maybe what you’re trying to capture is how your “confidence” about a prediction ties into the evaluation of the reward or penalty. This would just be modulated by adjusting how wide/uniform your probability distribution is and the amount that you bet, but perhaps the websites could add some tools to help people visualize this better.
- OscarCunningham 3y ago
  Yes, I agree that in principle every person should have a probability for each event. But what does the market tell us about what our own belief should be? If you don't have any nonpublic information and you trust the market to be efficient then your assumption should be that you yourself cannot make an expected profit in the market. So the useful information from the market can be given in terms of the bounds within which you can't bet profitably. You yourself should update your probabilities to be within those bounds.
jrm4 3y ago
Again, the assumption of rationality, along with the lack of appreciation for the diminishing value of money from, e.g. whales is the silly part here. While I'd concede that "they're stupid" is probably the primary reason someone might go for the Michelle Obama bet, I can think of AT LEAST one other -- e.g, I'm insanely rich Tyler Perry, and I just like the idea of that being in the air?

Xcelerate 3y ago

> instead of an absurd point estimate like "Michelle Obama has a 6.90% of winning the election" A probability distribution is defined over a set of outcomes. If “Michelle Obama winning” is one independent, categorical outcome, then there is one probability associated with that outcome. > you'd get something like "the probability of Michelle Obama winning the election is between 7.0% and 0.01%" Stacking another layer of probability on top of probability distributions still results in only one final distribution for prediction purposes. I think maybe what you’re trying to capture is how your “confidence” about a prediction ties into the evaluation of the reward or penalty. This would just be modulated by adjusting how wide/uniform your probability distribution is and the amount that you bet, but perhaps the websites could add some tools to help people visualize this better.

OscarCunningham 3y ago
Yes, I agree that in principle every person should have a probability for each event. But what does the market tell us about what our own belief should be? If you don't have any nonpublic information and you trust the market to be efficient then your assumption should be that you yourself cannot make an expected profit in the market. So the useful information from the market can be given in terms of the bounds within which you can't bet profitably. You yourself should update your probabilities to be within those bounds.

jrm4 3y ago

Again, the assumption of rationality, along with the lack of appreciation for the diminishing value of money from, e.g. whales is the silly part here. While I'd concede that "they're stupid" is probably the primary reason someone might go for the Michelle Obama bet, I can think of AT LEAST one other -- e.g, I'm insanely rich Tyler Perry, and I just like the idea of that being in the air?