These problems seem less acute if you instead break apart conditionals into a base question and a conjunctive market (like this one for the Democratic VP question), where you don’t have the possibility of a N/A resolution blowing a hole in the pricing.
But now you have the new problem that most of the probabilities in the conjunctive market are so close to the risk free interest rate that it’s hard to get signal out of them.
For example, suppose I believed that Mark Kelly would be a terrible pick and cut Harris’s chances in half, and I conclude that therefore his price on the conjunctive market should be 2% rather than 4%. Buying NO shares for 96 cents on a market that lasts for several months is not an attractive proposition when I could be investing mana elsewhere for better returns, so I won’t bother and the market won’t incorporate my opinion.
Also, I believe prices on Manifold can only be whole number percents, which is another obstacle to getting sane conditional probabilities out of conjunctive markets.
I agree, these conditionals are pretty sensitive to small inefficiencies in pricing when the probability is low. It does suck. Perhaps one day we will have markets denominated in appreciating assets, so you can be exposed to general growth while you’re also exposed to your bet on the market.
Also, I believe prices on Manifold can only be whole number percents, which is another obstacle to getting sane conditional probabilities out of conjunctive markets.
Fortunately that’s not true, though it does seem to only display one decimal place below the integer percent.
Could you make it more clear how you would change the original Harris market to avoid the problem? I’m not sure what exactly you mean by “base question and a conjunctive market”. I figure you’re talking about the “other” option in the market you link, which prevents N/A. But how do you add that to the Harris market? Is it just adding one more option “Another person not listed here is nominee and Harris wins”?
Similar to what Ben said, you work out the conditional probabilities from other markets.
First, here’s a fact about probabilities that you’ll need to use: the probability of “A conditional on B” (for example, “Harris wins conditional on choosing Walz as her VP”) is equal to probability of “A and B” ÷ probability of “B” (so, “The Harris-Walz ticket wins” ÷ “Walz is the VP”) .
So whenever you want to know P(A|B) (the probability of “A conditional on B”), you can instead ask P(A&B) (probability of “A and B”) and P(B).
That’s what the linked market (more-or-less) does. It asks “who will be the next US VP?”. This is basically asking “if the presidential candidate picks this person as the VP, will their ticket win?”. You can divide this by the probability “will the relevant presidential candidate pick this person as VP”, to get the conditional probability you want.
My guess is that you just don’t have any conditionals, but work them out from other markets.
Eg. One market on “Harris wins with X on the ticket”, one on “Harris looses with X on the ticket”, “Harris chooses X for VP” and so on. Then the chances of her winning, conditional on different candidates, can be worked out by comparing how these markets are doing.
These problems seem less acute if you instead break apart conditionals into a base question and a conjunctive market (like this one for the Democratic VP question), where you don’t have the possibility of a N/A resolution blowing a hole in the pricing.
Yes, and I gained some easy mana from such markets; but the market that got the most attention by far was the intrinsically flawed conditional market.
But now you have the new problem that most of the probabilities in the conjunctive market are so close to the risk free interest rate that it’s hard to get signal out of them.
For example, suppose I believed that Mark Kelly would be a terrible pick and cut Harris’s chances in half, and I conclude that therefore his price on the conjunctive market should be 2% rather than 4%. Buying NO shares for 96 cents on a market that lasts for several months is not an attractive proposition when I could be investing mana elsewhere for better returns, so I won’t bother and the market won’t incorporate my opinion.
Also, I believe prices on Manifold can only be whole number percents, which is another obstacle to getting sane conditional probabilities out of conjunctive markets.
I agree, these conditionals are pretty sensitive to small inefficiencies in pricing when the probability is low. It does suck. Perhaps one day we will have markets denominated in appreciating assets, so you can be exposed to general growth while you’re also exposed to your bet on the market.
Fortunately that’s not true, though it does seem to only display one decimal place below the integer percent.
Could you make it more clear how you would change the original Harris market to avoid the problem? I’m not sure what exactly you mean by “base question and a conjunctive market”. I figure you’re talking about the “other” option in the market you link, which prevents N/A. But how do you add that to the Harris market? Is it just adding one more option “Another person not listed here is nominee and Harris wins”?
Happy to clarify.
Similar to what Ben said, you work out the conditional probabilities from other markets.
First, here’s a fact about probabilities that you’ll need to use: the probability of “A conditional on B” (for example, “Harris wins conditional on choosing Walz as her VP”) is equal to probability of “A and B” ÷ probability of “B” (so, “The Harris-Walz ticket wins” ÷ “Walz is the VP”) .
So whenever you want to know P(A|B) (the probability of “A conditional on B”), you can instead ask P(A&B) (probability of “A and B”) and P(B).
That’s what the linked market (more-or-less) does. It asks “who will be the next US VP?”. This is basically asking “if the presidential candidate picks this person as the VP, will their ticket win?”. You can divide this by the probability “will the relevant presidential candidate pick this person as VP”, to get the conditional probability you want.
My guess is that you just don’t have any conditionals, but work them out from other markets.
Eg. One market on “Harris wins with X on the ticket”, one on “Harris looses with X on the ticket”, “Harris chooses X for VP” and so on. Then the chances of her winning, conditional on different candidates, can be worked out by comparing how these markets are doing.