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.
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.