# Summary

• Nathan Young thinks conditional prediction markets can provide a lot of value
• It will be easy to run them in a way that upsets consumers or costs a lot
• Conditional markets don’t resolve ambiguously they resolve positively for the outcome that happens and negatively for everything else
• It will be easy to run them in a way that doesn’t create value
• Conditions and outcomes aren’t independent for unlikely conditions, many outcomes may be very skewed
• Will the UK Prime Minister win an election if she hold one in 6 weeks? At first glance, probably not. But she will only hold an election if she thinks it is advantageous. The chance of an election is very small, and most outcomes are more favourable than the mental picture we see at first.
• There is a way to run them well, in Nathan’s opinion

# The case for conditional markets:

• I assume the reader believes in the information value of prediction markets
• Information is valuable because it helps make better choices in the world
• Therefore, if the information is valuable, information conditional on decisions focuses that information on the correct point

Problems explained and solutions explained next

# Conditional markets could cause money and create problems

Ways to lose money running conditional prediction markets

• Consider the following example
• You run a market on if X will happen or not, given Y (imagine it’s arsenal win, given they start with Holding)
• Aaron buys some X|Y for $20 • The price rises to$50
• He sells it to Bella and makes $30 • Y doesn’t happen. The market resolves ambiguously • How much do we pay Aaron and Bella? • Do we pay Bella$50? Here we will have lost money, since we only sold to Aaron at $20 • Do we pay Bella nothing, and Aaron$20? This seems deeply unfair. Bella would never have bought the share if she knew this was happening
• Do we pay Bella the last price the market was at? This would lead to the market being pumped before close
• What do we do?
• The correct answer is that one part of the question is flawed. The market does not resolve ambiguously. It resolves negatively. We aren’t predicting X|Y we are predicting X∩Y. If someone wants to predict X|Y they will end up buying shares that behave differently before and afterwards
• The right want to run this market
• There are four types of shares.
• X∩Y, (not X)∩Y, X∩(not Y) and (not X)∩(not Y)
• Aaron buys some shares for $20 at 20% • He gets an amount of X∩Y and X∩(not Y) • Together these shares are equivalent to shares on X (together, he’ll get a payout of$100 if arsenal win)
• Let’s assume that both of X∩Y and X∩(not Y) start at 20% too. If Y happens, the X∩Y shares are worth $20 if Y doesn’t happen the X∩(not Y) are worth$20
• Now if the X∩Y shares go up in value (20% to 50%) and he sells them to Bella, he can’t sell them for $50. That’s not what they are worth. They are only part of the shares he originally bought. • To know the price he sells, we need to know the likelihood of Y. If Y is very likely, then 50% in the X∩Y market is worth nearly$50

The process solution

• Frame them like [multiplier] bets where many outcomes have to happen in a row
• I’m told horse racing already has this

Questions:

• Can’t you just bet on if it happen and if it doesn’t.
• Not if you want people to be able to take money out halfway through

## Conditional markets with useful probabilities

• What’s the chance that if UK PM, Liz Truss, calls an election in 3 months and she wins it?
• The chance might seem low. But Truss isn’t stupid, she will only call elections she might win.
• So really, the chance of an election is mostly full of outcomes which do better than we expect, because we imagine her being forced to call an election
• Likely many of these are very unlikely situations where she experiences once in a generation popularity increases
• So to let us know whether it would be a good decision, we need to cut the probability space so that the good outcomes we remove are roughly equivalent to the bad outcomes that our condition removes.
• That way we are conditioning on a space which looks roughly like the real space.

The process solution

• Consider what kind of outcomes the condition will cause
• Attempt to balance in the other direction
• UK early election
• PM’s approval rating goes above +2
• Rating below +2, early election, wins
• Rating below +2, early election, loses
• Rating below +2, later election, wins
• Rating below +2, later election, wins
• Fire the CEO market
• Stock market tanks more than 2 weeks before shareholder meeting
• Stock goes up with CEO
• Stock goes up with new CEO
• Stock goes down with CEO
• Stock goes down with new CEO
• The nice thing is, that if the unlikely scenarios become relevant you can create new options and give people bets in both.

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