Imagine two prediction markets, both with shares that give you $1 if they pay out and $0 otherwise.
One is predicting some event in the real world (and pays out if this event occurs within some timeframe) and has shares currently priced at $X.
The other is predicting the behaviour of the first prediction market. Specifically, it pays out if the price of the first prediction market exceeds an upper threshhold $T before it goes below a lower threshhold $R.
Is there anything that can be said in general about the price of the second prediction market? For example, it feels intuitively like if T >> X, but R is only a little bit smaller than X, then assigning a high price to shares of the second prediction market violates conservation of evidence—is this true, and can it be quantified?
Imagine two prediction markets, both with shares that give you $1 if they pay out and $0 otherwise.
One is predicting some event in the real world (and pays out if this event occurs within some timeframe) and has shares currently priced at $X.
The other is predicting the behaviour of the first prediction market. Specifically, it pays out if the price of the first prediction market exceeds an upper threshhold $T before it goes below a lower threshhold $R.
Is there anything that can be said in general about the price of the second prediction market? For example, it feels intuitively like if T >> X, but R is only a little bit smaller than X, then assigning a high price to shares of the second prediction market violates conservation of evidence—is this true, and can it be quantified?