Suppose that the Ebborians gamble. What odds would it give for event X?
Suppose ve gives odds of 2:1 (probability of 2⁄3). A bookie takes the bet, and in half of the branches, collects 2 (from the two “descendants”), and in half of the branches, pays out 1, for an average profit of 0.5.
I think your argument leads to the Ebborians being vulnerable to Dutch books.
Er, your math is the wrong way around, but your point at first seems right: the Ebborian sees 2⁄3 odds, so ve is willing to pay the bookie 2 if X doesn’t happen, and get paid 1 (split between copies, as in correlated decision theory) if X does happen.
However, if instead the Ebborian insists on paying 2 for X not happening, but on each copy receiving 1 if X happens, the Dutch book goes away. Are there any inconsistencies that could arise from this sort of policy? Perhaps the (thus developed) correlated decision theory only works for the human form of subjective probability? Or more probably, I’m missing something.
Suppose that the Ebborians gamble. What odds would it give for event X?
Suppose ve gives odds of 2:1 (probability of 2⁄3). A bookie takes the bet, and in half of the branches, collects 2 (from the two “descendants”), and in half of the branches, pays out 1, for an average profit of 0.5.
I think your argument leads to the Ebborians being vulnerable to Dutch books.
Er, your math is the wrong way around, but your point at first seems right: the Ebborian sees 2⁄3 odds, so ve is willing to pay the bookie 2 if X doesn’t happen, and get paid 1 (split between copies, as in correlated decision theory) if X does happen.
However, if instead the Ebborian insists on paying 2 for X not happening, but on each copy receiving 1 if X happens, the Dutch book goes away. Are there any inconsistencies that could arise from this sort of policy? Perhaps the (thus developed) correlated decision theory only works for the human form of subjective probability? Or more probably, I’m missing something.
From the bookie’s perspective, the “each copy” deal corresponds to 1:1 odds, right?