EY believes he deserves the money with probability p.
NB believes he deserves the money with probability q.
The following rules would, I think, be considered fair by most people:
If p=q, f(p,q) should be 1⁄2.
If p=0, f(p,q) should be 0 (EY gets nothing).
If q=0, f(p,q) should be 1 (EY gets everything).
The simplest rational function obeying these conditions is f(p,q) = p/(p+q)
EY believes that EY deserves it with probability p, while NB believes that EY deserves it with probability q.
You are using the same notation the OP used to mean something different!
Really?
EY believes that EY deserves it with probability p, while NB believes that EY deserves it with probability q
Oh! You’re right. The OP’s q is 1-(my q), so this solution reduces to option (1) in the OP.
EY believes he deserves the money with probability p.
NB believes he deserves the money with probability q.
The following rules would, I think, be considered fair by most people:
If p=q, f(p,q) should be 1⁄2.
If p=0, f(p,q) should be 0 (EY gets nothing).
If q=0, f(p,q) should be 1 (EY gets everything).
The simplest rational function obeying these conditions is f(p,q) = p/(p+q)
You are using the same notation the OP used to mean something different!
Really?
Oh! You’re right. The OP’s q is 1-(my q), so this solution reduces to option (1) in the OP.