Exercise for the Reader: By separately tracking the ’s on the two redundancy conditions through the proof, show that, for this example, the coin’s true bias approximately mediates between the coinflips and Carol’s median to within , i.e., roughly 0.058 bits.
(anyone reading this should try it themselves before reading my solution—it’s immediate, you can probably do it).
To prove the mediator determines redund theorem, you apply dangly bits to each branch of the mediation diagram, each time using one of the redundancy conditions. Dangly Bits makes the errors add, so theorem really is .
(anyone reading this should try it themselves before reading my solution—it’s immediate, you can probably do it).
To prove the mediator determines redund theorem, you apply dangly bits to each branch of the mediation diagram, each time using one of the redundancy conditions. Dangly Bits makes the errors add, so theorem really is