"Yup.  It's one of several coherence properties that this solution has, called 'equal treatment of equals'.  Another example of an obvious coherence property is that the sum over every agent's fair distribution equals the total distribution - we don't have any jellychips left over.  Yet another coherence property is that combining two games into a single game will make the agent's fair reward be the sum of their fair rewards in the component games.  Or another obvious-sounding one, if your marginal production is zero for every permutation, your fair reward is also zero."

"Would you say those four properties sound like properties that every fair formula for a game like this one ought to have?  Again, that's identical agents being treated identically, distributing all of the gains, the reward for playing two games is the sum of the reward for playing the games separately, and agents who contribute nothing receive nothing."

"Yup.  Identical tokens getting identical payouts is one of several coherence properties that this solution has, called 'equal treatment of equals'.  Another example of an obvious coherence property is that the sum over every agent's fair distribution equals the total distribution - we don't have any jellychips left over.  Yet another coherence property is that combining two games into a single game will make the agent's fair reward be the sum of their fair rewards in the component games.  Or another obvious-sounding one, if your marginal production is zero for every permutation, your fair reward is also zero."

"Would you say those four properties sound like properties that every fair formula for a game like this one ought to have?  Again, that's identical agents being treated identically, distributing all of the gains, the reward for playing two games is the sum of the reward for playing the games separately, and agents who contribute nothing receive nothing."

"Yup.  Identical tokens getting identical payouts is one of several coherence properties that this solution has, called 'equal treatment of equals'.  Another example of an obvious coherence property is that the sum over every agent's fair distribution equals the total distribution - we don't have any jellychips left over.  Yet another coherence property is that combining two games into a single game will make the agent's fair reward be the sum of their fair rewards in the component games.  Or another obvious-sounding one, if your marginal production is zero for every permutation, your fair reward is also zero."

"Would you say those four properties sound like properties that any fair formula for a game like this one ought to have?  Again, that's identical agents being treated identically, distributing all of the gains, the reward for playing two games is the sum of the reward for playing the games separately, and agents who contribute nothing receive nothing."