I think Yvain is right and you’re wrong. The Shapley value takes as input the whole game, not a certain play of the game, so it doesn’t know that you actually voted for Hitler and the other guy didn’t.
The formula for the Shapley value (from the wiki article):
What this means is you take all sub coalition S of the total coalition N, excluding sub coalition that include yourself. Then average over the difference in value of the sub coalition S plus yourself and just the sub coalition S. (The first term in the sum makes it a weighted average depending on the sizes of S and N.) These sub coalitions S, and S plus yourself, did not actually happen, you are considering the counterfactual value of those being the actual coalitions.
The point is that the formula knows how your inclusion in a coalition changes its value.
I think Yvain is right and you’re wrong. The Shapley value takes as input the whole game, not a certain play of the game, so it doesn’t know that you actually voted for Hitler and the other guy didn’t.
The formula for the Shapley value (from the wiki article):
What this means is you take all sub coalition S of the total coalition N, excluding sub coalition that include yourself. Then average over the difference in value of the sub coalition S plus yourself and just the sub coalition S. (The first term in the sum makes it a weighted average depending on the sizes of S and N.) These sub coalitions S, and S plus yourself, did not actually happen, you are considering the counterfactual value of those being the actual coalitions.
The point is that the formula knows how your inclusion in a coalition changes its value.