Proves no anonymous strict tie-breaking rule exists when symmetric inputs are possible, characterizes a unique orbit-partition rule for non-strict outputs, and shows every reasonable strict rule decomposes into that partition plus arbitrary completion.
Shapley,A value forn-person games, inContributions to the Theory of Games, Volume II(H
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An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition
Proves no anonymous strict tie-breaking rule exists when symmetric inputs are possible, characterizes a unique orbit-partition rule for non-strict outputs, and shows every reasonable strict rule decomposes into that partition plus arbitrary completion.