Rationality's definition must remain independent of symmetry to stay testable. [definitional]
We must be careful not to make symmetry part of the definition of rationality; to do so would destroy the empirical relevance of the theory and simply make symmetry an independent axiom. We must have a plausible definition of rationality that does not mention symmetry and show that asymmetry in the bargaining expectations would be inconsistent with that definition.
DEFINE: Clarifies that rationality must be defined without reference to symmetry, so that symmetry can be derived as a consequence rather than assumed.
Thomas C. Schelling, The Strategy of Conflict, loc. 650