Mathematical symmetry fails as a guiding principle when values remain hidden [causal]
The uncertainty that can usually be presumed to exist about each other’s value systems also reduces the usefulness of the concept of mathematical symmetry as a normative or predictive principle. Mathematical symmetry cannot be perceived if one has access to only half the relevant magnitudes. To the extent that symmetry is helpful to the players in accommodating their movements to each other’s, it would tend to be symmetry of a more qualitative sort, of the kind that depends on visible context rather than underlying values.
Thomas C. Schelling, The Strategy of Conflict, loc. 283