A NEW DEGREE OF FREEDOM FOR OPINION DYNAMICS MODELS: THE ARBITRARINESS OF SCALES

The paper explicitly proves MG(e^S) = e(MA(S)) and notes the analogous equivalence for MH via h(x)=1/x, establishing that MA, MG, and MH are conjugate under scale transforms; it also shows MA’s affine equivariance and MG’s failure under linear rescaling, and gives MG’s power-rescaling invariance MG(β x^n)=β[MG(x)]^n, thereby refuting the idea of a single universally best scale . The candidate solution follows the same algebraic conjugacy and invariance arguments and reaches the same conclusions, with a minor slip claiming MG(0,1) is undefined (it is defined and equals 0 on [0,1]).