Equivalent changes/differences for percentages and probabilities

For percentages and probabilities or other fractions that have to lie between zero and one, it is not legitimate to take equal proportionate or absolute differences for two variables to register equivalent changes, since this may require one variable to exceed one. Reasonable properties for equivalent changes including Interchangeability, Parity, Identity, Differentiability, Monotonicity, Complementarity, Anonymity, and Transitivity are proposed. A specific function satisfying all these properties is provided and the question of the uniqueness of this function is discussed. The acceptance of the proposed function may lead to widespread practical application.