Multiplicative and additive interaction in contingency tables

The ‘multiplicative’ and ‘additive’ definitions of no-interaction in contingency tables are compared according to whether they possess or fail to possess the properties of being partitionable, closest to independence, implied by independence, amalgamation invariant, subtable invariant and of placing no constraints on the marginal probabilities. It is shown that both definitions fall short of the ideal. The author believes that the multiplicative definition is preferable by a small margin.