This paper introduces an axiomatic approach to the measures of electoral volatility between two consecutive elections, when these measures depend on the number of competing parties and the absolute value of the change in vote shares of the parties. The mathematical results on inequalities are in the basis of the theoretical developments. A one-parameter family of electoral volatility indices, based on \textit{M. N. Pedersen}'s [Eur. J. Polit. Res. 7, No. 1, 1--26 (1979; \url{doi:10.1111/j.1475-6765.1979.tb01267.x})] volatility measure, is defined. The electoral volatility measures satisfying a set of axioms (including additive separability) are characterized as those equivalent to some member of this family. Two quasi orders which permit ranking two party systems according to a class of electoral volatility indices satisfying certain axioms are studied. Finally, applications of the theoretical results to Indian state elections are considered.