Measuring electoral competitiveness: A Probability ratio index

We propose an index of electoral competition based on the vote shares of parties competing in the election. This index is the ratio between the probabilities that the two voters drawn at random with (without) replacement have voted for different parties under actual vote shares across the competing parties and under equal vote shares across them. The measure is characterized using two simple axioms, consistency in aggregation and competitive indifference. The former expresses the index as a weighted sum of competitiveness in two party elections. The latter is concerned with redistribution of vote shares across parties.