A Vote-Share Concentration-Based Axiomatic Characterisation of the Probability-Ratio Index of Electoral Competition

We axiomatically characterise the probability-ratio index of electoralcompetition, which is based on the vote shares of parties competing in anelection. It is the ratio between the probabilities that two voters drawn atrandom with (without) replacement voted for different parties under actualvote shares across the competing parties and under equal vote shares acrossthem. This vote-share concentration-based measure is characterised usingtwo simple axioms, consistency in aggregation and competitive indifference.The former expresses the index as a weighted sum of competitiveness intwo-party elections. The latter is concerned with the redistribution of voteshares across parties.