Median and average as tools for measuring, electing and ranking: new prospects

Impossibility theorems expose inconsistencies and paradoxes related to voting systems. Recently, Michel Balinski and Rida Laraki proposed a new voting theory called Majority Judgment which tries to circumvent this limitation. In Majority Judgment, voters are invited to evaluate candidates in terms taken in a well-known common language. The winner is then the one that obtains the highest median. Since the Majority Judgment proposal was made, authors have detected insufficiencies with this new voting system. This article aims at reducing these insufficiencies by proposing a voting system to decide between the median-based voting and the mean-based one. It proposes, moreover, a new tie-breaking method computing intermedian ranks mean.