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A Linguistic Group Decision Making Method based on Distances

It is common knowledge that the political voting systems suffer inconsistencies and paradoxes such that Arrow has shown in his well-known Impossibility Theorem. Recently Balinski and Laraki have introduced a new voting system called Majority Judgement (MJ) which tries to solve some of these limitations. In MJ voters have to asses the candidates through linguistic terms belonging to a common language. From this information, MJ assigns as the collective assessment the lower median of the individual assessments and it considers a sequential tie-breaking method for ranking the candidates. The present paper provides an extension of MJ focused to reduce some of the drawbacks that have been detected in MJ by several authors. The model assigns as the collective assessment a label that minimizes the distance to the individual assessments. In addition, we propose a new tie-breaking method also based on distances.