On the reversal bias of the Minimax social choice correspondence

• Three versions of the reversal bias for social choice correspondences are proposed.
• A new description of Minimax correspondence is proposed.
• We characterize when Minimax correspondence suffers the reversal bias of each type.
• Condorcet and Borda correspondences are immune to the reversal bias of each type.
• Graph theory is used as the main tool.

We introduce three different qualifications of the reversal bias in the framework of social choice correspondences. For each of them, we prove that the Minimax social choice correspondence is immune to it if and only if the number of voters and the number of alternatives satisfy suitable arithmetical conditions. We prove those facts thanks to a new characterization of the Minimax social choice correspondence and using a graph theoretical approach. We discuss the same issue for the Borda and Copeland social choice correspondences.