Least Manipulable "Reasonable'' Voting Rules (for a Few Voters and Candidates)

We address the search of voting rules with minimal probability of coalitional manipulation among those that possess the Conditional Majority Determination property. Since this problem is difficult in general, we solve it for a small number of voters and candidates in the impartial culture. We propose an approach that uses a graph representation of potential manipulations and the assistance of an optimization software. We exhibit voting rules with minimal manipulability rates, and compare the result with usual voting rules. By developing mathematical tools and providing results that may guide the intuition in more general cases, this work is a first step towards identifying least manipulable ``reasonable'' voting rules in larger settings.