Preserving Condorcet Winners under Strategic Manipulation

Condorcet extensions have long held a prominent place in social choice theory. A extension will return the winner as unique whenever such an alternative exists. However, definition of does not take into account possible manipulation by voters. profile where all agents vote truthfully may winner, but this end up set winners if are acting strategically. Focusing on class tournament solutions, we show that many natural functions class, well-known Copeland and Slater rules, cannot guarantee preservation when behave Our main result respect is impossibility theorem establishes no solution satisfying very weak decisiveness requirement can provide guarantee. On bright side, identify several indecisive otherwise attractive solutions do under strategic for large preference extensions.