The semivalues (as well as the least square values) propose different linear solutions for cooperative games with transferable utility. As a byproduct, they also induce a ranking of the players. So far, no systematic analysis has studied to which extent these rankings could vary for different semivalues. The aim of this paper is to compare the rankings given by different semivalues or least square values for several classes of games. Our main result states that there exist games, possibly superadditive or convex, such that the rankings of the players given by several semivalues are completely different. These results are similar to the ones D. Saari discovered in voting theory: There exist profiles of preferences such that there is no relationship among the rankings of the candidates given by different voting rules. <!--ID="" This research has been supported by the Training and Mobility of Researchers program Cooperation and Exchange of Information, with Economic Applications, contract FMRX-CT966-0055, initiated by the European Commission. A previous version of this work, was untitled Millions of Paradoxes for a Class of Cooperative Game Solutions. The authors are grateful to Donald Saari and Katri Sieberg for helpful discussions; They also aknowledge an anonymous referee for helpful comments.-->
