ATL>Scoring rules cannot respect majority in choice and elimination simultaneously.

I show that there exists no scoring rule which ensures that an alternative considered as best by a strict majority is chosen while an alternative considered as worst by a strict majority remains outside of the choice set. The negative result is valid for standard scoring rules where scores depend on the number of alternatives only, as well as for generalized ones defined via vectors of scores which are functions of both the number of alternatives and agents. [Copyright &y& Elsevier]