In many intellective tasks groups consistently outperform individuals. One factor is that the individual(s) with the best answer is able to convince the other group members using sound argumentation. Another factor is that the most confident group member imposes her answer whether it is right or wrong. In Experiments 1 and 2, individual participants were given arguments against their answer in intellective tasks. Demonstrating sound argumentative competence, many participants changed their minds to adopt the correct answer, even though the arguments had no confidence markers, and barely any participants changed their minds to adopt an incorrect answer. Confidence could not explain who changed their mind, as the least confident participants were as likely to change their minds as the most confident. In Experiments 3 (adults) and 4 (10-year-olds), participants solved intellective tasks individually and then in groups, before solving transfer problems individually. Demonstrating again sound argumentative competence, participants adopted the correct answer when it was present in the group, and many succeeded in transferring this understanding to novel problems. Moreover, the group member with the right answer nearly always managed to convince the group even when she was not the most confident. These results show that argument quality can overcome confidence among the factors influencing the discussion of intellective tasks. Explanations for apparent exceptions are discussed.