Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme.