The authoritative parent attempts to direct the child's activities but in a rational, issue-oriented manner. She [the parent] encourages verbal give and take, shares with the child the reasoning behind her policy, and solicits his objections when he refuses to conform. Both autonomous self-will and disciplined conformity are valued. [She values both expressive and instrumental attributes, both autonomous self-will and disciplined conformity] ... Therefore she exerts firm control at points of parent-child divergence, but does not hem the child in with restrictions. She enforces her own perspective as an adult, but recognizes the child's individual interests and special ways. The authoritative parent affirms the child's present qualities, but also sets standards for future conduct. She uses reason, power, and shaping by regime and reinforcement to achieve her objectives, and does not base her decisions on group consensus or the individual child's desires. [... but also does not regard herself as infallible, or divinely inspired.] (p. 891) [Note that portions in brackets are significant additions to the prototype in Baumrind (1967).]
Now this is, I'd say, more or less how I was parented. And it seems pretty right to me. Children don't have the brain development to make many of the decisions that their parents should make. It is important to respect each child as an individual who has different needs and different preferences to others. But this description of a parenting style doesn't seem very "democratic". If the parent is in control at points of divergence, and does not base her decisions on group consensus, that's not democracy. It does seem to me like sensible parenting, though.

I think I must be misunderstanding the material on the PET website.

Thanks for the advice and comments, everyone.