My dad is LSI-N and wasn't authoritarian but I did get corporal punishment at the behest of my mom. My mom is SEE-D and she was authoritarian and wanted my dad to be strict on me and impose more rules and structure on me. She ended up doing that and didn't like that my dad didn't back her up because she has to be the "bad guy" while my dad spoiled me.
I'm fairly authoritarian with my god-children. I do discipline them more than their parents. Everything has to have a reason. I want them to articulate why they should get something or have something. Their parents just give them stuff because they feel proud they can financially support their kids. I'm sorta the drill sergeant when I come over (but a really fun one). I make them work for their "rewards."
I don't think parenting style has to do with cognitive type, but it could possibly be a subtype of a type.