What kind of parenting produces free thinking open-minded children?

I'm wondering why I grew up under two authoritarian parents, yet never cared for traditions or gave any credence to authority for authority's sake.What kind of parenting produces free thinking open-minded children?
Some of us reject the values our parents attempted to instill in us - particularly if those values were promoted in an authoritarian manner. I think if you wanted to try and allow your children to become free thinking and open minded, you would - at developmentally appropriate times and in a manner appropriate to the child's age - promote independence and autonomy. You would place value on negotiation and discussion as ways of coming to decisions and would allow your child some input into decisions made about him / her. You would encourage your child to seek out her / his own ways of being in and understanding the world. All, of course, within the bounds of appropriate parental responsibility (definitely not suggesting laissez-faire or permissive parenting).