Math,
"Running in the sense of making executive decisions on safety and diet and clothing and where they went to school and what sort of activities and toys and books for them I spent my money on until they were gradually able to make those decisions themselves. Running in the sense of teaching them to negotiate and compromise and manage their own environment."
You shoot yourself in the foot every time. Your choice of vocabulary such as "run" and "make executive decisions" bespeak of a power structure. They are words which are normally used by executives in corporations and senior people in government, those at the head of clear power structures. I also assume that when they were young you made "executive decisions" about bedtimes, mealtimes, not running across busy roads etc and enforced those somehow. So, in effect, your parenting is the same unashamed use of a power structure as mine, you just prefer to term it something else.
All good parents try to allow their children as much autonomy as possible within an overall power structure. We all want our children to grow into intelligent and thinking adults. However, to teach children to question adult authority is a bit crazy, especially when they are young (aside from very specific warnings about going with strangers etc). How do you want your children to approach school, going to friends' houses. Do you want them to argue with the teacher when the teacher asks them to sit down at their desk or to refuse to come to lunch when a friends' parent tells them it is lunchtime. Teaching a child to think for themselves but nonetheless respect authority is a real challenge for parents. Teaching them merely to think for themselves and that their thoughts and opinions are always very important merely creates entitled boring adults.
"A sharp slap on the back of the hands is really very painful. Much more painful than a slap on the palm or buttocks. It stings horribly and the hand hurts for a good while afterwards, especially if you knock it against something accidentally."
This is the problem of discussing smacking with people who have been physically abused. They don't get it. What you are describing above is abuse, not a smack. When I smack my son on the back of the hand, there is no mark at all and it stings for a few seconds and is then forgotten. You are talking about tissue damage. They are really not the same thing.
Icbineg and whoever made the suggestion,
"Loving the idea of Larry-junior-one attacking his dad in an attempt to save his younger sibling from pain and bullying. I'll bring my pom-poms and cheer him on! "
You couldn't make it up! You believe I am a bully to my children (I'm really not) so what would you love to see happen....I get a big fat smack! Were I a bully, I would totally agree with you, actually. It does rather go against your anti-violence agenda, though. It is funny the visceral appeal to us all of bullies meeting violent retribution.