A long comment and one that seems to draw conclusions that are not really supported by my too short post (I really shouldn't have posted in Comments). But the comment poses a few point's I'd like to address.
The core problem here is that the child is behaving in a way that you do not want them to behave in.
Wanting the child to do something is one reason. Concrete needs another. You wouldn't disagree that I'd need to call back a small child from a high traffic street or a cliff or a dangerous animal or a poisonous thing. These are immediate and obvious.
How much time to take with a child that want's to pick up stones when you are on the way to kindergarten or the job is a moderate need you have to balance your own desires with the childs.
Maintaining a household with six persons can mean one does everything or all share a part of the work. And there are lots of differnt ways to achieve some balance of needs in this. But whatever the balance is - it involves certain feedback. Talking alone will not do it - although it is necccessary to establish a context.
the trump card: "If you do X, I will be sad and disappointed in you."
I can't use that. First of all it would be a lie. I wouldn't be sad or disappointed. At worst I would ask me what I did wrong in the first place. Second I can't bear applying emotional pressure. Third I have seen it used on my children and it didn't work.
The main trouble with my approach is that [...] older parents try this approach, and find themselves consistently losing arguments [and then] switch to lazy shortcuts, such as playing the part of an authority [...]
Sure that is a way out that sometimes has to be taken - because sometimes you are tired and the smaller children need to sleep because they don't understand that they have to go to kindergarten the next day early...
And I have lots arguments with my older children and not played the authority card. I accepted that I erred.
One problem with arguments with children can be that they want to win and use all the rhetoric tricks they have at their disposal. They didn't read EYs posts on the dangers of rhetoric and fully general counter arguments. An argument with a child isn't neccessarily a harmonious thing. At least not when a significant issue is on the line. You will not resolve such an issue with patience. I try often enough. And I can 'win' by patience. Once I lost an hour of range and no agreement in the middle of the day while three other children were unattended.
Just consider though - if this were an adult, you'd have to do it the hard way.
The hard way with an adult would often enough mean to go different ways. That is an option that is closed for parents. Both by their affection toward their children as well as by our society.
these are just my interactions with parents, interactions with children
Interacting with other persons children is quite different from with your own. And exactly beause they are not yours. You can send them back to their parents and they can go back their parents and in such a situation they basically behave like autonomous persons (if they feel safe but aduls also have to feel safe).
Wanting the child to do something is one reason. Concrete needs another. You wouldn't disagree that I'd need to call back a small child from a high traffic street or a cliff or a dangerous animal or a poisonous thing. These are immediate and obvious.
But there are still parents who handle those occasions just fine without resorting to punishments and rewards. My parents never seriously resorted to modeling my behavior though behavorism.
It may be that you lack a relationship with your kids where that's possible. Especially if you already have rules that...
Followup to: Strategic ignorance and plausible deniability
My in-law always says: "For children it is easier be forgiven then to get permission."
EDIT: This post is superseeded by my Book Review: Kazdin's The Everyday Parenting Toolkit I recommend reading only that. The remaining insight of this post is: Children expend more brain power on their parents than the parents on them.
I can say from experience: That is risky.
Children (esp. small ones) expend significantly more brain power on their parents than the parents on their children (your mileage may vary). I can assure you that they will notice these cases - at least some - and take that into account one way or the other.
If the children notice this they may assume that you either condone, accept, bear or ignore it. None of these has positive effects.
Possible alternative strategies:
I am influenced by The Adlerian School. Of relevance here is Striving for significance.
The testing of limits and the resulting interaction with the parent give the child a feeling of significance if the parent acknoledges the act of the child even if he doesn't agree with it. On the other hand ignoring the act of the child is negative feedback about significance.
EDIT: The asymmetry between parents and children with respect to the effectiveness of deniability can be generalized to any situation where one actor has significantly less overall information about the situation than another actor and thus might not be able to reliably estimate whether deniability is possible.
ADDED: tadamsmar pointed out that ignoring is scientifically known to be effective and the advice or rather personal expierence I have related in this post may be contraproductive (at least if applied in isolation).