Analogous to “doctor shopping,” children practice parent shopping. My son comes to me and asks if he can play his computer game. When I say no, he goes and asks his mother. That is, assuming he hasn’t already asked her. After all how can I know that I’m not his second chance?
There are two possible states of the world: you are first or you are second. Assuming the child has chosen parental order strategically -- that is, to maximise the probability of a 'yes' outcome -- Jeff argues that, in equilibrium, regardless of inference about order, you will be tough on requests you are tough on and lenient on requests you are relatively lenient on.
Of course, there is a subtly here in that there may be an ex post parental negotiation and dispute resolution. "You let him do what?" or, even worse, "You let her do that after I explicitly said no?" This suggests that you need to hedge. In particular, I believe the first question you should always ask is "Did you ask your mother?" Now, regardless of the answer to that question, you buy yourself a hedge against the accusation that you had overruled the other parent. You are still on the hook for your basic decision in which case I pretty sure that erring on the side of 'no' is the best policy -- Jeff makes this case as well.
There is another strategy where you ask: "Why don't you ask your mother?" If the children digs their heels in and tries to extract a decision from you then it is clear they are parent shopping -- otherwise it is surely pretty costless to move on when you impose some transaction costs on them.
Even better in terms of saving some time is "Well, you can do that if your mother also says you can." That way, you are the good guy, digging heels in is a sure sign there is shopping going on and, on the surface you are being a consultative partner with your spouse. Of course, passing off can pose issues. In our house, it regularly leads to both parents saying this -- something that happens with the "Why don't you ask ..." strategy and the child sent into a loop of frustration and despair. As that amuses me, this is not something I am too worried about. It also allows children to understand the futility in asking for anything and generally leaving us alone.
That said, at least one strategic child in our household -- I'm looking at you Child No.3 -- has exploited the loop to her advantage. She has undertaken the activity in question on her own accord claiming that "Mum (or Dad) said I could do it." That either worked or leads to a round of "You let her do what?" which, for the child, takes the heat off her.
That same child also employs another parent shopping activity. When she has misbehaved in the care of one parent, she greets the other parent very warmly when they get home. Her theory being "her past crimes are about to be exposed and she will build in some 'can you really imagine someone was cute and loving as me was so horrible' priming." I'm on to that. A hug is often greeted now with "what did you do?"
