Every parent with more than one child knows the trick.
If you have one piece of cake and two children, the piece of cake must be cut in half. Under no circumstance can you be the one who cuts the cake. Neither can you be the one who allocates the slices, nor can you allow any child to perform both the cutting and the choosing. There is but one solution: You must allow one child to cut and the other to choose their slice. Anything else is asking for violence, recriminations and wasted cake.
It is a classic game theory problem in the field of envy-free choice. It also explains some of the thinking behind most nudges, the worst of many terrible ideas to come from the desk of Cass Sunstein. The perception of agency does a lot to help us accept an outcome. After all, if we were responsible for it, surely we made a good decision.
In practice, however, the designer of the Nudge doesn't always play fair. Especially if they have stakes. Especially if they are a principal, too. Hey, even the most soft-hearted libertarian paternalist can't be a perfect parent all the time.
Which is why I set up a little principal-involved variation on the envy-free cake experiment with my son. Because kids are weird, his favorite thing to drink is Orange Fanta. Plus, it's his birthday today and he wanted to have what is a pretty rare treat around our house for breakfast. So I filled up one glass with a half cup of Fanta. I filled up another glass with a full cup of it. I added a cup of ice to the glass with half as much. I then presented him with the choice between the tall, well-presented glass with half as much and the short, unassuming glass with twice as much.