Essentially, our daughter is much more likely to partake in an activity (be it eating her veggies or anything else) if she feels like it was her idea to do so. I'm not entirely sure if it's the choice aspect, or the preparation aspect (in other words, that she knows in advance what to expect).

We're careful to emphasize the sanctity of personal choice wherever we can, and to encourage her to make her own decisions based on an evaluation of her options (really, we're fine with her picking any of the menu options we give her; if she picks a gross combination it's hers to eat, not ours). The important thing seems to be that once she makes a decision, she becomes invested in it and is much more likely to see it through.

I probably shouldn't discount the preparation aspect, however. She eats much more of her lunch when she helps to prepare it (and thus knows what to expect when she opens it at school). Similarly, we have a countdown for bed ('bedtime in t-5 minutes! Bedtime in t-2 minutes!') that makes the transition to nighttime more or less painless.

My wife and I do something similar. We give our daughter (she's almost three) a few choices with most anything that involves a decision.

A trivial example would be that if we're eating something that is traditionally a finger food and she wants to use a fork. We'll respond "You can use your right hand or left hand, it's up to you." and it avoids the confrontation completely because she gets to decide. She chooses a hand and life goes on.

Another example is sitting in her chair at the table. She'll normally ignore me when I ask her to climb in her chair but the moment I put a decision before her of getting in the chair on her own or I'll do it for her she hops right up.

It becomes second nature after a while and for us it's been a lot less stress and a time saver.