I love the idea of the coin-flip diet. Although it can be gamed by proposing to eat things more often. Maybe you could roll a 6-sided die for each meal. 1 = oatmeal and prune juice, 2-3 = lentil soup, 4-5 = teriyaki chicken, 6 = Big Mac or ice cream.

If you know the weight, and you have a way of sorting the things you would flip a coin for, you can use the sorting order instead. For instance, I typically buy rather than torrent if the artist is in the bottom half of artists sorted by income.