Greater than the sum of its parts

Listening to the Science Talk (the podcast of Scientific American) the other day, I was intrigued to learn that it is possible to get more than 100% satisfaction with the cutting of a cake. In the old days - well, this was how it was taught to us - if you had to share a scrumptious goodie with someone, one of you would cut and the other would choose. This was guaranteed to have the cut made as fairly as possible. But with a theory which includes the world "equitability" somewhere in its name, Science Talk reports it is possible to have both people 100% happy with the cut - especially, if, as in the example used, the cake is half chocolate and half vanilla and IF both parties have different preferences for chocolate and vanilla AND if both parties let those wishes be known. In that way, the cake can be cut according to their preferences eg the person who prefers chocolate more, gets more chocolate, the vanilla person, more vanilla. While this works in theory, said the podcast, in application it is not as successful as it appears people are not quite so forthright about saying what they want.