Food is a drug.
Once you start from the working premise that food is a drug, everything about the difficulties of weight loss makes sense. Fat people are addicted to food. Could you pay a heroin addict to stop using? A cigarette smoker?
The wagerers noted in the post, above, are both economist-like people. Economics is more-or-less useless on any important existential question, and so a bet based on economic incentives is designed to fail.
How does a drug user decide to stop using drugs? That's an existential question. The person makes the life decision to stop using. Many external events often precipitate that decision, but nevertheless, a junkie decides to redefine himself.
A junkie will always tell you that they are a recovering drug user. They have killed the old self - the user - and created a new self. Thus, in drug discussions, use of the Phoenix Metaphor is common. Through painful fire comes rebirth.
A fat person exists as a junkie. Using drugs (food) is part of that junkie's existence. Thus, the only way to lose weight is to redefine one's existence - to create a new self.