I remember reading that the amount of measured willpower is uncorrelated with dieting success. On the other hand there are various popular article that suggest that there a link.
What does the science on the subject say?
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There was a study that was published in 2009, which focused on food and self-control. This study, revealed that self-control didn’t have much of an effect one way or another on whether or not the volunteers were able to constrain themselves from eating the presented food (in this case, chips)
In addition, professor and health psychologist Traci L Mann Ph.D. concluded ,through her studies, that willpower is a myth when it comes to dieting. You can view the multiple papers she has written here or purchase her book on this topic on amazon.