Historically, there has been a bias against the election of women for public offices in India. Since the mid-1990's, one third of village head positions have been randomly reserved for a woman: In these councils only women could run and be elected to the position of head. Assume that we care about the average welfare of individuals in Indian villages, i.e., we put equal weight on each individual's utility. Design a model, where political candidates act strategically, that justies the implementation of such a reservation system. Please include a diagram.