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The Stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already widely adopted and stable due to deviants' sanctions. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a local social optimum configuration to achieve an optimum global state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We considered group-structured populations where individuals play the Stag-hunt game in all groups. We model the diversity incentive as a Snow-drift game played in a single focus group where the individual is more prone to adopt a deviant norm. We show that moderate diversity incentives can change the system dynamics, leading the whole population to move from the locally optimal social normal to the globally optimal one. Thus, an initial fraction of adopters of the new norm can drive the system toward the new social optimum norm. After the new social contract becomes the new equilibrium, it remains stable even without the incentive. The results are obtained using Monte Carlo simulations and analytical approximation methods.