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We develop a multi-level selection model in the framework of indirect reciprocity. Using two levels of selection, one at the individual level and another at the group level, we propose a competitive scenario among social norms, in which all individuals in each group undergo pairwise interactions, whereas all groups also engage in pairwise conflicts, modeled by different games. Norms evolve as a result of groups' conflicts whereas evolution inside each group promotes the selection of best strategies for each ruling social norm. Different types of inter-group conflict and intensities of selection are considered. The proposed evolutionary model leads to the emergence of one of the recently obtained leading-eight social norms, irrespective of the type of conflict between groups employed. We also compared the individual performance of the norm obtained in the evolutionary process with several other popular norms, showing that it performs better than any the other norms. This reputation assignment rule gives rise to a stern and unambiguous response to each individual behavior, where prompt forgiving coexists with implacable punishment.