We introduce two new majoritarian social choice correspondences. We initially assign to every alternative in a preference profile a weight equal to one. Using (cooperative) game theoretic considerations we redistribute these weights, and use these redistributed weights to define a social choice correspondence. Then we apply this procedure iteratively by taking in each step as weights the redistributed weights obtained in the previous step. The resulting limit is used to define a second social choice correspondence. Both social choice correspondences are Pareto optimal and refinements of the Top cycle correspondence. Properties and comparisons with related social choice correspondences are discussed.