Democratic societies have been increasingly confronted with extreme, knife-edge election outcomes that affect everybody’s lives and contribute to social instability. Even if political compromises based on social conventions as equity or economic arguments as efficiency are available, polarized societies might fail to select them. We demonstrate that part of the problem might be purely technical and, hence, potentially solvable. We study different voting methods in three experiments (total N = 5, 820), including small, medium-sized, and large electorates, and find that currently-used methods (Plurality Voting and Rank-Order systems) can lead voters to overwhelmingly support egoistic options. In contrast, alternative, more nuanced methods (Approval Voting and Borda Count) reduce the support for egoistic options and favor equity and efficiency, avoiding extreme outcomes. Those methods differ in whether they favor equity or efficiency when the latter benefits a majority. Our evidence suggests that targeted changes in the electoral system could favor socially-desirable compromises and increase social stability.