We show that framing an election as a “competition” compared to “cooperation” reduces the chances that egalitarian alternatives will win under Plurality Voting, but not under Approval Voting. Individual voting behavior shows that the effect is mainly driven by voters who switch to their selfishly payoff-maximizing alternatives under a competitive framework, but only when those are also payoff-efficient (in terms of sum of payoffs for the group). This shift does not happen for voters whose payoff-maximizing alternatives are not payoff-efficient, or even if a majority of voters are better off under the payoff-efficient alternative. This suggests that voters are more likely to switch to selfish payoff-maximizing alternatives under a competitive frame if they can (self-)justify the switch in terms of the common good.