In established democracies, the decision of whether to extend the right to vote is sometimes taken by the current electorate. Popular votes thus represent a hurdle to the widening of the demos and merit study as a distinct enfranchisement path. A key question for this path is under what conditions the electorate is willing to extend the right to vote to a new demographic. Existing explanations are based on structural conditions, overlooking the extent to which cognitive biases—especially the compromise effect—impact popular support for enfranchisement. To make this argument, I focus on one of the most hotly debated forms of contemporary enfranchisement: voting rights for immigrants. Through observational data from 31 referendums in Switzerland and a survey experiment fielded in the United States, I show that support for an enfranchisement proposal is higher when voters are simultaneously presented with an even more liberal version. I complement these findings with case study evidence revealing that not only scholars but also parties have overlooked this. Instead of leveraging simultaneous referendums, pro-enfranchisement parties often try to avoid presenting voters with more than one question, unknowingly reducing their chances of success. The implications of these findings go beyond enfranchisement and call on scholars to consider the compromise effect in the study of multi-option referendums more generally.