Mass election predictions are increasingly used by election forecasters and public opinion scholars. While they are potentially powerful tools for answering a variety of social science questions, existing measures are limited in that they ask about victors rather than voteshares. We show that asking survey respondents to predict voteshares is a viable and superior alternative to asking them to predict winners. After showing respondents can make sensible quantitative predictions, we demonstrate how traditional qualitative forecasts lead to mistaken inferences. In particular, qualitative predictions vastly overstate the degree of partisan bias in election forecasts, and lead to wrong conclusions regarding how political knowledge exacerbates this bias. We also show how election predictions can aid in the use of elections as natural experiments, using the effect of the 2012 election on partisan economic perceptions as an example. Our results have implications for multiple constituencies, from methodologists and pollsters to political scientists and interdisciplinary scholars of collective intelligence.