Are ambitious women punished in politics? Building on literature from negotiation, we argue that women candidates who are perceived to be ambitious are more likely to face social backlash. We first explore what the term 'ambitious' means to voters, developing and testing a new multidimensional concept of perceived ambition, from desire to run for higher office to scope of agenda. We then test the link between these 'ambitious' traits and voter support for candidates using five conjoint experiments in two countries, the U.S. and the U.K. Our results show that while ambitious women are not penalized overall, the aggregate results hide differences in taste for ambitious women across parties. We find that in the U.S. left-wing voters are more likely to support women with progressive ambition than right-wing voters (difference of 7 percentage points), while in the U.K. parties are not as divided. Our results suggest that ambitious women candidates in the U.S. face bias particularly in the context of non-partisan races (like primaries and local elections), when voters cannot rely on party labels to make decisions.