Voters’ perceptions of parties’ positions play a key role in representative democracy. If voters can place parties on the primary dimension that structures politics, they can select parties that largely reflect their policy priorities and hold parties accountable for failing to offer consistent messages or for pursuing policies that run counter to their promises. Responsible party government, however, breaks down if voters are unable or unwilling to place the parties. In this project, we first illustrate the magnitude of missing data problems in the study of party brands, then we show how missingness varies systematically across demographic groups and political variables. We use the Party Brands Dataset – a massive corpus containing all available data on voters’ perceptions of parties’ positions in advanced democracies – to reveal how voters’ refusal to place parties induces non-response bias that fundamentally changes inferences on topics related to party brands, accuracy of placements, and perceived proximity to parties. We then demonstrate how a simple solute involving multiple imputation can help correct these inferential problems.