How much can namedropping a politician matter? Conveniently, Republican front-runner Donald Trump shares a couple of policy positions with Obama and other leading Democrats. In a new HuffPost/YouGov poll, we randomly assigned one half of the 1,000 Americans surveyed to say whether they agreed with positions Trump held. The rest were asked whether they agreed with positions held by Obama, Secretary of State John Kerry or current Democratic presidential candidate Hillary Clinton. The trick: the positions were actually the same.

Yet respondents’ reactions were decidedly different. Hearing that Trump supported a certain policy was enough to cause Democrats to reconsider ideas they’d otherwise support, and for Republicans to endorse positions they’d usually avoid.

Still, associating a particular politician with a certain position wasn’t enough for people to abandon their most deeply held convictions. Protecting Social Security, for instance, is an overwhelmingly popular idea, whether it’s being proposed by Clinton or by Trump.