Golem, self-identification polls tells us something about how people perceive themselves, or wish to be perceived, which can be pretty illuminating for example on questions of identity. There's a margin of error, usually social pressure (for example during the Trump campaign many people dared not admit to voting Trump due to legacy media and public shaming of Trump voters), but it is usually negligible. Even if people poll how they think they are expected to identify it can still be useful (as it says something about biases). In a poll about whether you view yourself as a citizen or the World or the US it can say something about where your loyalties lie, how much you identify with the local culture and your view on things such as nationalism and globalism. The poll Oberyn posted showed that white Americans identify stronger with America than other racial groups in America and that natives identify stronger with America than people born abroad.