straw poll

a straw poll AND a straw vote (a small survey of opinion or ballot to find out what people think about an issue, esp. unofficial, casual, or ad hoc) — выборочный опрос общественного мнения (для выяснения настроения избирателей и т. п.)

to win / take / etc. a straw poll

This idiom alludes to a straw used to show in what direction the wind blows, in this case the wind of public opinion. (The American Heritage Dictionary of Idioms)