If hypothetically 10% of the population said A but you slice up B into specific enough buckets then A wins even if the overwhelming majority dislike A.
Brexit was only a policy question if you combined two different questions. “Should we stay in the EU?” and “What kind of foreign policy should we have?” People answering Yes to the first question also had plenty of diversity in how they wanted to answer the second question.
> If hypothetically 10% of the population said A but you slice up B into specific enough buckets then A wins even if the overwhelming majority dislike A.
Yes, if you're only allowed to vote for a single option. If you're allowed to vote yes/no for each option, or rank them from best to worst, then this problem doesn't happen.
This overestimates support because you're vague on what the policy actually is, so everyone thinks that it's going to be their preferred variant being implemented. See: the brexit vote which got a majority vote for "yes", but in reality the none of the individual proposals got majority approval.