privacy – How many people would need to answer a survey of 1000 questions before the aggregate data from the survey is sufficiently anonymous?

Websites release statistics on their user base all the time and it’s not considered a breach of privacy because their user bases are so large that it’s impossible to pick apart who thinks or watches what. Additionally when nations or states or counties release election results it is impossible to figure out who voted for what even if the county has a miniscule population.

To be clear if the population is 1 then the results are never anonymous, and the more people there are the harder it is to see who answered what. Assuming that we know everyone in the voting pool.

But let’s say a survey with 1000 yes or no questions is released to all the residents of a county and when the survey was over results were shown which were based on a system of 1 for yes answers and 0 for no answers giving you totals for each question.

Do the more detailed results make it easier to piece together who said yes or no to what?

And if so how many people would need to answer the survey before the results were completely anonymous? Or sufficiently anonymous?