On the Reconstruction Method for Negative Surveys with Application to Education Surveys

Negative surveys, as a novel way of collecting sensitive information, have wide applicability because of their simple operation and capability to preserve privacy. However, existing methods for estimating positive survey results from negative survey results have disadvantages. Some methods might return negative values (i.e., the values less than 0) or some methods have high computational complexity. In this paper, the problem of estimating positive survey results from negative survey results is transformed into a linear programming problem, and the interior point method is used to solve this problem. In this way, we can not only obtain estimated positive survey results without negative values, but also achieve high efficiency. Simulation experimental results demonstrate that the proposed method is efficient and stable, and that it returns only nonnegative values (i.e., the values not less than 0). Furthermore, the experimental results of applying our method to collect educated persons' evaluations also show better performance than other methods with respect to efficiency and stability.