Alice is communicating with $n$ people. We do not assume that the $n$ people don't trust each other or trust Alice. Alice doesn't trust them either, and needs to assume that they will not form a coalition against her, so we assume the $n$ people cannot communicate with each other (except through Alice, if she agrees). Each of the $n$ people owns a secret bit $0$ or $1$. Let $m$ be the majority value, i.e., the bit owned by the largest number of people. (We assume that it is unique.)
Is it possible to design a protocol so that the $n$ people can commit to their value to Alice, and Alice can find out which of the people committed to the majority value $m$ without knowing what the value of $m$ is or gaining any other information about the values?