Let $U$ be the universe of a multiple choice questionnaire. We can say $|U| = 1$. We have $k \geq 3$ sets of answers in $U$ such that for all $k$, we have $ S= \sum_{u_i \in U} |u_i| > 1$. The answers are in percentages.
We are interested in the quality of a certain set, say $u_c'$, such that we want to know the percentage of people who answered to $u_c$ with only one choice in the questionnaire. So for $k = 3$ we'd want to know $|A \setminus (B \cup C)|$.
Using inclusion-exclusion principle we can conclude that almost always for large $k$, we have $u_c' \in [0, |u_c|]$ The trivial assumption would be to treat the interval as equal and use the mean. However, for large $k$ there has to be overlapping in the multiple choice questionnaire.
With no other information given, what models are there to estimate $u_c'$? If we have $4$ sets of answers with each $99 \text{%}$ answers, there is no way that $u_c'$ could be the mean, in a real world situation this would indicate that there is considerable overlap.
We could say that the questionnaire itself is Poisson. Meaning that each person answers independently and chooses $1$ to $k$ choices. For example if the questionnaire is like the above with $99 \text{%}$ answers, $\lambda \approx k$. If the Poisson distribution is a good fit to how people answer to the questionnaire, we can estimate the amount of people who only answered to a single choice and therefore get a better estimation to $u_c'$.
The question then follows: is $S$ a good estimation to $\lambda$?