Voting Aggregation Leads to (Interval) Median

When we have several results of measuring or estimating the same quantities, it is desirable to aggregate them into a single estimate for the desired quantities. A natural requirement is that if the majority of estimates has some property, then the aggregate estimate should have the same property. It turns out that it is not possible to require this for all possible properties – but we can require it for bounds, i.e., for properties that the value of the quantity is in between given bounds a and b. In this paper, we prove that if we restrict the above “voting” approach to such properties, then the resulting aggregate is an (interval) median. This result provides an additional justification for the use of median – in addition to the usual justification that median is the most robust aggregate operation.