Compiling the Votes of a Subelectorate

In many practical contexts where a number of agents have to find a common decision, the votes do not come all together at the same time. In such situations, we may want to preprocess the information given by the subelectorate (consisting of the voters who have expressed their votes) so as to “compile” the known votes for the time when the latecomers have expressed their votes. We study the amount of space necessary for such a compilation, as a function of the voting rule, the number of candidates, and the number of votes already known. We relate our results to existing work, especially on communication complexity.