Voting Compilation Revisited

Compiling a collection of votes (a profile) consists in compressing the information it contains in a minimal way, while still allowing to compute the winner after more votes are received. These additional votes can be understood temporally (when votes come in an asynchronous way) or spatially (when votes are gathered locally in polling stations, and their results published locally before being aggregated on a global level). Given a voting rule, two profiles are equivalent for this rule if for whichever profile we add to each of them, the winner in the two expanded profiles will be the same. An equivalence relation between profiles corresponds to a set of information structures (called compilation structures) encoding equivalence classes. It is well-known that some information structures, such as pairwise majority matrices are the compilation structure for some voting rules, while some others (such as the majority graph) are not. We fully characterise the equivalence relations (or equivalently the information structures) that correspond to some voting rules, and we review a number of interesting information structures and give known voting rules that correspond to them.