Voting, a commonly used group-decision process, usually aims to aggregate decision
recommendations in a way that is appropriate and balanced. The “cornerstone of democracy” is the opportunity to vote in a free, fair, and open electoral system. In fact, a multitude of electoral systems has been proposed, most to choose a single winner (as in the election of a mayor, governor, or president), but some to determine multiple winners (as in the election of a committee).
Many desirable properties for group-decision procedures have been formulated. Looking at the mathematics behind the various electoral systems, we assess their abilities to achieve these properties. No system achieves them all, and it seems very unlikely that anything close to a perfect system will ever be invented. Thus the choice of a voting system seems to come down to trade-offs, which themselves are difficult to assess. Yet there has been some progress toward making voting and elections, as group-decision processes, responsive, transparent, and fair.