Gaffes, murder plots, and hockey mums — the US election circus is in full swing. Personality politics is partly a consequence of the first-past-the-post system — but what are the alternatives? Can any system guarantee to represent the will of the people? Do opinion polls manage to capture its voice? The following selection of Plus articles provides mathematical answers, insights and paradoxes.

• A quick guide to voting: how does everyone else do it?
• Mathematics and democracy: Approving a president: Steven J Brams explores an alternative to the first-past-the-post system;
• Election issues: a look at some unavoidable election paradoxes;
• How to rig an election: some handy advice for would-be presidents;
• Relationships: democracy's tricky, even if there are just three of you...
• Stirring the electoral soup: how to make polls accurate;
• Are the polls right?: a basic introduction to opinion polls;
• Adam Smith and the invisible hand: can free markets guarantee social choice?

Happy reading!