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? And do populist politicians use rational strategies? The following selection of Plus articles provides mathematical answers, insights and paradoxes.

• Donald Trump, game theorist: Steven J. Brams looks at Trump's "tactics" from a game theoretical view point.
• A quick guide to voting: how does everyone else do it?
• Which voting system is best?: Tony Crilly uses a toy example to compare different voting systems.
• Electoral impossibilities: why perfect democracy is mathematically impossible.
• 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!