• What properties might we “like” a voting system to have?  Examples:

• Majority rule: if a majority supports a particular choice, that choice wins

• Universality: the voting system always comes to some decision

• Determinism: the system always decides the given for the same inputs

• Condorcet criterion: if a candidate A would beat all others in two-choice pairwise elections, then A should win

• Non-manipulability: encourages people to express their true opinions instead of being tempted to vote strategically

• Simplicity: Understand the voting system.

• Monotonicity: Adding vote for X does not hurt X

• What systems robustly represent [“true”] opinion?

• Robustness, manipulability depends on structure

• Strategic voting: can voters/groups manipulate the results?

• Example: “spoiler” effect on plurality elections

• Single-winner, two-choice

• majority voting: Incentive compatible; Universal, deterministic (apart from dexact tie)

• Single-winner, multi-choice

• Plurality

• Runoff elections

• Instant runoff voting

• Approval voting

• Multi-winner

• Proportional versus district representation

• District: reduces to set of simple winner-take-all elections

• Weakness: exclusion of spread-out minorities

• Weakness: gerrymandering

• Proportional: representative sample over wider area

• Weakness: much more complex, many systems

• Diversity of goals, philosophies

• Majority rule: satisfy the preference of a majority of voters

• Equiprobability of success

• Equal opportunity to avoid the worst

• Arrow’s theorem

• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

• If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).

• There is no "dictator": no single voter possesses the power to always determine the group's preference.

• Paradoxes: no system can be “perfect”

• Condorcet paradox: circular pairwise preferences

• Absolute majority paradox: ranked first by majority, loses

• Absolute loser paradox: ranked last by majority, but wins

• Party-list proportional

• Widely used in Europe, ensures proportional representation in parliament

• Threshold requirements often imposed, for better or worse

• To limit influence of small extremist parties

• To keep represented parties, coalition-building manageable

• Centralizes power on party leadership; voters can’t choose candidates

• Single transferable vote (STV)

• Multi-winner version of instant runoff voting

• Takes ranked-choice ballots from voters

• Runs multiple rounds just as computation to decide results

• In each round, elect candidate(s) who meet a quota

• If no candidate meets quota, eliminate weakest candidate

• Repeat until all seats filled

• Key questions/challenges:

• Which quota?  (Hare, Droop, …)

• Which ballots to transfer from elected candidates?

• Ad hoc: just pick some off pile

• Random: pick a representative sample

• Meek: transfer all, but down-weight the ballots

Post-lecture blackboard snapshots 2019 - lectures over two consecutive weeks: