• 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 exact 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:





Modifié le: jeudi, 21 octobre 2021, 14:21