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
majority voting: Incentive compatible; Universal, deterministic (apart from dexact tie)
Instant runoff voting
Proportional versus district representation
District: reduces to set of simple winner-take-all elections
Weakness: exclusion of spread-out minorities
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
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
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
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: