In this note I compare different Voting systems. We have:
- Properties: A usually desired property that a voting system might or might not have
- Voting System: A way to make votes to a single winner. A vote is usually a choice of favorite candidates, rank of candidates, or a weighted list of candidate preferences
Properties
- 🔵 Condorcet compliance: If a candidate wins all head to head comparisons, then this candidate is declared the winner. This cannot be satisfied in non-ranking systems, as they do not provide a way to do head to head comparisons.
- 🟠 Unrestricted Domain: The voting system always produces a winner, no matter the votes submitted
- 🔴 Non-dictatorship: The voting system is not a function of a single voter
- 🟢 Non-imposition: It is always possible for any candidate to win
- 🟣 Independence of Irrelevant Alternatives: The winner should not change between two candidates and by only change the preferences for a third candidate .
- 🟡 No-split votes: Voters do not benefit by voting on a more likely candidate, rather than their true preference
Remark: Arrow’s Impossibility Theorem states that the combination 🟠🔴🟢 is impossible: no voting system will satisfy all three properties.
Voting Systems
The colors below represent which properties, described above, are satisfied by each system. ⚫️ is used as a placeholder for when a property is not satisfied.
- ⚫️⚫️🔴🟢⚫️⚫️ First Past the Post: However has the most #1 votes wins.
- ⚫️⚫️🔴🟢🟣🟡 Instant Runoff Voting: Count up the #1 choices. If someone has more than 50%, they win. If not, eliminate the last-place candidate. Run a new “round” of the election, minus the last-place candidate. Repeat until someone has 50% or more.
- 🔵⚫️🔴🟢🟣🟡 Borda: Add up the rank numbers. Whoever has the lowest score, wins.
- ⚫️⚫️🔴🟢🟣⚫️ Approval: Which voter simply approves or disapproves a candidate. Highest approval wins.
- Check that the above properties match the voting systems, and add more