> **Social choice theory** is the study of collective [[Decision-Making|decision]] procedures and mechanisms.^[https://plato.stanford.edu/entries/social-choice/] --- ## Central Questions How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members’ individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? --- ## Theory ### Voting Systems **Rational Voting System** > Every *rational* voting system should satisfy the following 5 conditions: > 1. Unanimity > 2. No Dictators > 3. Unrestricted Domain > 4. Transitive > 5. Independence of Irrelevant Alternatives > > Kenneth Arrow - Social Choice and Individual Values (1951) **Types of Voting Systems** - Ranked Voting - Rated Voting - Approval Voting --- #### Ranked Voting > **Ranked voting** is any voting system that uses voters' orderings (rankings) of candidates to choose a single winner or multiple winners.^[[Wikipedia](https://en.wikipedia.org/wiki/Ranked_voting)] *Example of a ranked ballot:* ![[Pasted image 20240827193340.png]] #### No ranked voting system can be rational. This theorem was proved by Kenneth Archer in 1951. Satisfying all conditions in a ranked voting system with 3 or more candidates is impossible. #### Condorcet Cycles > The Condorcet winner is the candidate preferred over all others by a majority of voters. However, it is possible for an election to have no Condorcet winner, a situation called a Condorcet Cycle.^[[Wikipedia - Ranked Voting - Majority Rule](https://en.wikipedia.org/wiki/Ranked_voting#Majority-rule)] *Example: 3 Candidates, 3 Voters. The Voters votes are:* 1. A-C-B 2. B-A-C 3. C-B-A *A cannot be the Condorcet winner, because 2/3 of voters prefer B over A.* *Nor can B be the Condorcet winner, because 2/3 of voters prefer C over B.* *Similar logic applies for C.* #### Rated Voting Systems --- #### Approval Voting Systems --- ## Sources - Fundamentals of Social Choice Theory - https://www.eecs.harvard.edu/cs286r/courses/fall11/papers/Myerson96.pdf --- - Arrow, K. J. (2012). Social choice and individual values (Vol. 12). 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