I Everybody has individual preferences I Want to transform individual preferences to a single societal preference I Want to do this fairly Voting Theory I Big question: what is the best way to hold an election? I Want to transform individual preferences to a single societal preference I Want to do this fairly Voting Theory I Big question: what is the best way to hold an election? I Everybody has individual preferences I Want to do this fairly Voting Theory I Big question: what is the best way to hold an election? I Everybody has individual preferences I Want to transform individual preferences to a single societal preference Voting Theory I Big question: what is the best way to hold an election? I Everybody has individual preferences I Want to transform individual preferences to a single societal preference I Want to do this fairly I Don't require majority to win I A gets 32% I B gets 40% I C gets 28% I B I Candidate with most votes wins I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I A gets 32% I B gets 40% I C gets 28% I B I Don't require majority to win I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I A gets 32% I B gets 40% I C gets 28% I B I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I Don't require majority to win I A gets 32% I B gets 40% I C gets 28% I B I Example: I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I Don't require majority to win I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I B I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I Don't require majority to win I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I A gets 32% I B gets 40% I C gets 28% I B Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I Don't require majority to win I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I A gets 32% I B gets 40% I C gets 28% I Who wins? Plurality Voting Plurality Voting I Everyone gets one vote I Candidate with most votes wins I Don't require majority to win I Method for voting Governors, Congressmen, President (ignoring electoral colleges) I Example: I A gets 32% I B gets 40% I C gets 28% I Who wins? I B I B should win I The least preferred candidate wins! I Example of vote splitting I 1: Supporters of both A and C have B as their second choice I 2: Supporters of both A and C have B as their last choice I Possible scenarios: Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I B should win I The least preferred candidate wins! I Example of vote splitting I 1: Supporters of both A and C have B as their second choice I 2: Supporters of both A and C have B as their last choice Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I The least preferred candidate wins! I Example of vote splitting I B should win I 2: Supporters of both A and C have B as their last choice Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I 1: Supporters of both A and C have B as their second choice I The least preferred candidate wins! I Example of vote splitting I 2: Supporters of both A and C have B as their last choice Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I 1: Supporters of both A and C have B as their second choice I B should win I The least preferred candidate wins! I Example of vote splitting Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I 1: Supporters of both A and C have B as their second choice I B should win I 2: Supporters of both A and C have B as their last choice I Example of vote splitting Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I 1: Supporters of both A and C have B as their second choice I B should win I 2: Supporters of both A and C have B as their last choice I The least preferred candidate wins! Plurality Voting I Example: I A gets 32% I B gets 40% I C gets 28% I Possible scenarios: I 1: Supporters of both A and C have B as their second choice I B should win I 2: Supporters of both A and C have B as their last choice I The least preferred candidate wins! I Example of vote splitting I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Probable that many preferred Nader, but did not want to \throw away their vote" I From game theory: it is rarely a dominant strategy to enter the race I 2000 Presidential election: I Do these numbers truly reflect first preference? I Makes new third candidates unviable Plurality Voting I If there's only two candidates, the most preferred candidate wins I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Probable that many preferred Nader, but did not want to \throw away their vote" I From game theory: it is rarely a dominant strategy to enter the race I 2000 Presidential election: I Do these numbers truly reflect first preference? Plurality Voting I If there's only two candidates, the most preferred candidate wins I Makes new third candidates unviable I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Probable that many preferred Nader, but did not want to \throw away their vote" I 2000 Presidential election: I Do these numbers truly reflect first preference? Plurality Voting I If there's only two candidates, the most preferred candidate wins I Makes new third candidates unviable I From game theory: it is rarely a dominant strategy to enter the race I Probable that many preferred Nader, but did not want to \throw away their vote" I Do these numbers truly reflect first preference? Plurality Voting I If there's only two candidates, the most preferred candidate wins I Makes new third candidates unviable I From game theory: it is rarely a dominant strategy to enter the race I 2000 Presidential election: I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Probable that many preferred Nader, but did not want to \throw away their vote" Plurality Voting I If there's only two candidates, the most preferred candidate wins I Makes new third candidates unviable I From game theory: it is rarely a dominant strategy to enter the race I 2000 Presidential election: I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Do these numbers truly reflect first preference? Plurality Voting I If there's only two candidates, the most preferred candidate wins I Makes new third candidates unviable I From game theory: it is rarely a dominant strategy to enter the race I 2000 Presidential election: I Bush: 48:38% I Gore: 47:87% I Nader: 2:74% I Do these numbers truly reflect first preference? I Probable that many preferred Nader, but did not want to \throw away their vote" I A gets 32% I B gets 40% I C gets 28% I After election, eliminate weakest candidate(s) I Hold another election I Round 1: I C gets eliminated I Round 2: people who voted for C get their second preference I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I A gets 32% I B gets 40% I C gets 28% I Hold another election I Round 1: I C gets eliminated I Round 2: people who voted for C get their second preference I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I A gets 32% I B gets 40% I C gets 28% I Round 1: I C gets eliminated I Round 2: people who voted for C get their second preference I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I Hold another election I C gets eliminated I Round 2: people who voted for C get their second preference I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I Hold another election I Round 1: I A gets 32% I B gets 40% I C gets 28% I Round 2: people who voted for C get their second preference I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I Hold another election I Round 1: I A gets 32% I B gets 40% I C gets 28% I C gets eliminated I Used in French presidential elections Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I Hold another election I Round 1: I A gets 32% I B gets 40% I C gets 28% I C gets eliminated I Round 2: people who voted for C get their second preference Runoff Elections I One possible solution: hold runoff elections I After election, eliminate weakest candidate(s) I Hold another election I Round 1: I A gets 32% I B gets 40% I C gets 28% I C gets eliminated I Round 2: people who voted for C get their second preference I Used in French presidential elections I Inefficient; need to hold election over multiple days I Voters will more likely vote their preference I Least preferred candidate can't win I Problems: Runoff Elections I Perks: I Inefficient; need to hold election over multiple days I Least preferred