NOTE: To change the image on this slide, select the picture and delete it. Then click the Pictures icon in the placeholder to insert your own image. CHOOSING IN GROUPS MUNGER AND MUNGER Slides for Chapter 3 Choosing in Groups: An Intuitive Presentation

Outline of Chapter 3  Preferences  Group choice  Importance of procedures  Strategic voting  Condorcet paradox  Discovery or existence of general will  Closing remarks Slides Produced by Jeremy Spater, Duke University. All rights reserved.2

Preferences  Thin conception of preferences: Ordering (rank) of all alternatives from best to worst  Ties allowed  Useful because general  Thick conception of preferences  Idiosyncratic and subjective  Tastes, judgments, prejudices, attitudes, and beliefs  Exogenous preferences  For purpose of analysis, assume preferences come from outside the model, and are fixed  Start with constituted group, with existing preferences over set of alternatives  Set aside question of where group, preferences, and alternatives came from Slides Produced by Jeremy Spater, Duke University. All rights reserved.3

Preferences (2)  Ordering  Rank alternatives from best to worst  Analyst doesn’t need to know the reasons  Two people with same ordering may have completely different reasons  Ordering may be contingent on many other factors  Ordering provides a basis for collective action  If many of us agree that A is preferable (ranked higher) than B, we can form a coalition Slides Produced by Jeremy Spater, Duke University. All rights reserved.4

Using preferences to predict group choices  To define group choice, we need:  Thick orderings  Set of alternatives  Decision rule  Group choice problem:  Resolving disagreement in a way everyone agrees is legitimate  Group choice is not the same as group preference  Disagreements about preferences  These disagreements cannot be resolved by discussion  Preferences are individual, so someone else’s preferences probably won’t influence mine  Need a way to reach decision without changing individual preferences Slides Produced by Jeremy Spater, Duke University. All rights reserved.5

Group choice example  How to decide?  Simple vote: Tie (one vote each)  Vegetables, Then Fruit (vote on favorite vegetable, then vote on that vegetable vs. Apples)  Apples wins!  This outcome is fair, because everyone agreed on decision rule beforehand Slides Produced by Jeremy Spater, Duke University. All rights reserved.6 EugeneJustinWillow Best ApplesBroccoliCarrots Middle BroccoliCarrotsApples Worst CarrotsApplesBroccoli Carrots EugeneWillow Justin BroccoliApples JustinWillow Eugene

Importance of procedures  Members and procedures characterize groups  Procedures matter as much as members  Sometimes procedure determines outcome  In previous example, “Vegetables Then Fruit” rule led to Apple being chosen  Choice procedure must be specified in group constitution  Many “logical” decision rules are possible  “Air First, Then Dirt” leads to carrots winning! Slides Produced by Jeremy Spater, Duke University. All rights reserved.7 BroccoliApples JustinWillow Eugene ApplesCarrots EugeneJustin Willow

Strategic voting  Voters might “game” the system by misrepresenting their preferences  In previous example, with “Vegetables, Then Fruit” rule  Justin knows that Apples will beat Broccoli in the second round  So a vote for Broccoli (in first round) is really a vote for Apples... which Justin hates  By voting “dishonestly” for Carrots, Justin ensures that Carrots win  Justin can get his second-favorite instead of least-favorite  Strategic Voting  Before final round, look down the decision tree to see outcome of votes Slides Produced by Jeremy Spater, Duke University. All rights reserved.8 BroccoliCarrots EugeneWillow Justin CarrotsApples JustinEugene Willow

Slides Produced by Jeremy Spater, Duke University. All rights reserved.9

Condorcet Paradox  “Apples, Broccoli, Carrots” is one example  Necessary conditions  Three or more choices  Three or more agents  Disagreement of a certain kind  Neither persuasion nor compromise possible  Definition of Condorcet Paradox “If there are at least three choices and at least three choosers who disagree, then pairwise majority rule decision processes can imply intransitive group choices, even if all the individual preference orders are transitive." Slides Produced by Jeremy Spater, Duke University. All rights reserved.10

Condorcet Paradox (2)  Transitivity  For some binary relation R:  X R Y; Y R Z  X R Z  Cycle  Relation among X, Y, Z is a cycle if:  X R Y; Y R Z; Z R X  Cycle implies not transitive  If there is a cycle, then the option chosen depends on the agenda Slides Produced by Jeremy Spater, Duke University. All rights reserved.11

Slides Produced by Jeremy Spater, Duke University. All rights reserved.12

Condorcet paradox (3)  Individual preferences are transitive  No cycles exist in individual preferences  Group preference has a cycle in Condorcet paradox  There is a “cycling majority”  Different majorities prefer X to Y, Y to Z, and Z to X  By giving one majority its wish, we deny another majority  Condorcet winner  X is a Condorcet winner if it wins majority vote against any alternative  If there is a Condorcet winner, there is no cycling or Condorcet paradox  In Apples / Broccoli / Carrots example, there is no Condorcet winner  In absence of Condorcet winner, there may be no objectively “best” choice Slides Produced by Jeremy Spater, Duke University. All rights reserved.13

Discovery or existence of general will  If there is no Condorcet winner (or other determinate choice)  Then any choice of outcome is arbitrary or imposed  Cycling and Manipulability  Agenda setter can determine winner in case of cycle  Agents can vote strategically to defeat agenda-setter  Indeterminacy  No unique mapping from preferences to outcomes  A majority will favor some other feasible alternative  This can give rise to a perpetual cycle of revolutions, leading to dictatorship  Example of French Revolution leading to Napoleon  Democratic constitution must be designed to ensure stability Slides Produced by Jeremy Spater, Duke University. All rights reserved.14

Closing remarks  In general, members’ preferences are not always known by others  But in many situations they are known fairly well  Agenda control can be defeated by disguising preferences  Coalitions can be formed to secure preferences  Political parties can be thought of as long-standing coalitions  Systems based on constitutions and parties can result in stable outcomes Slides Produced by Jeremy Spater, Duke University. All rights reserved.15