Dr. Y. İlker TOPCU. Dr. Özgür KABAK web.itu.edu.tr/kabak/
|
|
- Amie Lamb
- 5 years ago
- Views:
Transcription
1 Dr. Y. İlker TOPCU facebook.com/yitopcu twitter.com/yitopcu instagram.com/yitopcu Dr. Özgür KABAK web.itu.edu.tr/kabak/
2 Decision Making? Decision making may be defined as: Intentional and reflective choice in response to perceived needs (Kleindorfer et al., 1993) Decision maker s (DM s) choice of one alternative or a subset of alternatives among all possible alternatives with respect to her/his goal or goals (Evren and Ülengin, 1992) Solving a problem by choosing, ranking, or classifying over the available alternatives that are characterized by multiple criteria (Topcu, 1999) Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 2
3 Group Decision Making? Decision situation in which there are more than one decision maker involved (Lu et al., 2007). These group members have their own attitudes and motivations, recognise the existence of a common problem, and attempt to reach a collective decision (Hwang and Lin, 1987). The problem is no longer the selection of the most preferred alternative according to one single DM's preference structure. The analysis must be extended to account for the conflicts among different interest groups who have different objectives, goals, criteria, and so on. Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 3
4 Group Decision Making Process Oriented Approaches Content Oriented Approaches Implicit Multiattribute Evaluation Explicit Multiattribute Evaluation Game-Theoretic Approach Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 4
5 GDM Methods Content-oriented approaches Focuses on the content of the problem, attempting to find an optimal or satisfactory solution given certain social or group constraints, or objectives Process-oriented approaches Focuses on the process of making a group decision. The main objective is to generate new ideas. Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 5
6 Content-Oriented Methods Assumptions: All participants of the GDM share the same set of alternatives, but not necessarily the same set of evaluation criteria Prior to the GDM process, each group member must have performed her/his own assessment of preferences. The output is a vector of normalized and cardinal ranking, a vector of ordinal ranking, or a vector of outranking relations performed on the alternatives. Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 6
7 Content-Oriented Approaches Implicit Multiattribute Evaluation (Social Choice Theory) Explicit Multiattribute Evaluation Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 7
8 SOCIAL CHOICE THEORY Voting Social Choice Function Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 8
9 Voting Methods Nonranked Voting System Preferential Voting System Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 9
10 Nonranked Voting System One member elected from two candidates One member elected from many candidates Election of two or more members Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 10
11 One member elected from two candidates Election by simple majority Each voter can vote for one candidate The candidate with the greater vote total wins the election Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 11
12 One member elected from many candidates The first-past-the-post system Election by simple majority Majority representation system Repeated ballots Voting goes on through a series of ballots until some candidate obtains an absolute majority of the votes cast The second ballot On the first ballot a candidate can t be elected unless he obtains an absolute majority of the votes cast The second ballot is a simple plurality ballot involving the two candidates who had been highest in the first ballot Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 12
13 Election of two or more members The single non-transferable vote Each voter has one vote Multiple vote Each voter has as many votes as the number of seats to be filled Voters can t cast more than one vote for each candidate Limited vote Each voter has a number of votes smaller than the number of seats to be filled Voters can t cast more than one vote for each candidate Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 13
14 Election of two or more members ctd. Cumulative vote Each voter has as many votes as the number of seats to be filled Voters can cast more than one vote for candidates List systems Voter chooses between lists of candidates Highest average (d Hondt s rule) Greatest remainder Approval voting Each voter can vote for as many candidates as he/she wishes Voters can t cast more than one vote for each candidate Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 14
15 EXAMPLE Suppose an constituency in which 200,000 votes are cast for four party lists contesting five seats and suppose the distribution of votes is: A 86,000 B 56,000 C 38,000 D 20,000 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 15
16 Solution with Highest average (d Hondt s) method The seats are allocated one by one and each goes to the list which would have the highest average number of votes At each allocation, each list s original total of votes is divided by one more than the number of seats that list has already won in order to find what its average would be /2 /3 A 86,000 43,000 43,000 28,667 28,667 3 B 56,000 56,000 28,000 28,000 28,000 1 C 38,000 38,000 38,000 38,000 19,000 1 D 20,000 20,000 20,000 20,000 20,000 0 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 16
17 Solution with Greatest remainder method An electoral quotient is calculated by dividing total votes by the number of seats Each list s total of votes is divided by the quotient and each list is given as many seats as its poll contains the quotient. If any seats remain, these are allocated successively between the competing lists according to the sizes of the remainder 200,000 / 5 = 40,000 List Votes Seats Remainder Seats A B C D Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 17
18 Disadvantages of Nonranked Voting Nonranked voting systems arise serious questions as to whether these are fair and proper representations of the voters will Extraordinary injustices may result unless preferential voting systems are used Contradictions (3 cases of Dodgson) Dr. Y. İlker Topcu ( & Dr. Özgür Kabak 18
19 Case 1 of Dodgson Contradiction in simple majority: Candidate A and B Order of preference V1 V2 V3 V4 V5 Voters V6 V7 V8 V9 V10 V11 1 A A A B B B B C C C D 2 C C C A A A A A A A A 3 D D D C C C C D D D C 4 B B B D D D D B B B B Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 19
20 Case 2 of Dodgson Contradiction in absolute majority: Candidate A and B Order of Preference V1 V2 V3 V4 V5 Voters V6 V7 V8 V9 V10 V11 1 B B B B B B A A A A A 2 A A A A A A C C C D D 3 C C C D D D D D D C C 4 D D D C C C B B B B B Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 20
21 Case 3 of Dodgson Contradiction in absolute majority, the second ballot: Elimination of candidate A Order of Preference V1 V2 V3 V4 V5 Voters V6 V7 V8 V9 V10 V11 1 B B B C C C C D D A A 2 A A A A A A A A A B D 3 D C D B B B D C B D C 4 C D C D D D B B C C B Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 21
22 Preferential Voting System The voter places 1 on the ballot paper against the name of the candidate whom he considers most suitable He/she places a figure 2 against the name of his second choice, and so on... The votes are counted and the individual preferences are aggregated with the principle of simple majority rule Strict Simple Majority xpy: #(i:xp i y) > #(i:yp i x) Weak Simple Majority xry: #(i:xp i y) > #(i:yp i x) Tie xiy: #(i:xp i y) = #(i:yp i x) Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 22
23 Preferential Voting System More than Two Alternative Case: According to Condorcet Principle, if a candidate beats every other candidate under simple majority, this will be the Condorcet winner and there will not be any paradox of voting Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 23
24 EXAMPLE Suppose the 100 voters preferential judgments are as follows: 38 votes: a P c P b 32 votes: b P c P a 27 votes: c P b P a 3 votes: c P a P b All candidates are compared two by two: a P b: 41 votes; b P a 59 votes a P c: 38 votes; c P a 62 votes c P b P a b P c: 32 votes; c P b 68 votes c is condorcet winner Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 24
25 Advantages of Preferential Voting Simple Majority Second ballot If nonranked voting is utilized for the example: 38 votes: a P c P b 32 votes: b P c P a 27 votes: c P b P a 3 votes: c P a P b Absolute majority is 51 votes: c is eliminated The second ballot is a simple plurality ballot Suppose preferential ranks are not changed a: 38 votes b: 32 votes c: 27+3=30 votes a: 41 votes b: 59 votes Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 25
26 Disadvantages of Preferential Voting Committee would have a circular preference among the alternatives: would not be able to arrive at a transitive ranking 23 votes: a P b P c 17 votes: b P c P a 2 votes: b P a P c 10 votes: c P a P b 8 votes: c P b P a b P c (42>18), c P a (35>25), a P b (33>27) Intransitivity (paradox of voting) Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 26
27 Disadvantages of Preferential Voting ctd. Aggregate judgments can be incompatible Order of preference Voters V1 A B C D V2 D A B C V3 B C D A Winner BP D AP B AP C A DP A BP D BP C B AP B DP A CP D C AP B AP C DP A D Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 27
28 Social Choice Functions Condorcet s function Borda s function Copeland s function Nanson s function Dodgson s function Eigenvector function Kemeny s function Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 28
29 EXAMPLE Suppose the 100 voters preferential judgments are as follows: 38 votes: a P b P c 28 votes: b P c P a 17 votes: c P a P b 14 votes: c P b P a 3 votes: b P a P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 29
30 Condercet s Function The candidates are ranked in the order of the values of f C f C (x) = min #(i: x P i y) y A\{x} a P b 55 votes & b P a 45 votes a P c 41 votes & c P a 59 votes b P c 69 votes & c P b 31 votes a b c fc a b c b P a P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 30
31 Borda s Function The candidates are ranked in the order of the values of f B f B (x) = #(i: x P i y) y A a b c fb a b c b P a P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 31
32 Borda s Function (alternative approach) A rank order method is used. With m candidates competing, assign marks of m 1, m 2,..., 1, 0 to the first ranked, second ranked,..., last ranked but one, last ranked candidate for each voter. Determine the Borda score for each candidate as the sum of the voter marks for that candidate a: 2 * * * * * 3 = 96 b: 2 * ( ) + 1 * ( ) + 0 * 17 = 114 c: 2 * ( ) + 1 * * ( ) = 90 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 32
33 Copeland s Function The candidates are ranked in the order of the values of f CP f CP (x) is the number of candidates in A that x has a strict simple majority over, minus the number of candidates in A that have strict simple majorities over x f CP (x) = #(y: y A x P y) - #(y: y A y P x) #(i: a P i b) = 55 > #(i: b P i a) = 45 a P b #(i: a P i c) = 41 < #(i: c P i a) = 59 c P a #(i: b P i c) = 69 > #(i: c P i b) = 31 b P c f CP (a) = 1-1 = 0, f CP (b) = 1-1 = 0, f CP (c) = 1-1 = 0 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 33
34 Copeland s Function (another example) 38 votes: a P c P b 32 votes: b P c P a 27 votes: c P b P a 3 votes: c P a P b Judgments of simple majority: b P a, c P a and c P b f CP (a) = 0 2 = 2; f CP (b) = 1 1 = 0; f CP (c) = 2 0 = 2 The ranking of alternatives: c P b P a Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 34
35 Nanson s Function Let A 1 = A and for each j > 1 let A j+1 = A j \ {x A j : f B (x) < f B (y) for all y A j, and f B (x) < f B (y) for some y A j } where f B (x) is the Borda score Then f N (x) = lim A j gives the winning candidate A 1 = A = {a, b, c} f B (a) = 96 f B (b) =114 f B (c) = 90 j Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 35
36 Nanson s Function ctd. Candidate c is eliminated as s/he has the lowest score: A 2 = {a, b} 38 votes: a P b 28 votes: b P a 17 votes: a P b 14 votes: b P a 3 votes: b P a f B (a) = 55 f B (b) = 45 Candidate b is eliminated and candidate a is the winner: a P b P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 36
37 Dodgson s Function Based on the idea that the candidates are scored on the basis of the smallest number of changes needed in voters preference orders to create a simple majority winner (or nonloser). a b c change a - 55/45 41/59 b 45/55-69/31 c 59/41 31/ b P a P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 37
38 Eigenvector Function Based on pairwise comparisons on the number of voters between pair of alternatives The idea is based on finding the eigenvector corresponding to the largest eigenvalue of a positive matrice(pairwise comparison matrix: D) X 1 X 2. X m X 1 1 n 12 / n 21 n 1m / n m1 X 2 n 21 / n 12 1 n 2m / n m2 X m n m1 / n 1m n m2 / n 2m 1 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 38
39 Eigenvector Function First construct the pairwise comparison matrix A: Then find the eigenvector of A: a b c a b c sum a b c a 1 55/45 41/59 b 45/ /31 c 59/41 31/69 1 a b c a b c b P a P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 39
40 Which one to choose? The most appropriate compromise or consensus ranking should be defined according to Kemeny s function Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 40
41 Kemeny s function Based on finding the maximization of the total amount of agreement or similarity between the consensus rankings and voters preference orderings on the alternatives Let L be the consensus ranking matrix E be a translated election matrix: M-M t f K = max <E, L> where <E, L> is the inner product of E and L Inner (dot) product of vectors [1, 3, 5] and [4, 2, 1]: (1)(4) + (3)(-2) + (-5)(-1) = 3 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 41
42 Example Social Choice Functions Condercet s Function Borda s Function Dodgson s Function Nanson s Function Eigenvector Function Ranking b P a P c b P a P c b P a P c a P b P c b P a P c Evaluate two rankings according to Kemeny s function: b P a P c a P b P c Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 42
43 f K = max <E, L> E = M-M T M a b c a b c E a b c a b c L a b c a b c b P a P c F k (bpapc) = = 20 a P b P c L a b c a b c F k (apbpc) = = 60 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 43
44 Additional Example Voting, List System Suppose the results of the last election for Muğla is as follows. If Muğla is represented by 8 deputies in the parliament, how many deputies should each party get? Parties Votes A B C D E Total Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 44
45 Additional Example Social Choice Functions The professors of ITU The Industrial Engineering department wants to select the head of the department. The preferences of 60 professors are listed in the Table. Who should be selected as the head? a P b P c 23 b P c P a 17 b P a P c 2 c P a P b 10 c P b P a 8 60 Dr. Y. İlker Topcu ( & Dr. Özgür Kabak (kabak@itu.edu.tr) 45
Dr. Y. İlker TOPCU. Dr. Özgür KABAK web.itu.edu.tr/kabak/
Dr. Y. İlker TOPCU www.ilkertopcu.net www.ilkertopcu.org www.ilkertopcu.info facebook.com/yitopcu twitter.com/yitopcu instagram.com/yitopcu Dr. Özgür KABAK web.itu.edu.tr/kabak/ MADM Methods Elementary
More informationSurvey of Voting Procedures and Paradoxes
Survey of Voting Procedures and Paradoxes Stanford University ai.stanford.edu/ epacuit/lmh Fall, 2008 :, 1 The Voting Problem Given a (finite) set X of candidates and a (finite) set A of voters each of
More informationPartial lecture notes THE PROBABILITY OF VIOLATING ARROW S CONDITIONS
Partial lecture notes THE PROBABILITY OF VIOLATING ARROW S CONDITIONS 1 B. Preference Aggregation Rules 3. Anti-Plurality a. Assign zero points to a voter's last preference and one point to all other preferences.
More informationAlgorithmic Game Theory Introduction to Mechanism Design
Algorithmic Game Theory Introduction to Mechanism Design Makis Arsenis National Technical University of Athens April 216 Makis Arsenis (NTUA) AGT April 216 1 / 41 Outline 1 Social Choice Social Choice
More informationChoosing Collectively Optimal Sets of Alternatives Based on the Condorcet Criterion
1 / 24 Choosing Collectively Optimal Sets of Alternatives Based on the Condorcet Criterion Edith Elkind 1 Jérôme Lang 2 Abdallah Saffidine 2 1 Nanyang Technological University, Singapore 2 LAMSADE, Université
More informationInequality of Representation
Inequality of Representation Hannu Nurmi Public Choice Research Centre University of Turku Institutions in Context: Inequality (HN/PCRC) Inequality of Representation June 3 9, 2013 1 / 31 The main points
More informationCMU Social choice 2: Manipulation. Teacher: Ariel Procaccia
CMU 15-896 Social choice 2: Manipulation Teacher: Ariel Procaccia Reminder: Voting Set of voters Set of alternatives Each voter has a ranking over the alternatives means that voter prefers to Preference
More informationProbabilistic Aspects of Voting
Probabilistic Aspects of Voting UUGANBAATAR NINJBAT DEPARTMENT OF MATHEMATICS THE NATIONAL UNIVERSITY OF MONGOLIA SAAM 2015 Outline 1. Introduction to voting theory 2. Probability and voting 2.1. Aggregating
More information6.207/14.15: Networks Lecture 24: Decisions in Groups
6.207/14.15: Networks Lecture 24: Decisions in Groups Daron Acemoglu and Asu Ozdaglar MIT December 9, 2009 1 Introduction Outline Group and collective choices Arrow s Impossibility Theorem Gibbard-Satterthwaite
More informationChapter 1. The Mathematics of Voting
Introduction to Contemporary Mathematics Math 112 1.1. Preference Ballots and Preference Schedules Example (The Math Club Election) The math club is electing a new president. The candidates are Alisha
More informationGROUP DECISION MAKING
1 GROUP DECISION MAKING How to join the preferences of individuals into the choice of the whole society Main subject of interest: elections = pillar of democracy Examples of voting methods Consider n alternatives,
More informationVoting Handout. Election from the text, p. 47 (for use during class)
Voting Handout Election from the text, p. 47 (for use during class) 3 2 1 1 2 1 1 1 1 2 A B B B D D E B B E C C A C A A C E E C D D C A B E D C C A E E E E E B B A D B B A D D C C A D A D 1. Use the following
More informationIntroduction to Formal Epistemology Lecture 5
Introduction to Formal Epistemology Lecture 5 Eric Pacuit and Rohit Parikh August 17, 2007 Eric Pacuit and Rohit Parikh: Introduction to Formal Epistemology, Lecture 5 1 Plan for the Course Introduction,
More informationCONNECTING PAIRWISE AND POSITIONAL ELECTION OUTCOMES
CONNECTING PAIRWISE AND POSITIONAL ELECTION OUTCOMES DONALD G SAARI AND TOMAS J MCINTEE INSTITUTE FOR MATHEMATICAL BEHAVIORAL SCIENCE UNIVERSITY OF CALIFORNIA, IRVINE, CA 9697-5100 Abstract General conclusions
More informationSocial Dichotomy Functions (extended abstract)
Social Dichotomy Functions (extended abstract) Conal Duddy, Nicolas Houy, Jérôme Lang, Ashley Piggins, and William S. Zwicker February 22, 2014 1 What is a Social Dichotomy Function? A dichotomy A = (A
More informationVolume 31, Issue 1. Manipulation of the Borda rule by introduction of a similar candidate. Jérôme Serais CREM UMR 6211 University of Caen
Volume 31, Issue 1 Manipulation of the Borda rule by introduction of a similar candidate Jérôme Serais CREM UMR 6211 University of Caen Abstract In an election contest, a losing candidate a can manipulate
More informationNontransitive Dice and Arrow s Theorem
Nontransitive Dice and Arrow s Theorem Undergraduates: Arthur Vartanyan, Jueyi Liu, Satvik Agarwal, Dorothy Truong Graduate Mentor: Lucas Van Meter Project Mentor: Jonah Ostroff 3 Chapter 1 Dice proofs
More informationAPPLIED MECHANISM DESIGN FOR SOCIAL GOOD
APPLIED MECHANISM DESIGN FOR SOCIAL GOOD JOHN P DICKERSON Lecture #3 09/06/2016 CMSC828M Tuesdays & Thursdays 12:30pm 1:45pm REMINDER: SEND ME TOP 3 PRESENTATION PREFERENCES! I LL POST THE SCHEDULE TODAY
More informationThe Best Way to Choose a Winner
The Best Way to Choose a Winner Vicki Powers Emory University, Atlanta, GA currently: National Science Foundation, Division of Mathematical Sciences Universität Konstanz, April 14, 2014 What is this talk
More informationAntipodality in committee selection. Abstract
Antipodality in committee selection Daniel Eckert University of Graz Christian Klamler University of Graz Abstract In this paper we compare a minisum and a minimax procedure as suggested by Brams et al.
More informationSpring 2016 Indiana Collegiate Mathematics Competition (ICMC) Exam
Spring 2016 Indiana Collegiate Mathematics Competition (ICMC) Exam Mathematical Association of America Indiana Section Written by: Paul Fonstad, Justin Gash, and Stacy Hoehn (Franklin College) PROBLEM
More information3.1 Arrow s Theorem. We study now the general case in which the society has to choose among a number of alternatives
3.- Social Choice and Welfare Economics 3.1 Arrow s Theorem We study now the general case in which the society has to choose among a number of alternatives Let R denote the set of all preference relations
More informationUsing a hierarchical properties ranking with AHP for the ranking of electoral systems
Università di Pisa Dipartimento di Informatica Technical Report: TR-08-26 Using a hierarchical properties ranking with AHP for the ranking of electoral systems Lorenzo Cioni lcioni@di.unipi.it September
More informationApproval Voting: Three Examples
Approval Voting: Three Examples Francesco De Sinopoli, Bhaskar Dutta and Jean-François Laslier August, 2005 Abstract In this paper we discuss three examples of approval voting games. The first one illustrates
More informationPoints-based rules respecting a pairwise-change-symmetric ordering
Points-based rules respecting a pairwise-change-symmetric ordering AMS Special Session on Voting Theory Karl-Dieter Crisman, Gordon College January 7th, 2008 A simple idea Our usual representations of
More informationLose Big, Win Big, Sum Big: An Exploration of Ranked Voting Systems
Bard College Bard Digital Commons Senior Projects Spring 016 Bard Undergraduate Senior Projects 016 Lose Big, Win Big, Sum Big: An Exploration of Ranked Voting Systems Erin Else Stuckenbruck Bard College
More informationSocial Choice. Jan-Michael van Linthoudt
Social Choice Jan-Michael van Linthoudt Summer term 2017 Version: March 15, 2018 CONTENTS Remarks 1 0 Introduction 2 1 The Case of 2 Alternatives 3 1.1 Examples for social choice rules............................
More informationThema Working Paper n Université de Cergy Pontoise, France
Thema Working Paper n 2010-02 Université de Cergy Pontoise, France Sincere Scoring Rules Nunez Matias May, 2010 Sincere Scoring Rules Matías Núñez May 2010 Abstract Approval Voting is shown to be the unique
More informationRecap Social Choice Fun Game Voting Paradoxes Properties. Social Choice. Lecture 11. Social Choice Lecture 11, Slide 1
Social Choice Lecture 11 Social Choice Lecture 11, Slide 1 Lecture Overview 1 Recap 2 Social Choice 3 Fun Game 4 Voting Paradoxes 5 Properties Social Choice Lecture 11, Slide 2 Formal Definition Definition
More informationPolitical Economy of Institutions and Development. Lectures 2 and 3: Static Voting Models
14.773 Political Economy of Institutions and Development. Lectures 2 and 3: Static Voting Models Daron Acemoglu MIT February 7 and 12, 2013. Daron Acemoglu (MIT) Political Economy Lectures 2 and 3 February
More informationComplexity of Shift Bribery in Hare, Coombs, Baldwin, and Nanson Elections
Complexity of Shift Bribery in Hare, Coombs, Baldwin, and Nanson Elections Cynthia Maushagen, Marc Neveling, Jörg Rothe, and Ann-Kathrin Selker Institut für Informatik Heinrich-Heine-Universität Düsseldorf
More informationVoting Theory: Pairwise Comparison
If is removed, which candidate will win if Plurality is used? If C is removed, which candidate will win if Plurality is used? If B is removed, which candidate will win if Plurality is used? Voting Method:
More informationHow Credible is the Prediction of a Party-Based Election?
How Credible is the Prediction of a Party-Based Election? Jiong Guo Shandong University School of Computer Science and Technology SunHua Road 1500, 250101 Jinan, China. jguo@mmci.unisaarland.de Yash Raj
More informationInstituto de Engenharia de Sistemas e Computadores de Coimbra Institute of Systems Engineering and Computers INESC - Coimbra
Instituto de Engenharia de Sistemas e Computadores de Coimbra Institute of Systems Engineering and Computers INESC - Coimbra Claude Lamboray Luis C. Dias Pairwise support maximization methods to exploit
More information14.770: Introduction to Political Economy Lectures 1 and 2: Collective Choice and Voting
14.770: Introduction to Political Economy Lectures 1 and 2: Collective Choice and Voting Daron Acemoglu MIT September 6 and 11, 2017. Daron Acemoglu (MIT) Political Economy Lectures 1 and 2 September 6
More informationEmpirical Comparisons of Various Voting Methods in Bagging
Empirical Comparisons of Various Voting Methods in Bagging Kelvin T. Leung, D. Stott Parker UCLA Computer Science Department Los Angeles, California 90095-1596 {kelvin,stott}@cs.ucla.edu ABSTRACT Finding
More informationComputing Spanning Trees in a Social Choice Context
Computing Spanning Trees in a Social Choice Context Andreas Darmann, Christian Klamler and Ulrich Pferschy Abstract This paper combines social choice theory with discrete optimization. We assume that individuals
More informationAn equity-efficiency trade-off in a geometric approach to committee selection Daniel Eckert and Christian Klamler
An equity-efficiency trade-off in a geometric approach to committee selection Daniel Eckert and Christian Klamler An equity-efficiency trade-off in a geometric approach to committee selection Daniel Eckert
More informationSocial choice theory, Arrow s impossibility theorem and majority judgment
Université Paris-Dauphine - PSL Cycle Pluridisciplinaire d Etudes Supérieures Social choice theory, Arrow s impossibility theorem and majority judgment Victor Elie supervised by Miquel Oliu Barton June
More informationCondorcet Efficiency: A Preference for Indifference
Condorcet Efficiency: A Preference for Indifference William V. Gehrlein Department of Business Administration University of Delaware Newark, DE 976 USA Fabrice Valognes GREBE Department of Economics The
More informationComputational Aspects of Strategic Behaviour in Elections with Top-Truncated Ballots
Computational Aspects of Strategic Behaviour in Elections with Top-Truncated Ballots by Vijay Menon A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree
More information13 Social choice B = 2 X X. is the collection of all binary relations on X. R = { X X : is complete and transitive}
13 Social choice So far, all of our models involved a single decision maker. An important, perhaps the important, question for economics is whether the desires and wants of various agents can be rationally
More informationFinite Dictatorships and Infinite Democracies
Finite Dictatorships and Infinite Democracies Iian B. Smythe October 20, 2015 Abstract Does there exist a reasonable method of voting that when presented with three or more alternatives avoids the undue
More informationA Failure of Representative Democracy
A Failure of Representative Democracy Katherine Baldiga Harvard University August 30, 2011 Abstract We compare direct democracy, in which members of a population cast votes for alternatives as choice problems
More informationAPPLIED MECHANISM DESIGN FOR SOCIAL GOOD
APPLIED MECHANISM DESIGN FOR SOCIAL GOOD JOHN P DICKERSON Lecture #21 11/8/2016 CMSC828M Tuesdays & Thursdays 12:30pm 1:45pm IMPOSSIBILITY RESULTS IN VOTING THEORY / SOCIAL CHOICE Thanks to: Tuomas Sandholm
More informationWinning probabilities in a pairwise lottery system with three alternatives
Economic Theory 26, 607 617 (2005) DOI: 10.1007/s00199-004-059-8 Winning probabilities in a pairwise lottery system with three alternatives Frederick H. Chen and Jac C. Heckelman Department of Economics,
More informationThe Pairwise-Comparison Method
The Pairwise-Comparison Method Lecture 12 Section 1.5 Robb T. Koether Hampden-Sydney College Mon, Sep 19, 2016 Robb T. Koether (Hampden-Sydney College) The Pairwise-Comparison Method Mon, Sep 19, 2016
More informationStackelberg Voting Games: Computational Aspects and Paradoxes
Stackelberg Voting Games: Computational Aspects and Paradoxes Lirong Xia Department of Computer Science Duke University Durham, NC 7708, USA lxia@cs.duke.edu Vincent Conitzer Department of Computer Science
More informationCondorcet Consistency and the strong no show paradoxes
Condorcet Consistency and the strong no show paradoxes Laura Kasper Hans Peters Dries Vermeulen July 10, 2018 Abstract We consider voting correspondences that are, besides Condorcet Consistent, immune
More informationGeometry of distance-rationalization
Geometry of distance-rationalization B.Hadjibeyli M.C.Wilson Department of Computer Science, University of Auckland Benjamin Hadjibeyli (ENS Lyon) Geometry of distance-rationalization Talk CMSS 1 / 31
More informationAn NTU Cooperative Game Theoretic View of Manipulating Elections
An NTU Cooperative Game Theoretic View of Manipulating Elections Michael Zuckerman 1, Piotr Faliszewski 2, Vincent Conitzer 3, and Jeffrey S. Rosenschein 1 1 School of Computer Science and Engineering,
More informationFrom Sentiment Analysis to Preference Aggregation
From Sentiment Analysis to Preference Aggregation Umberto Grandi Department of Mathematics University of Padova 22 November 2013 [Joint work with Andrea Loreggia, Francesca Rossi and Vijay Saraswat] What
More informationOn the Strategy-proof Social Choice of Fixed-sized Subsets
Nationalekonomiska institutionen MASTER S THESIS, 30 ECTS On the Strategy-proof Social Choice of Fixed-sized Subsets AUTHOR: ALEXANDER REFFGEN SUPERVISOR: LARS-GUNNAR SVENSSON SEPTEMBER, 2006 Contents
More informationEfficient Algorithms for Hard Problems on Structured Electorates
Aspects of Computation 2017 Efficient Algorithms for Hard Problems on Structured Electorates Neeldhara Misra The standard Voting Setup and some problems that we will encounter. The standard Voting Setup
More informationA STRONG NO SHOW PARADOX IS A COMMON FLAW IN CONDORCET VOTING CORRESPONDENCES
A STRONG NO SHOW PARADOX IS A COMMON FLAW IN CONDORCET VOTING CORRESPONDENCES Joaquín PEREZ Departamento de Fundamentos de Economía e Historia Económica. Universidad de Alcalá. Plaza de la Victoria. 28802
More informationWho wins the election? Polarizing outranking relations with large performance differences. Condorcet s Approach. Condorcet s method
Who wins the election? Polarizing outranking relations with large performance differences Raymond Bisdorff Université du Luxembourg FSTC/ILAS ORBEL 26, Bruxelles, February 2012 Working hypothesis: 1. Each
More informationMultiple Equilibria in the Citizen-Candidate Model of Representative Democracy.
Multiple Equilibria in the Citizen-Candidate Model of Representative Democracy. Amrita Dhillon and Ben Lockwood This version: March 2001 Abstract De Sinopoli and Turrini (1999) present an example to show
More informationMATH : FINAL EXAM INFO/LOGISTICS/ADVICE
INFO: MATH 1300-01: FINAL EXAM INFO/LOGISTICS/ADVICE WHEN: Thursday (08/06) at 11:00am DURATION: 150 mins PROBLEM COUNT: Eleven BONUS COUNT: Two There will be three Ch13 problems, three Ch14 problems,
More informationA C B D D B C A C B A D
Sample Exam 1 Name SOLUTIONS T Name e sure to use a #2 pencil. alculators are allowed, but cell phones or palm pilots are NOT acceptable. Please turn cell phones off. MULTIPLE HOIE. hoose the one alternative
More informationChapter 12: Social Choice Theory
Chapter 12: Social Choice Theory Felix Munoz-Garcia School of Economic Sciences Washington State University 1 1 Introduction In this chapter, we consider a society with I 2 individuals, each of them endowed
More informationChabot College Fall Course Outline for Mathematics 47 MATHEMATICS FOR LIBERAL ARTS
Chabot College Fall 2013 Course Outline for Mathematics 47 Catalog Description: MATHEMATICS FOR LIBERAL ARTS MTH 47 - Mathematics for Liberal Arts 3.00 units An introduction to a variety of mathematical
More informationFair Divsion in Theory and Practice
Fair Divsion in Theory and Practice Ron Cytron (Computer Science) Maggie Penn (Political Science) Lecture 6-b: Arrow s Theorem 1 Arrow s Theorem The general question: Given a collection of individuals
More informationRepeated Downsian Electoral Competition
Repeated Downsian Electoral Competition John Duggan Department of Political Science and Department of Economics University of Rochester Mark Fey Department of Political Science University of Rochester
More informationApproval Voting for Committees: Threshold Approaches
Approval Voting for Committees: Threshold Approaches Peter Fishburn Aleksandar Pekeč WORKING DRAFT PLEASE DO NOT CITE WITHOUT PERMISSION Abstract When electing a committee from the pool of individual candidates,
More informationArrow s Impossibility Theorem and Experimental Tests of Preference Aggregation
Arrow s Impossibility Theorem and Experimental Tests of Preference Aggregation Todd Davies Symbolic Systems Program Stanford University joint work with Raja Shah, Renee Trochet, and Katarina Ling Decision
More informationOn the probabilistic modeling of consistency for iterated positional election procedures
University of Iowa Iowa Research Online Theses and Dissertations Spring 2014 On the probabilistic modeling of consistency for iterated positional election procedures Mark A. Krines University of Iowa Copyright
More informationMechanism Design for Bounded Agents
Chapter 8 Mechanism Design for Bounded Agents Any fool can tell the truth, but it requires a man of some sense to know how to lie well. Samuel Butler Mechanism design has traditionally taken the conservative
More informationLecture Notes, Lectures 22, 23, 24. Voter preferences: Majority votes A > B, B > C. Transitivity requires A > C but majority votes C > A.
Lecture Notes, Lectures 22, 23, 24 Social Choice Theory, Arrow Possibility Theorem Paradox of Voting (Condorcet) Cyclic majority: Voter preferences: 1 2 3 A B C B C A C A B Majority votes A > B, B > C.
More informationTowards a Borda count for judgment aggregation
Towards a Borda count for judgment aggregation William S. Zwicker a a Department of Mathematics, Union College, Schenectady, NY 12308 Abstract In social choice theory the Borda count is typically defined
More informationApproximation algorithms and mechanism design for minimax approval voting
Approximation algorithms and mechanism design for minimax approval voting Ioannis Caragiannis Dimitris Kalaitzis University of Patras Vangelis Markakis Athens University of Economics and Business Outline
More informationNon compensatory Multicriteria Methods
Non compensatory Multicriteria Methods andrea.saltelli@jrc.ec.europa.eu 12 th JRC Annual Training on Composite Indicators & Multicriteria Decision Analysis (COIN 2014) European Commission Joint Research
More informationMultiwinner Elections Under Preferences that Are Single-Peaked on a Tree
Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Multiwinner Elections Under Preferences that Are Single-Peaked on a Tree Lan Yu 1, Hau Chan 2, and Edith Elkind
More informationThema Working Paper n Université de Cergy Pontoise, France
Thema Working Paper n -36 Université de Cergy Pontoise, France Positional rules and q- Condorcet consistency Sébastien Courtin Mathieu Martin Bertrand Tchantcho September, Positional rules and q Condorcet
More informationSocial Algorithms. Umberto Grandi University of Toulouse. IRIT Seminar - 5 June 2015
Social Algorithms Umberto Grandi University of Toulouse IRIT Seminar - 5 June 2015 Short presentation PhD from Universiteit van Amsterdam, 2012 Institute for Logic, Language and Computation Supervisor:
More informationConsistent Approval-Based Multi-Winner Rules
Consistent Approval-Based Multi-Winner Rules arxiv:1704.02453v3 [cs.gt] 20 Jul 2017 Martin Lackner University of Oxford Oxford, UK Piotr Skowron Technische Universität Berlin Berlin, Germany Abstract This
More informationComplexity of Shift Bribery in Iterative Elections
Complexity of Shift Bribery in Iterative Elections Cynthia Maushagen, Marc Neveling, Jörg Rothe, and Ann-Kathrin Selker Heinrich-Heine-Universität Düsseldorf Düsseldorf, Germany {maushagen,neveling,rothe,selker}@cs.uni-duesseldorf.de
More informationStrategy-Proofness on the Condorcet Domain
College of William and Mary W&M ScholarWorks Undergraduate Honors Theses Theses, Dissertations, & Master Projects 5-2008 Strategy-Proofness on the Condorcet Domain Lauren Nicole Merrill College of William
More informationLecture: Aggregation of General Biased Signals
Social Networks and Social Choice Lecture Date: September 7, 2010 Lecture: Aggregation of General Biased Signals Lecturer: Elchanan Mossel Scribe: Miklos Racz So far we have talked about Condorcet s Jury
More informationFORM-20 [See Rule 56 (7) ] FINAL RESULT SHEET
Election to the Lok Sabha from the 06 - BALASORE Parliamentary Constitutency PART - 1 (To be used both for Parliamentary and Assembly Elections) Total No of Electors in Assembly Constituency / Segment
More informationSYSU Lectures on the Theory of Aggregation Lecture 2: Binary Aggregation with Integrity Constraints
SYSU Lectures on the Theory of Aggregation Lecture 2: Binary Aggregation with Integrity Constraints Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam [ http://www.illc.uva.nl/~ulle/sysu-2014/
More informationCMU Social choice: Advanced manipulation. Teachers: Avrim Blum Ariel Procaccia (this time)
CMU 15-896 Social choice: Advanced manipulation Teachers: Avrim Blum Ariel Procaccia (this time) Recap A Complexity-theoretic barrier to manipulation Polynomial-time greedy alg can successfully decide
More informationFollow links for Class Use and other Permissions. For more information send to:
COPYRIGHT NOTICE: Ariel Rubinstein: Lecture Notes in Microeconomic Theory is published by Princeton University Press and copyrighted, c 2006, by Princeton University Press. All rights reserved. No part
More informationVoting. José M Vidal. September 29, Abstract. The problems with voting.
Voting José M Vidal Department of Computer Science and Engineering, University of South Carolina September 29, 2005 The problems with voting. Abstract The Problem The Problem The Problem Plurality The
More informationA preference aggregation method through the estimation of utility intervals
Available online at www.sciencedirect.com Computers & Operations Research 32 (2005) 2027 2049 www.elsevier.com/locate/dsw A preference aggregation method through the estimation of utility intervals Ying-Ming
More informationNon-Manipulable Domains for the Borda Count
Non-Manipulable Domains for the Borda Count Martin Barbie, Clemens Puppe * Department of Economics, University of Karlsruhe D 76128 Karlsruhe, Germany and Attila Tasnádi ** Department of Mathematics, Budapest
More informationLower Bound Issues in Computational Social Choice
Lower Bound Issues in Computational Social Choice Rolf Niedermeier Fakultät IV, Institut für Softwaretechnik und Theoretische Informatik, TU Berlin www.akt.tu-berlin.de Rolf Niedermeier (TU Berlin) Lower
More informationINFLUENCE IN BLOCK VOTING SYSTEMS. September 27, 2010
INFLUENCE IN BLOCK VOTING SYSTEMS KENNETH HALPERN Abstract. Motivated by the examples of the electoral college and Supreme Court, we consider the behavior of binary voting systems in which votes are cast
More informationTHE PROFILE STRUCTURE FOR LUCE S CHOICE AXIOM
THE PROFILE STRUCTURE FOR LUCE S CHOICE AXIOM DONALD G SAARI Abstract A geometric approach is developed to explain several phenomena that arise with Luce s choice axiom such as where differences occur
More informationPreference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates
Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates Bonifacio Llamazares, Teresa Peña Dep. de Economía Aplicada, PRESAD Research Group, Universidad
More informationIntroduction to Game Theory Lecture Note 2: Strategic-Form Games and Nash Equilibrium (2)
Introduction to Game Theory Lecture Note 2: Strategic-Form Games and Nash Equilibrium (2) Haifeng Huang University of California, Merced Best response functions: example In simple games we can examine
More informationSocial Choice and Social Networks. Aggregation of General Biased Signals (DRAFT)
Social Choice and Social Networks Aggregation of General Biased Signals (DRAFT) All rights reserved Elchanan Mossel UC Berkeley 8 Sep 2010 Extending Condorect s Jury Theorem We want to consider extensions
More informationSocial Choice and Mechanism Design - Part I.2. Part I.2: Social Choice Theory Summer Term 2011
Social Choice and Mechanism Design Part I.2: Social Choice Theory Summer Term 2011 Alexander Westkamp April 2011 Introduction Two concerns regarding our previous approach to collective decision making:
More informationAlgebraic Voting Theory
Algebraic Voting Theory Michael Orrison Harvey Mudd College Collaborators and Sounding Boards Don Saari (UC Irvine) Anna Bargagliotti (University of Memphis) Steven Brams (NYU) Brian Lawson (Santa Monica
More informationModel Building: Selected Case Studies
Chapter 2 Model Building: Selected Case Studies The goal of Chapter 2 is to illustrate the basic process in a variety of selfcontained situations where the process of model building can be well illustrated
More informationApproximation Algorithms and Mechanism Design for Minimax Approval Voting
Approximation Algorithms and Mechanism Design for Minimax Approval Voting Ioannis Caragiannis RACTI & Department of Computer Engineering and Informatics University of Patras, Greece caragian@ceid.upatras.gr
More informationBest reply dynamics for scoring rules
Best reply dynamics for scoring rules R. Reyhani M.C Wilson Department of Computer Science University of Auckland 3rd Summer workshop of CMSS, 20-22 Feb 2012 Introduction Voting game Player (voter) action
More informationA geometric examination of Kemeny's rule
Soc Choice Welfare (2000) 17: 403±438 9999 2000 A geometric examination of Kemeny's rule Donald G. Saari1, Vincent R. Merlin2 1 Department of Mathematics, Northwestern University, Evanston, IL 60208-2730
More informationREMOVING INCONSISTENCY IN PAIRWISE COMPARISON MATRIX IN THE AHP
MULTIPLE CRITERIA DECISION MAKING Vol. 11 2016 Sławomir Jarek * REMOVING INCONSISTENCY IN PAIRWISE COMPARISON MATRIX IN THE AHP DOI: 10.22367/mcdm.2016.11.05 Abstract The Analytic Hierarchy Process (AHP)
More informationEmpowering the Voter: A Mathematical Analysis of Borda Count Elections with Non-Linear Preferences
Empowering the Voter: A Mathematical Analysis of Borda Count Elections with Non-Linear Preferences A Senior Project submitted to The Division of Science, Mathematics, and Computing of Bard College by David
More informationWreath Products in Algebraic Voting Theory
Wreath Products in Algebraic Voting Theory Committed to Committees Ian Calaway 1 Joshua Csapo 2 Dr. Erin McNicholas 3 Eric Samelson 4 1 Macalester College 2 University of Michigan-Flint 3 Faculty Advisor
More information