VOTING TO ELECT A SINGLE CANDIDATE: EXAMPLES

Preference Profile 1

            # of voters                    46                                         20                            34

            1st pref.                       Labour                        Liberal                        Conservative

            2nd pref.                     Liberal                        Conservative               Liberal

            3rd pref.                      Conservative               Labour                        Labour

Plurality Ranking for Profile 1

                                    Candidates                              Votes Received (= First Preferences)

                                    Labour                                    46 votes (plurality winner)

                                    Conservative                           34 votes

                                    Liberal                                    20 votes

Borda Ranking for Profile 1

                                    Candidates                                               Points Received

                                    Liberal                                                220 points (Borda winner)

                                    Labour                                                192 points

                                    Conservative                                       188 points

Straight Fights for Profile 1

                                    Liberal vs. Conservative:       Liberal wins by 66-34

                                    Conservative vs. Labour:       Conservative wins by 54-46

                                    Liberal vs. Labour:                 Liberal wins by 54-46

Majority (or Condorcet) Ranking for Profile 1

                                    1st pref.                                   Liberal (Condorcet winner)

                                    2nd pref.                                 Conservative 

                                    3rd pref.                                  Labour (Condorcet loser)

Preference Profile 2

            # of voters                       46                                20                                 34

            1st pref.                       Labour                        Liberal                        Conservative

            2nd pref.                     Liberal                        Conservative               Labour

            3rd pref.                      Conservative               Labour                        Liberal

Straight fights for Profile 2

                                    Liberal vs. Conservative:      Liberal wins by 66-34

                                    Conservative vs. Labour:      Conservative wins by 54-46

                                    Labour vs. Liberal:               Labour wins by 80-20

Preference Profile 3

                        # of voters                              35                     33                  32

                        1st pref.                                   B                     C                     D          

                        2nd pref.                                 A                     A                     A

                        3rd pref.                                  C                     D                     B

                        4th pref.                                  D                     B                     C

“Single-Peaked Preferences”

                                               Admissible Orderings                                       Inadmissible

                    leftwingers                  centrists                   rightwingers                     Orderings

1st pref.           Lab              Lib                  Lib                  Con                       Con               Lab

2nd pref.         Lib               Lab                 Con                 Lib                         Lab               Con

3rd pref.          Con              Con                 Lab                 Lab                       Lib                Lib

Preference Profile 4

                                                                46                             54 

                        1st pref.                       Labour                        Conservative

                        2nd pref.                     Liberal                        Labour

                        3rd pref.                      Conservative               Liberal

                   Original Preference Profile 5                   Revised Preference Profile 5

                        35         10          25       30                             35         10        25        30

A            B          B        C                                A         A         B         C

                         B          A         C         A                                 B         B         C         A        

                         C          C         A         B                                 C         C         A         B

                                                                 Preference Profile 6

                                                            5          6          4          [2] 

                                                             B         C         A         [A] 

                                                             C         B         B         [B] 

                                                             A         A         C         [C]

Preference Profile (and Sincere Ballot Profile) 1A

                              Democrats                                                  Republicans

                        35%                25%                                        25%                15%

                         D1                    D2                                           R                    R

                         D2                    D1                                           D1                   D2

                          R                     R                                            D2                   D1

Preference Profile (and Sincere Ballot Profile) 1B (without and with Candidate R2)

                        60 voters                     40 voters                     Borda Ranking (Points)

                              D                            R1                                       D        (160)

                             R1                             D                                       R1       (140)

                         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                              D                             R1                                      R1       (220)

                             R1                            R2                                       D        (180)

                             R2                            D                                        R2       (140)

Preference (and Sincere Ballot) Profile 1C (with Strategic Ballot Profiles)

         50 voters     48 voters              1 voter            1 voter                      Borda Ranking (Points)

              D                    R                     T                     T                                 D         (249)

             R                     D                     D                     R                                 R         (247)

              T                    T                     R                     D                                 T         (104)

         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

             D                    R                     T                     T                                 R         (247)

             R                    T                     D                     R                                 D         (201)

             T                    D                     R                     D                                 T         (152)

         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

            D                    R                     T                     T                                 T         (202)

            T                    T                     D                     R                                 D         (201)

            R                    D                     R                     D                                 R         (197)