1 / 18

Understanding Group Ranking Methods in Decision Making

Explore different group-ranking approaches like Borda, Runoff, and Sequential Runoff methods. Learn how preferences are ranked, winners determined, and outcomes influenced. Practice calculations and examples to enhance understanding. Enhance your problem-solving skills in fair outcomes and decision-making processes.

talane
Download Presentation

Understanding Group Ranking Methods in Decision Making

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Group-Ranking How is group ranking accomplished?

  2. NC Standard Course of Study • Competency Goal 2: The learner will analyze data and apply probability concepts to solve problems. • Objective 2.03: Model and solve problems involving fair outcomes: • Apportionment. • Election Theory. • Voting Power. • Fair Division.

  3. Types of Winners • There are several ways that the winner can be chosen from a group-ranking situation. • When the winner is chosen because they are ranked first more than any other choice, the winner is known as the plurality winner. • If the winner is chosen because they are first on more than half of the preferences, the winner is known as the majority winner.

  4. Group-Ranking • There are many methods used to rank preferences. These methods include: • The Borda Method • The Runoff Method, and • The Sequential Runoff Method

  5. The Borda Method • In the Borda method, points are assigned to the choices by the order they come, this is known as a Borda count. • To do a Borda count you rank n number of choices by assigning n points to the first choice, n-1 to the second, n-2 to the third, … and 1 point to the last. • The group ranks are then made by adding each choice’s points.

  6. For this example, to calculate the Borda winner we would do: A: 8(4)+5(1)+6(1)+7(1)=50 B: 8(3)+5(4)+6(3)+7(3)=83 C: 8(2)+5(3)+6(4)+7(2)=69 D: 8(1)+5(2)+6(2)+7(4)=58 Borda Example A B B C C D D A 8 5 C D B B D C A A 6 7

  7. You try! • Determine the plurality and Borda winner for the set of preferences shown below: C C A B D D B D C A D A C B B A 16 20 12 7

  8. The Runoff Method • This is a very popular method, that we currently use (as in runoff elections) • Is expensive and time-consuming. • Use preference schedules to avoid hassles.

  9. Runoff Method Process • To conduct a runoff, • Determine the number of firsts for each choice • Eliminate all but the two highest totals • Then consider each preference schedule on which the eliminated choices were chosen first and the points from that preference awarded to the choice that ranked highest

  10. Runoff Method Example D A B C B C B B C D D C D A A A 8 5 6 7 A D D D D A A A 8 5 6 7

  11. Runoff Example (continued) • Notice that the runoff method eliminates all choices except the two with the most firsts: • Therefore, B and C were eliminated • Because those two are eliminated, the choice that ranks highest of the remaining choices gets the votes for that group. A:8 D: 7 + 5 + 6 =18 • Therefore, D is the runoff winner.

  12. You try! • Determine the Runoff winner for the set of preferences shown below: C C A B D D B D C A D A C B B A 16 20 12 7

  13. Sequential Runoff Method • The sequential runoff method differs from the runoff method because it eliminates choices one at a time. • It eliminates the one that is ranked first the fewest times, and the points are awarded to the next highest choice.

  14. Sequential Runoff Method Example • B is eliminated since it has the fewest firsts. D A B C B C B B C D D C D A A A 8 5 6 7

  15. Sequential Runoff Method (cont’d) • The five votes for B are awarded to C: A: 8 C: 6+5= 11 D:7 (D is eliminated) D A C C C D D C D A A A 8 5 6 7

  16. Sequential Runoff Method (cont’d) • The seven votes for D are awarded to C: A: 8 C: 11+ 7 = 18 A C C C A C A A 8 5 6 7

  17. You try! • Determine the sequential runoff winner for the set of preferences shown below: C C A B D D B D C A D A C B B A 16 20 12 7

  18. Homework • A panel of sportswriters is selecting the best football team in a league, and the preferences are distributed as shown below. C B A B B A C C A 10 52 38

More Related