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Approximating Maximum Satisfaction in Group Formation

This study proposes a method to maximize happiness or satisfaction in forming groups by considering individual preferences and work style preferences. It explores different approximation techniques and evaluates the results.

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Approximating Maximum Satisfaction in Group Formation

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  1. Approximating Maximum Satisfaction in Group Formation Sean Munson, Grant HutchinsOlin College Exposition21 December 2004 Design • Lifelong Learning • Communication • Qualitative Analysis

  2. goal • Maximize happiness, or satisfaction • Input • Preferences: -1, 0, or 1 for each person • Worked with before • Work style preferences • Satisfaction: how many preferences you meet

  3. satisfaction • For each team, the sum of how each person feels about the each other person in the group. • Maximize this for each set of teams +1 -1 +1 -1 -1 = -2 +1 -1 -1

  4. possible combinations in our class • Teams of 4: • Teams of 2:

  5. approximations

  6. form teams of three based on preferences

  7. chain approximation 1 0 1 0 -5 0 -2 -2 3

  8. chain approximation 1 0 1 0 -5 0 -2 -2 3

  9. chain approximation 1 0 1 0 -5 0 -2 -2 3

  10. chain approximation • Fast, simple • Variation: choose on most popular or pickiness • Problem: only looks at one person’s preferences at a time

  11. group approximation, teams of 3

  12. 1 0 1 0 -5 0 -2 -2 3

  13. 1 0 1 0 -5 0 -2 -2 3

  14. 0 -5 1 0 1 0 -2 -2 3

  15. 0 -5 1 0 1 0 -2 -2 3

  16. 0 -5 3 1 0 1 0 -2 -2

  17. 0 -5 3 0 1 1 0 -2 -2

  18. 0 -5 3 1 0 1 0 -2 -2

  19. 0 -5 3 0 1 1 0 -2 -2

  20. group approximation • Includes everyone’s preferences • Still explores very little space

  21. hill climbing

  22. D E B F A G H I C hill climbing 10 4 3

  23. D E B F A G H I C hill climbing 10 4 3

  24. D E B F A G H I C hill climbing 10 4 3

  25. D E B F A G H I C hill climbing 10 6 5

  26. results: prediction accurate?

  27. results

  28. future work? • Assess more seed and convergent processes • Weight edges based on prior experience • Break ties with work style • Conduct long-term study to evaluate performance of formed teams • Evaluate effects of number of preferences expressed

  29. questions

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