1. Barbara Keller, Panda Metaiel
Majority Voting: San Rocco or Ulisse?
Barbara Keller, Panda Metaiel
ETH Zurich – Distributed Computing –

7. Opinion changes: Whatever the majority of my friends think
Simple World
2 Opinions:
Opinion changes: Whatever the majority of my friends think

8. b

9. b

10. b

11. b

12. b

13. What Can Happen?
and/or
Goles and Olivios 1980

16. Easy Lower Bound: Ω(n)

17. Easy Lower Bound: Ω(n)

18. Easy Lower Bound: Ω(n)

19. Easy Lower Bound: Ω(n)

20. Upper Bound?
Winkler 2008

21. Upper Bound: v

22. Upper Bound: v

23. Upper Bound: v

24. Upper Bound:
Good edge: Friend takes advised opinion on next day Bad edge: Friend does not take the proposed opinion v

25. Upper Bound:
Good edge: Friend takes advised opinion on next day Bad edge: Friend does not take the proposed opinion t
t+1
t+2 g
g: Nr. of good edges
b: Nr. of bad edges v v b
case g > b

26. Upper Bound:
Good edge: Friend takes advised opinion on next day Bad edge: Friend does not take the proposed opinion t
t+1
t+2 g
g: Nr. of good edges
b: Nr. of bad edges v v b
case g > b

27. Upper Bound:
Good edge: Friend takes advised opinion on next day Bad edge: Friend does not take the proposed opinion t
t+1
t+2 g
g: Nr. of good edges
b: Nr. of bad edges v v b
case g > b

28. Upper Bound: g: Nr. of good edges b: Nr. of bad edges t t+1 t+2 g v v
case b > g

29. Upper Bound: g: Nr. of good edges b: Nr. of bad edges t t+1 t+2 g v v
case b > g

30. Upper Bound: g: Nr. of good edges b: Nr. of bad edges t t+1 t+2 g v v
case b > g

31. Upper Bound: g: Nr. of good edges b: Nr. of bad edges t t+1 t+2 g g v
case b > g

32. Upper Bound:
Winkler 2008

33. Tight Bound?
Lower bound Upper bound vs.

34. Let`s Vote
vs.

36. Simpler Example:

37. Different Models

40. Let`s Vote Again!
No!
Only a Little Bit!
Yes!
𝑂( 𝑛 2 )
𝑛 2+𝑂(1)
2 Θ(𝑛)

41. Let`s Vote Again!
No!
Only a Little Bit!
Yes!
𝑂( 𝑛 2 )
𝑛 2+𝑂(1)
2 Θ(𝑛)

42. Animations

43. 9001
-9001

44. No Changes

47. Exponentially long circles!

49. San Rocco or Ulisse?

51. Grazie!