1. ETH Zurich – Distributed Computing – www.disco.ethz.ch Silvio Frischknecht, Barbara Keller, Roger Wattenhofer Convergence in (Social) Influence Networks

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

4. b

5. b

6. b

7. b

8. b

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

11. Easy Lower Bound: Ω(n)

16. Upper Bound: v

17. v

18. v

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

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

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

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

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

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

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

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

27. Tight Bound? Lower boundUpper bound vs.

28. Let`s Vote vs.

30. Simpler Example:

33. A Transistor

35. B C E B C E

36. B C E E C B B C E B E C

37. BB C EE C B C E

38. BBB EEE CCC B E C BB CC EE

44. Other Results Iterative model: Adversary picks nodes instead of synchronous rounds: 1 Step = 1 node change its opinion

45. Convergence Time: θ(n²)

46. Iterative Model Benevolent algorithm: θ(n)

47. תודה רבה