ETH Zurich – Distributed Computing – Silvio Frischknecht, Barbara Keller, Roger Wattenhofer Convergence in (Social) Influence Networks

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

b

b

b

b

b

What Can Happen? and/or Goles and Olivios 1980

Easy Lower Bound: Ω(n)

Upper Bound: v

v

v

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

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:

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:

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:

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

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

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

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

Tight Bound? Lower boundUpper bound vs.

Let`s Vote vs.

Simpler Example:

A Transistor

B C E B C E

B C E E C B B C E B E C

BB C EE C B C E

BBB EEE CCC B E C BB CC EE

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

Convergence Time: θ(n²)

Iterative Model Benevolent algorithm: θ(n)

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