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ETH Zurich Distributed Computing www.disco.ethz.chSilvio Frischknecht, Barbara Keller, Roger WattenhoferConvergence in (Social) Influence Networks

Simple World2 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: (n)

Easy Lower Bound: (n)

Easy Lower Bound: (n)

Easy Lower Bound: (n)

Easy Lower Bound: (n)

Upper Bound: v

vUpper Bound:

vUpper Bound:

Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion

vUpper Bound:

Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion

vtt+1t+2vgbg: Nr. of good edges b: Nr. of bad edges

case g > bUpper Bound:

Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion

vtt+1t+2vgbg: Nr. of good edges b: Nr. of bad edges

case g > bUpper Bound:

Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion

vtt+1t+2vgbg: Nr. of good edges b: Nr. of bad edges

case g > bUpper Bound:

vtt+1t+2vgb case b > gg: Nr. of good edges b: Nr. of bad edges

Upper Bound:

vtt+1t+2vgb case b > gg: Nr. of good edges b: Nr. of bad edges

Upper Bound:

vtt+1t+2vgb case b > gg: Nr. of good edges b: Nr. of bad edges

Upper Bound:

vtt+1t+2vgb case b > gg: Nr. of good edges b: Nr. of bad edges

Upper Bound:

bgTight Bound?Lower boundUpper bound vs.

Let`s Vote vs.

Simpler Example:

Simpler Example:

A Transistor

A Transistor

BCEBCE

BCEECBBCEBEC

BBCEECBCE

BBBEEECCCBECBBCCEE

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

Convergence Time: (n)

Iterative ModelBenevolent algorithm: (n)