ETH Zurich – Distributed Computing – www.disco.ethz.ch

Barbara Keller, Panda Metaiel

Majority Voting: San Rocco or Ulisse?

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)

Easy Lower Bound: Ω(n)

Easy Lower Bound: Ω(n)

Easy Lower Bound: Ω(n)

Upper Bound?

Winkler 2008

Upper Bound:

v

)( 2nO

v

Upper Bound: )( 2nO

v

Upper Bound: )( 2nO

Good edge: Friend takes advised opinion on next day

Bad edge: Friend does not take the proposed opinion

v

Upper Bound: )( 2nO

Good edge: Friend takes advised opinion on next day

Bad edge: Friend does not take the proposed opinion

v

t t+1 t+2

v g

b

g: Nr. of good edges b: Nr. of bad edges

case g > b

Upper Bound: )( 2nO

Good edge: Friend takes advised opinion on next day

Bad edge: Friend does not take the proposed opinion

v

t t+1 t+2

v g

b

g: Nr. of good edges b: Nr. of bad edges

case g > b

Upper Bound: )( 2nO

Good edge: Friend takes advised opinion on next day

Bad edge: Friend does not take the proposed opinion

v

t t+1 t+2

v g

b

g: Nr. of good edges b: Nr. of bad edges

case g > b

Upper Bound: )( 2nO

v

t t+1 t+2

v g

b

case b > g

g: Nr. of good edges b: Nr. of bad edges

Upper Bound: )( 2nO

v

t t+1 t+2

v g

b

case b > g

g: Nr. of good edges b: Nr. of bad edges

Upper Bound: )( 2nO

v

t t+1 t+2

v g

b

case b > g

g: Nr. of good edges b: Nr. of bad edges

Upper Bound: )( 2nO

v

t t+1 t+2

v g

b

case b > g

g: Nr. of good edges b: Nr. of bad edges

Upper Bound: )( 2nO

b

g

Upper Bound:

)( 2nO

Winkler 2008

Tight Bound?

Lower bound Upper bound

vs. 2nn

Let`s Vote

vs. 2nn

n

n2

2

log

Simpler Example: nn

Different Models

Yes! No!

2Θ(𝑛) 𝑛2+𝑂(1) 𝑂(𝑛2)

Let`s Vote Again!

Only a Little Bit!

Yes! No!

2Θ(𝑛) 𝑛2+𝑂(1) 𝑂(𝑛2)

Let`s Vote Again!

Only a Little Bit!

Animations

http://www.disco.ethz.ch/members/barkelle/FUN.zip

-9001 9001

No Changes

Exponentially long circles!

San Rocco or Ulisse?

Grazie!