On the impact of social cost in opinion dynamics Panagiotis Liakos - - PowerPoint PPT Presentation

On the impact of social cost in opinion dynamics

Panagiotis Liakos Katia Papakonstantinopoulou

University of Athens Algorithmic Game Theory Athens NTUA, July 20th, 2016

Formation of opinions in a social context intrinsic belief + friends’ expressed

• pinions

expressed

• pinion

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 2/18

Motivation

exponential growth of online social networks ⇓ ever-increasing amount of social activity information available ⇓ ability to analyze user behavior and interpret sociological phenomena at a large scale [AKM08] ⇓ Investigating game theoretic models of networks against real data We consider the phenomenon of opinion formation under social

• influence. Given a network dataset, we want to be able to:

verify the existence of influence among users build a model that describes user behavior in the network.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 3/18

Contribution

Our contributions:

1 We analyze user activity in

and verify that social interaction results in influence on opinions among the participants.

2 We initialize a sociological model using real data. Based on the

Game Theory framework, we experimentally show that the repeated averaging process results to Nash equilibria which are illustrative of how users really behave.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 4/18

What is ?

is a news aggregator with a curated front page, aiming to select stories specifically for the Internet audience such as science, trending political issues, and viral Internet issues.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 5/18

lets you:

Submit stories. Digg (give a thumbs-up/positive vote to) a story you want other people to see. Follow users you consider interesting to get informed about their diggs in your news feed.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 6/18

Why ?

The dataset is appropriate for our study because: was very popular at the time the dataset was collected [LGS12] digging a story has a sense of opinion expression and an urge to influence both diggs and follower links are timestamped

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Intro – Motivation 7/18

The model: Basic notions

We use: a variation of the DeGroot model due to Friedkin and Johnsen [FJ90] and the corresponding game of [BKO11]. Each user i maintains: An intrinsic belief si An expressed opinion zi Remains constant Updated iteratively through averaging The cost a user suffers emanates from: Suppressing her intrinsic belief Disagreeing with her friends

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Our Approach 8/18

The model: Repeated Averaging

Repeated Averaging At each time step user i updates zi to minimize her cost: zi =

si+

j∈N(i) wijzj

1+

j∈N(i) wij

N(i): the set of nodes that i follows wij: the strength of the influence of j on i The averaging process terminates when z converges to the unique Nash equilibrium, where the social cost is minimized.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Our Approach 9/18

The model: Determining the influence strength

Our intuition: The influence of j on i regarding a specific matter depends on: The impact aij of j on i The expertise bj of j

Does i respect j’s opinion in general? Is j authoritative on this matter?

We define:

wij = aijbj

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Our Approach 10/18

Empirical Analysis of Top-20 Cascade Patterns

1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 5 10 15 20

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Empirical Analysis 11/18

Empirical Analysis of (cont.)

the total infections were less than the initial seeders in more than 92%

• f the stories of digg

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Empirical Analysis 12/18

Empirical Analysis of (cont.)

the total infections were less than the initial seeders in more than 92%

• f the stories of digg

a few users caused many cascades while most were unable to cause any

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Empirical Analysis 12/18

Empirical Analysis of (cont.)

the total infections were less than the initial seeders in more than 92%

• f the stories of digg

a few users caused many cascades while most were unable to cause any even the most authoritative users were not effective in all stories

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Empirical Analysis 12/18

Our Experiments and Assumptions

We performed repeated averaging in our model for stories of until the opinions, expressed by votes, converged to the unique Nash equilibrium. We compared against predictions obtained using a Neural Network classifier. Model initialization assumptions Intrinsic belief si

si =        1 if i voted a story be- fore any user she fol- lows

• therwise

Influential strength wij

Two variants: i) aij = bj = 1 ⇒ wij = 1 ii) aij = # times i is influenced by j

# votes of j

bj = # users influenced by j in this story

# followers of j

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 13/18

Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 14/18

Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

• u

r 2 n d v a r i a n t c l

• s

e l y m i m i c s t h e

• r

i g i n a l s

• c

i a l a c t i v i t y

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 14/18

Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

• u

r 2 n d v a r i a n t c l

• s

e l y m i m i c s t h e

• r

i g i n a l s

• c

i a l a c t i v i t y t h e s i m p l i s t i c v a r i a n t b e h a v e s p

• r

l y a s e x p e c t e d

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 14/18

Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

• u

r 2 n d v a r i a n t c l

• s

e l y m i m i c s t h e

• r

i g i n a l s

• c

i a l a c t i v i t y t h e s i m p l i s t i c v a r i a n t b e h a v e s p

• r

l y a s e x p e c t e d w e c

• n

s i s t e n t l y

• u

t

• p

e r f

• r

m t h e N e u r a l N e t w

• r

k c l a s s i fi e r

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 14/18

Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

• u

r 2 n d v a r i a n t c l

• s

e l y m i m i c s t h e

• r

i g i n a l s

• c

i a l a c t i v i t y t h e s i m p l i s t i c v a r i a n t b e h a v e s p

• r

l y a s e x p e c t e d w e c

• n

s i s t e n t l y

• u

t

• p

e r f

• r

m t h e N e u r a l N e t w

• r

k c l a s s i fi e r 2 4 . 4 6 p e r c e n t a g e p

• i

n t s ,

• n

a v e r a g e , h i g h e r p r e c i s i

• n

f

• r

9 % r e c a l l !

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 14/18

Conclusion

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.7 0.8 0.9 1

Precision Recall 8,521 votes 6,809 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 585 votes 335 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 401 votes 178 seeders

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1

Precision Recall 271 votes 145 seeders

Repeated Averaging (wij=1) Repeated Averaging (wij=aijbj) Neural Network

The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted:

• u

r 2 n d v a r i a n t c l

• s

e l y m i m i c s t h e

• r

i g i n a l s

• c

i a l a c t i v i t y t h e s i m p l i s t i c v a r i a n t b e h a v e s p

• r

l y a s e x p e c t e d w e c

• n

s i s t e n t l y

• u

t

• p

e r f

• r

m t h e N e u r a l N e t w

• r

k c l a s s i fi e r

The repeated averaging process, combined with proper influence weights, results to Nash equilibria which are illustrative of how users really behave.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Experimental Part 15/18

References

[AKM08] Aris Anagnostopoulos, Ravi Kumar, and Mohammad Mahdian, Influence and correlation in social networks, SIGKDD (Las Vegas, Nevada, USA), 2008, pp. 7–15. [BKO11] David Bindel, Jon M. Kleinberg, and Sigal Oren, How bad is forming your own opinion?, FOCS, 2011,

• pp. 57–66.

[FJ90] N.E. Friedkin and E.C. Johnsen, Social influence and opinions, Journal of Mathematical Sociology 15 (1990), no. 3-4, 193–206. [LGS12] Kristina Lerman, Rumi Ghosh, and Tawan Surachawala, Social contagion: An empirical study of information spread on digg and twitter follower graphs, arXiv preprint arXiv:1202.3162 (2012). UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• References 16/18

Future Directions

We can estimate the price of anarchy in such a network, by comparing the social cost of the Nash equilibrium we computed here with the cost of the optimal setting of this network. We can investigate approaches that may reduce the cost of such networks.

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Future Directions 17/18

thank you!

for further details visit: http://hive.di.uoa.gr/network-analysis/

• r email me at: katia@di.uoa.gr

UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics-• Contact 18/18