On the impact of social cost in opinion dynamics Panagiotis Liakos Katia Papakonstantinopoulou University of Athens Algorithmic Game Theory Athens NTUA, July 20 th , 2016
Formation of opinions in a social context intrinsic belief + friends’ expressed opinions expressed opinion 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 s i An expressed opinion z i 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 z i to minimize her cost: s i + � j ∈ N ( i ) w ij z j z i = 1+ � j ∈ N ( i ) w ij N ( i ) : the set of nodes that i follows w ij : 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 a ij of j on i The expertise b j of j Does i respect j ’s opinion in general? Is j authoritative on this matter? We define: w ij = a ij b j 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 % of 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 % of 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 % of 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 Influential strength w ij Intrinsic belief s i Two variants: 1 if i voted a story be- fore any user she fol- i) a ij = b j = 1 ⇒ w ij = 1 s i = lows ii) a ij = # times i is influenced by j 0 otherwise # votes of j b j = # 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 The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted : 1 1 0.9 0.9 0.8 0.8 0.7 0.7 Precision Precision 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 8,521 votes 585 votes 0.1 0.1 6,809 seeders 335 seeders 0 0 0.7 0.8 0.9 1 0.4 0.6 0.8 1 Recall Recall 1 1 0.9 0.9 0.8 0.8 0.7 0.7 Precision Precision 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 401 votes 271 votes 0.1 0.1 178 seeders 145 seeders 0 0 0.4 0.6 0.8 1 0.4 0.6 0.8 1 Recall Recall Repeated Averaging (w ij =1) Repeated Averaging (w ij =a ij b j ) Neural Network UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics- • Experimental Part 14/18
Results The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted : 1 1 2 n d v a r i a n t o u r 0.9 0.9 0.8 0.8 m i c s t h e c l o s e l y m i 0.7 0.7 Precision Precision t y 0.6 0.6 s o c i a l a c t i v i o r i g i n a l 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 8,521 votes 585 votes 0.1 0.1 6,809 seeders 335 seeders 0 0 0.7 0.8 0.9 1 0.4 0.6 0.8 1 Recall Recall 1 1 0.9 0.9 0.8 0.8 0.7 0.7 Precision Precision 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 401 votes 271 votes 0.1 0.1 178 seeders 145 seeders 0 0 0.4 0.6 0.8 1 0.4 0.6 0.8 1 Recall Recall Repeated Averaging (w ij =1) Repeated Averaging (w ij =a ij b j ) Neural Network UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics- • Experimental Part 14/18
Results The fraction of predicted votes that were actually casted against the fraction of casted votes that are predicted : 1 1 2 n d v a r i a n t o u r 0.9 0.9 0.8 0.8 m i c s t h e c l o s e l y m i 0.7 0.7 Precision Precision t y 0.6 0.6 s o c i a l a c t i v i o r i g i n a l 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 8,521 votes 585 votes 0.1 0.1 6,809 seeders 335 seeders 0 0 0.7 0.8 0.9 1 0.4 0.6 0.8 1 t h e s i m p l i s t i c Recall Recall v a r i a n t b e h a v e s 1 1 0.9 0.9 p o o r l y a s e x p e c t e d 0.8 0.8 0.7 0.7 Precision Precision 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 401 votes 271 votes 0.1 0.1 178 seeders 145 seeders 0 0 0.4 0.6 0.8 1 0.4 0.6 0.8 1 Recall Recall Repeated Averaging (w ij =1) Repeated Averaging (w ij =a ij b j ) Neural Network UoA Katia Papakonstantinopoulou On the impact of social cost in opinion dynamics- • Experimental Part 14/18
Recommend
More recommend
