A Quantitative Model and Analysis for Information Confusion in Social - PowerPoint PPT Presentation

A Quantitative Model and Analysis for Information Confusion in Social Networks Anand Santhanakrishnan Research Associate WINLAB Rutgers

Outline • Motivation • Problem Formulation • System Model • Analysis • Results • Conclusion

Confusion in Social Networks • Users seek information from a primary source • Users receive auxiliary information from several other sources – Information from some of the other sources could contradict the one from the primary source – Causes confusion for the receiving user

Some examples of Confusion • Are social networks a more trusted by people than google? – http://www.google.com/hostednews/afp/article/ALeqM5iiH9iSZwSVn nc3g6ybW2N3CzrC6g suggests they are – http://news.slashdot.org/story/10/06/24/0116240/Study ‐ Finds ‐ Google ‐ Is ‐ More ‐ Trusted ‐ Than ‐ Traditional ‐ Media?from=rss suggests Google is more popular Are cell phone radiations harmful? • – C. Johansen, J. D. B. Jr., , J. K. Mclaughlin, J. H. Olsen, Cellular telephones and cancer ‐ A nation ‐ wide cohort study in Denmark, Jl. of National Cancer Institute 93 (3) (2001) 203–207 suggests that they are now – S. Kovach, The hidden dangers of cell ‐ phone radiation, Life Extension Magazine suggests they are

Twitter Data on Full Body Scan in Airports User likes to obtain opinion from his/her friends on full body scan • Friends from North America are likely to support full body scan – Friends from Asia are likely to oppose –

Modeling Confusion • Is it possible to model confusion? • What are the parameters that affect confusion? – The power or intensity with which a source transmits information • Represented by the authenticity, aggression level of the source, confidence, propaganda, etc – The trust between the sources and the receiving user – The level of contradiction in the information obtained from different sources – The natural dilemma or instability or cognitive reflexivity of the user in processing information – Amount of auxiliary/training resources expended by the source to educate the user • Define a term called “Information ‐ to ‐ Confusion ‐ Noise ‐ Ratio (ICNR)” to model confusion

Description of Parameters P. Adams, “Social networking,” The Noisy Channel, Jul. 2010. • http://thenoisychannel.com/2010/07/08/pauladamsspresentation ‐ on ‐ social ‐ networking The power or intensity of information transmission • – You must eat in this restaurant. It is delicious !! – Never eat here. The service is awful !! The auxiliary resource or intensity of information transmission • – Paul eats in this restaurant three times a week The relevance of information • – If someone is first of all interested in dining in the restaurant or has dined before in the restaurant The natural dilemma or cognitive reflexivity of information • transmission – People who have a natural affinity towards or natural resistance to dine in the restaurant

Measurement of Intensity R1= Restaurant 1, R2= Restaurant 2, R3= Restaurant 3 NI=Normalized Intensity Normalized Intensity for R1=0.2 φ 1 ++0.33 φ 2 +0.5 φ 3 +0.33 φ 4 ; φ 1 + φ 2 + φ 3 + φ 4=1 • Normalized Intensity for R2=0.5 φ 1 ++0.25 φ 2 +0.33 φ 3 +0.42 φ 4 ; φ 1 + φ 2 + φ 3 + φ 4=1 •

Measurement of Contradiction Percentage of tweets supporting full body scan in USA= 967/(967+753)=56.22% • Percentage of tweets supporting full body scan in Canada=14/(14+19)=42.42% • Contradiction between USA and Canada= 0.5622(1 ‐ 0.4242)+0.4242(1 ‐ 0.5622)=0.5094 • Neglect neutral tweets •

Measurement of Auxiliary Resources L. Corteville and M. Sun, “An interorganizational social network analysis of Michigan diabetic outreach • networks,” White Paper, MichiganState Univ., Sep. 2009. http://www.techrepublic.com/research ‐ library/michigan+state+university Ratings by patients on a scale of 1 ‐ 7. •

ICNR Trust between the i th user and j th source ICNR Auxiliary resources expended by j th source Power or intensity of the i th source Cognitive reflexivity of i th user Contradiction between i th and j th sources Relevance of the i th source

Problem Definition Utility ; • – π i is an increasing concave function – Obtained from Bernoullian utility theory of human behavior Net utility • λ is the pricing parameter, f i (x i ) is the pricing function • – Represents the penalty incurred due to aggressive presentation of information Loss of relationship/reputation • – f i (x i ) is an increasing convex function – Can be linear or non ‐ linear Determine the optimal P i ’s so that the net utility, , is maximized • for all the users A non ‐ cooperative game with pricing •

Preliminary Results (1/3) • Theorem 1: Let . Let aaand . Then the Nash equilibrium . Then the non ‐ cooperative game with pricing is feasible only if – Indicates that there is an upper cut off on the pricing parameter above which sources are averse to giving any information • Theorem 2: such that , the non ‐ cooperative game with pricing has a unique feasible Nash equilibrium – Indicates that there is a lower cut off on the pricing parameter below which sources tend to be highly aggressive in presenting information.

Preliminary Results (2/3) • A network is said to be ε‐ aggressive if the average power or intensity with which information is transmitted is . A network is said to be aggressive if it is ε‐ aggressive for ε =1 – Represents how aggressive sources can be • A network is said to be δ‐ passive if the average power or intensity with which information is transmitted is A network is said to be passive if it is δ‐ passive for δ =0. – Represents how passive the sources can become • Can we make a network as aggressive or as passive as desired?

Preliminary Results (3/3) • Theorem 3: For all 0 ≤ε≤ 1 there exists λ min ( ε ) such that the network is ε‐ aggressive for λ < λ min ( ε ). – Indicates that it is possible to make a network as aggressive as desired by keeping the pricing parameter sufficiently low, i.e., not penalizing sources for being aggressive • Theorem 4: For all 0 ≤δ≤ 1 there exists λ max ( δ ) such that the network is δ ‐ aggressive for λ > λ max ( δ ). – Indicates that it is possible to make a network as passive as desired by making the pricing parameter sufficiently high, i.e., penalizing sources heavily for being aggressive

Numerical Results • A network with 10 sources and 10 users • 3 scenarios – Distributed trust • users place almost equal trust on all sources – Moderately concentrated trust • users place high trust on few sources and low trust on others – Highly concentrated trust • Users place high trust on one or two sources and low trust on others

Price Variation • Higher price to obtain same net utility when users place distributed trust

Aggression Levels Network switches from highly aggressive to highly passive very • quickly (i.e., is unstable) when users place distributed trust.

Conclusion • A quantitative model for information confusion • Networks can be made as aggressive or as passive as desired • Networks in which users trust all sources equally are susceptible to be unstable – Switch from being aggressive to being passive very quickly • When users place highly concentrated trust, networks are more stable

Additional Applications • Task prioritization – A user is assigned a set of n tasks by a set of m people – The productivity us analogous to relevance – The influence is analogous to trust – The intensity is analogous to priority assigned to the tasks – Determine the optimal priorities to maximize productivity • Admission control – A set of users are discussing on a topic – Each user is looking for a level of clarity (ICNR) from the discussion – The information providers need to control their intensity to meet the desired ICNR for all users – Admit a new user only if ICNR requirements are met

Questions?

Thank You !!!