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‐

• n‐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

• Normalized Intensity for R1=0.2φ1++0.33φ2+0.5φ3+0.33φ4; φ1+φ2+φ3+φ4=1
• Normalized Intensity for R2=0.5φ1++0.25φ2+0.33φ3+0.42φ4; φ1+φ2+φ3+φ4=1

R1= Restaurant 1, R2= Restaurant 2, R3= Restaurant 3 NI=Normalized Intensity

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

Power or intensity of the ith source Trust between the ithuser and jth source Cognitive reflexivity of ithuser Auxiliary resources expended by jth source Contradiction between ithand jth sources Relevance of the ith source ICNR

Problem Definition

• Utility ;

– πi is an increasing concave function – Obtained from Bernoullian utility theory of human behavior

• Net utility
• λ is the pricing parameter, fi(xi) is the pricing function

– Represents the penalty incurred due to aggressive presentation of information

• Loss of relationship/reputation

– fi(xi) is an increasing convex function – Can be linear or non‐linear

• Determine the optimal Pi’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 λmin (ε) such that the

network is ε‐aggressive for λ <λmin (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 λmax (δ) such that the

network is δ ‐aggressive for λ > λmax (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
• thers

– 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 !!!