# Information Spread by Search Engines.

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## WHAT IS IT?

A model of diffusion of ideas in a many opinion environment that include two methods of spread. 1) WOM -> word of mouth 2) WEB -> search engines spread dynamics

## HOW IT WORKS

The model starts with "num-infected-init" (see slider) nodes which can have any of the "num-opinions" (see slider) opinions. At each step, the opinions might spread to any of their neighbors along a WOM dynamics, (word of mouth), by which each node can adopt the opinion of its social neighbors, or according to WEB dynamics (web search engine), by which a node adopts an opinion according to its likelihood to appear in a search engine query.

## HOW TO USE IT

Press "Setup" to create a power law network.

Press "Reinfect-once" to distribute the initial opinions to few random nodes.

Set the k-opinion slider, which represents the number of opinion which a user reads before choosing his/her own opinion.

Choose the model in the "group-influence-type" selection, to WOM or to WEB.

Press "spread" to repeatedly spreading the different ideas along the population.

## THINGS TO NOTICE

The distribution of ideas is more narrow (less ideas spread to more nodes, while rare ideas disappear) in the WEB as compared to the WOM model. This can be seen by the histogram, (bottom right) as well as the "proportion of opinion" and "#opinion" monitors

## CREDITS AND REFERENCES

For more detail, see the Europhysics letters (EPL) article

Alon Sela, Louis Shekhtman, Shlomo Havlin and Irad Ben-Gal, Comparing the diversity of information by word-of-mouth vs. web spread, Europhysics letters (EPL), 114(5)

http://iopscience.iop.org/article/10.1209/0295-5075/114/58003/meta

Based on an initial model Copyright 2008 Uri Wilensky. Modified by Lada Adamic 2009.

## Comments and Questions

; Adapted from models library by Lada Adamic (see copyright below) ; for the purposes of SI708/CSCS608 ; also now contains major improvements by Eytan Bakshy ;This version is created by Alon Sela 7/2013-9/2015 on the base of the above... extensions [nw] ;correct - method of choice in WOM - globals [ new-node ;; the last node we created degrees ;; this is an array that contains each node in proportion to its degree num-infected tree-mode? time-to-90 ;; Alon time-to-1 ;; Alon time-to-10 ;; Alon time-from-1-to-90 global-infect-rate ;; Alon cured? ;; Alon memory-of-t-0 ;; Alon prob-to-inf-of-t-0 ;Alon final-distribution ;; Alon dist-non-zero;;Alon initial-num-infected ;;Alon remove-zero? ] turtles-own [ group-mates ;; ALONs addition prob-to-inf ;; ALONs addition, probability of infection memory message ;;ALONs addition, message spreading ] ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) ca __clear-all-and-reset-ticks let partner nobody set remove-zero? true set-default-shape turtles "circle" set degrees [] ;; initialize the array to be empty ;; make the initial network of two turtles and an edge crt (m + 1) ask turtles [ repeat m [set degrees lput self degrees] ; insert nodes into array ask other turtles with [not link-neighbor? myself] [ create-link-with myself ] ] ;set num-infected 0 no-display repeat (num-nodes - m - 1) [ crt 1 [ set new-node self ;; set the new-node global repeat m [ ifelse (random-float 1.0 <= prob-pref) ; if pref attachment [set partner new-node while [partner = new-node] [ set partner one-of (degrees) ask partner [ if link-neighbor? self [ ; we can't link to someone we already share an edge with set partner new-node ; so set to self so we redo ] ] ] ] [ ; if not pref attachment set partner one-of other turtles with [(not link-neighbor? new-node)] ] move-to partner fd 5 create-link-with partner [set color green] set degrees lput new-node degrees set degrees lput partner degrees ] ] ] ;repeat 100 [do-layout] repeat 10 [do-layout] ask turtles [set color gray set shape "circle" set size 0.3 ;set infection-count 0 ;set infected? false ] ask links [set color gray] end ;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; REINFECT ONCE ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;; ; reset diffusion simulation to reinfect-once clear-all-plots ;let init-oppinion [] set num-infected 0 set time-to-90 0 set time-to-1 0 set time-to-10 0 set time-from-1-to-90 0 set memory-of-t-0 0 set final-distribution 0 set dist-non-zero 0 reset-ticks ask turtles [ set color gray set shape "circle" set size 0.3 ;set infection-count 0 ;set infected? false set prob-to-inf 0 set memory 0 set message 0 ] ask links [set color gray + 2] while [count turtles with [message != 0] < num-infected-init] [ ;repeat num-infected-init [ ask one-of turtles [if not (message != 0) [;set infected? true set memory 1 set size 3 set shape "target" set num-infected num-infected + 1 set message (random num-oppinions ) + 1 set color (message * 10 + 5)] ; set init-oppinion lput message init-oppinion ] ] update-plots set dist-non-zero distribution-no-zeroes set initial-num-infected length dist-non-zero end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; Main SPREAD procedure ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to spread ;first we construct alist of nodes with an opinion let myInfecttedAgentset [] set myInfecttedAgentset turtles with [message != 0] ;create the search engine result list sorten by the PageRank of the believers in the network let search-result-list create-search-engine-list myInfecttedAgentset ;this function reports a list of non-infected friends of infected nodes (Optional Infected List (OIL) let myOptionalToInfectlist [] ask myInfecttedAgentset [ask link-neighbors with [message = 0] [set myOptionalToInfectlist lput who myOptionalToInfectlist ] ] set myOptionalToInfectlist remove-duplicates myOptionalToInfectlist foreach myOptionalToInfectlist [ask turtle ? [set color green set size 1 ] ] ; chose opinion to adopt for every agent that is exposed to the message foreach optional-infect-list ; OIL [ask turtle ? [if (Group-influence-type = "WOM") [set message vote-message-WOM self ; good for remove-zero = TRUE as well as remove-zero = FALSE ] if (Group-influence-type = "WEB") [ set message vote-message-WEB2 search-result-list ] ] ] ask turtles with [message != 0] [ set size 1 show-turtle set color (message * 10 + 5) ;set infection-count infection-count + 1 ;; incremement infection-count of the node doing the infection set num-infected num-infected + 1 ] do-plotting compute-distributions tick if (all? turtles [message != 0]) [set final-distribution compute-reporter set dist-non-zero distribution-no-zeroes stop] end ;;;;;;;;;;;;;;;; ;;; Plotting ;;; ;;;;;;;;;;;;;;;; to do-plotting ;; plot the number of infected individuals at each step set-current-plot "Number infected" set-current-plot-pen "num-inf" set num-infected count turtles with [message != 0] plotxy ticks num-infected / num-nodes end to toggle-tree ;; toggle infection tree mode ;; when tree-mode is on, only links responsible for contagion and infected nodes ;; are displayed. tree-mode also affects layout ifelse tree-mode? ;on [ask turtles [show-turtle] ask links [show-link] set tree-mode? false] [ask turtles with [message = 0] [hide-turtle] ask turtles with [message != 0] [show-turtle] ask links with [color != red - 1] [hide-link] ask links with [color = green ] [show-link] set tree-mode? true ] end ;;;;;;;;;;;;;; ;;; Layout ;;; ;;;;;;;;;;;;;; to do-layout if layout? [repeat 10 [layout-spring turtles links 0.01 10 1] ;repeat 10 [layout-spring (turtles with [color = green]) (links with [color = green]) 0.01 10 5] repeat 10 [layout-spring (turtles with [message != 0]) (links with [color = red - 1]) 0.5 20 10] ] display end to-report vote-message-WOM [node] ; This reporter receives a non-infected node (in a turtle agent form not just a number) and ; reports the oppinion this node would choose if debating between several simmilar oppinions. ; The algorithm sample k (with repetition) neigbhors and builds a list "opp-list" of their oppinions. ; Then, it randomely choses one opinion from opp-list. let mylist [] ask node [ask link-neighbors [set mylist lput message mylist]] if remove-zero? [set mylist remove 0 mylist] if k-oppinion < length(mylist) [set mylist n-of k-oppinion mylist] let result one-of mylist report result end to-report create-search-engine-list [Agentset]; this function receives as INPUT of an agentset and returns ; as OUTPUT a list of nodes sorted by the PageRank of their holders let oplist [] let sortagents sort-on [nw:page-rank] Agentset foreach sortagents [set oplist fput [message] of ? oplist ] report oplist end ;OK to-report vote-message-WEB2 [mylist] ;turtle procedure ;this function reports the voted message in the WEB dynamics for one turtle ;create the list of k opinions of a debating user taking into consideration the SERP function let k-opp-list k-list mylist let chosenMessage [] ;choses one opinion by the most common or random of most commons if few have same comonness if length(k-opp-list) > 0 [;set chosenMessage one-of modes k-opp-list set chosenMessage one-of modes k-opp-list ] report chosenMessage end to-report histomize [ #list ] ; this amazing (fount in the internet) function receives a list and reports a list of two lists. ;; reports a list of two lists: ;; the first is a sorted list of unique values in given list, ;; the second is a list of corresponding counts of each value. set #list sort #list report list remove-duplicates #list but-first reduce [ifelse-value (first ?1 = ?2) ; if same value... [lput (1 + last ?1) but-last ?1] ; incr count [fput ?2 lput 1 but-first ?1]] ; new value fput list (first #list) 1 but-first #list end ;ok to-report compute-reporter ;this function reports the histomize results in a more fitting format let result [] let ans [message] of turtles let res histomize ans let res-length length ans foreach item 1 res [set result lput (precision (?1 / res-length) 4) result] report sort-by > result end to-report compute-reporter-new [chosen] ;this function reports the histomize results in a more fitting format let result [] let ans [message] of chosen let res histomize ans let res-length length ans foreach item 1 res [set result lput (precision (?1 / res-length) 4) result] report sort-by > result end to-report distribution-no-zeroes ; reports the list of non infected turtles let a turtles with [message != 0] report sort-by > compute-reporter-new a end ;used to-report optional-infect-list ;observer procedure ;this function reports a list of non-infected friends of infected nodes let mylist [] ask turtles with [message != 0][ask link-neighbors with [message = 0][set mylist lput who mylist ] ] set mylist remove-duplicates mylist foreach mylist [ask turtle ? [ set color green set size 1]] report mylist end to compute-distributions ;this function recompute all the distributions set final-distribution compute-reporter set dist-non-zero distribution-no-zeroes end ;OK to-report k-list [srl] ; this function receives as an INPUT the searth results opinion list ; and reurtns as OUTPUT a list of k opinions that would be read by a user according to the SERP function ; If the SERP function returns an opinion that is in position larger than the existing nuber of opinions, the function would not include this opinion in the list let klist [] ; the a and b are the parameters in the equation y=aX^-b which has an inverse inverse(y): y=(x/a)^(1/b) let a 0.11 let b 0.46 let lengthlist length srl repeat k-oppinion [ let u random-float 1 let rank exp(5 * u - (5 / 4) ) set rank int(rank) + 1 ifelse (rank < lengthlist) [set klist lput item rank srl klist] [] ] ; produce a list of opinions that are located in positon report klist end

There is only one version of this model, created almost 4 years ago by Alon Sela.

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