Propaganda Battle with Two-Component Agenda

MACSPro'2019 - Modeling and Analysis of Complex Systems and Processes, Vienna
21 - 23 March 2019

Alexander Petrov, Olga Proncheva

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Transcript

1. Moscow Institute of Physics and Technology
   MIPT / PHYSTECH
   

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2. Propaganda Battle with Two-Component Agenda
   A.P. Petrov (KIAM RAS), O.G. Proncheva (MIPT)
   22.03.2019
   

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3. Propaganda battle
   3
   Parties: broadcast their messages via mass-media
   Individuals: communicate, share their approvals, may toggle their support to the
   other party
   Population
   Supporters of the Party L Supporters of the Party R
   Bush Kerry
   Security 18.3 12.2
   Economy 24.5 35.7
   Press release topic frequencies
   (% of the candidate’s releases)
   for Bush for Kerry
   Security 86 14
   Economy 20 80
   % of the voters who believed that
   security/economy issue is more important
   

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4. 4
   φ
   a person’s
   predisposition towards
   a given object
   ψ(t)
   dynamic component,
   the same for all
   members
   The latent position of
   the individual:
   φ+ψ(t)>0 party R
   φ+ψ(t)<0 party L
   One - dimensional case
   Two - dimensional case
   g(φ
   1
   +ψ
   1
   )+(1- g)(φ
   2
   +ψ
   2
   )>0 party R
   g(φ
   1
   +ψ
   1
   )+(1- g)(φ
   2
   +ψ
   2
   )<0 party L
   {g ,1-g} is refer to as the agenda, characterizes the significance of the topics in comparison
   with each other
   Model
   The latent position of the individual:
   

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5. 5
   R – the number of Party R supporters
   L – the number of party L supporters
   n(φ) – the distribution of attitudes
   among individuals
   bR
   – the intensity of propaganda of
   party R
   bL
   – the intensity of propaganda of
   party L
   N0
   – the entire number of individuals
   Initial condition:
   Basic model
    
      
    
    
      
    
      
   t
   t
   R L
   R t n d
   L t n d
   d
   C R L b b a
   dt
   
   
     
     
   
     
   
   
   
   
   
   
       
    
    
   
   
    
    
   0
   2 R L
   t
   d
   C n d N b b a
   dt
   
   
     
   
   
    
    
       
    
    
    
   
    
    
    
   0
   0
   n d R
   
    
   
   
   
   
   

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6. 6
   Workhorse model
      
        
    
       
   1 1
   2 2
   1
   1 1 1 1 2 1 2 1 2 1 2
   2
   2 2 2 1 2 1 2 1 2 1 2
   1 1
   1 1 2 2
   1 1 1 2 2 1 1
   1 1
   , ,
   1 , ,
   1
   : 1 0, 0
   :
   R L
   R L
   R L
   R L
   L R
   L R L R
   d
   a b b gC N d d N d d
   dt
   d
   a b b g C N d d N d d
   dt
   dg b b
   kg g g
   dt b b b b
   R g g
   L g
    
   
    
                 
    
    
    
   
    
                  
    
    
    
   
     
    
     
    
               
   
    
    
       
       
       
   1 2 2 1 1
   2 1 1 2 2 2 2
   2 1 1 2 2 2 2
   1 0, 0
   : 1 0, 0
   : 1 0, 0
   g
   R g g
   L g g
              
               
               
    
       
    
       
   1 1 2 2
   1 1 2 2
   1 2 1 2
   1 0
   1 2 1 2
   1 0
   ,
   ,
   g g
   g g
   R N d d
   L N d d
         
         
       
       
   
   
   

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7. Influence of the parameters
   Parameters Initial advantage
   С is great enough important
   a is great enough unimportant
    
    
   0
   2
   R L
   t
   d
   C n d N b b a
   dt 
   
     
   
   
    
       
   
    
    
   If one of the parties has some advantage in the number of
   supporters, will it increase over time or not?
   

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8. 8
   is asymptotically stable if is negative
   Stability of the equilibrium state:
   • low C
   • high a
   • high M
   •
   The simplest case
   0
   1 2
   g 
    
        
    
   2 3 2
   0 0 0 0 0
   0
   0
   2 1 4 1 2
   2 1
   g g g g g
   f g
   g
        
   
   
   1 2
   0
          
   0 0
   2
   a CN M f g
      
    
    
   2
   0 1 2
   1 1 2 2 1 2
   1 2
   / 4 , ,
   ; ; ,
   0,
   R L R L
   N M M M
   b b b b N
   M or M
       
   
        
      
   
   
   

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9. 9
   •on each battlefield the party that has allocated the most soldiers will win
   •neither party knows how many soldiers the opposing party will allocate to each battlefield
   •both parties seek to maximize the number of battlefields they expect to win
   σ - the degree of homogeneity of the support
   p - polarization
   The Blotto game
      
    
   1 2
   0 0 0
   0 0.5
   g
    
    
   
   1 2
   1 2
   5
   6
   R R
   L L
   b b
   b b
    
    
    
      
   2
   1
   2
   2 2
   2 2 2
   1 2 2 2
   1 1 1
   , e exp exp
   2 2 2 2 2 2 2
   p p
   N
    
   
   
    
   
    
    
      
      
    
        
      
      
          
    
      
    
   

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10. The outcome of the battle
    10
    0+5 1+4 2+3 3+2 4+1 5+0
    0+6 0,16 0,32 0,46 0,52 0,49 0,33
    1+5 0,03 0,16 0,28 0,33 0,27 0,01
    2+4 -0,09 0,06 0,17 0,20 0,09 -0,26
    3+3 -0,14 0,03 0,16 0,18 0,02 -0,39
    4+2 -0,13 0,10 0,28 0,33 0,15 -0,30
    5+1 0,03 0,35 0,57 0,62 0,48 0,05
    6+0 0,40 0,73 0,73 0,87 0,79 0,52
       ,
    L t R t t
      
    1 2
    R R
    b b
    
    1 2
    L L
    b b
    
    

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11. Thank you for your
    attention!
    olga.proncheva@gmail.com
    11
    

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