Exactpro
PRO
March 23, 2019
10

# 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

Conference website http://macspro.club/

Website https://exactpro.com/
Instagram https://www.instagram.com/exactpro/

March 23, 2019

## Transcript

1. Moscow Institute of Physics and Technology
MIPT / PHYSTECH

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

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

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

1
)+(1- g)(φ
2

2
)>0 party R
g(φ
1

1
)+(1- g)(φ
2

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:

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

 

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
      
      
    
    



7. Influence of the parameters
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?

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
    

     
   

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
 

 

 
 
   
   
 
     
   
   
       
 
   
 

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

11. Thank you for your
attention!
[email protected]
11