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
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 +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:
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 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?
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! olga.proncheva@gmail.com 11