The chapter discusses a number of mathematical models of information battle in techno-social environments. Some models take into account such battle factors as the mass information media's incomplete coverage of the society, the individuals' acquisition of the information only after receiving it twice, the individuals' forgetting the information, a priori bias to support a party to the battle, and polarization of the society. For simpler models, the results are described in brief. For more complicated ones, mathematical research has been conducted with the sociological interpretation of the results.
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A review of sociological literature on this area of focus could be a multi-volume edition itself, so here it is only the works of Herman and Chomsky (2006), DiFonzo and Bordia, (2005, 2007), Pronchev and Muraviov (2011) that will be mentioned. The authors by no means claim their review to be neither exhaustive nor representative but they rather proceed from their own preferences.
The first mathematical single rumor spreading models were suggested quite a long ago (Daley & Kendall, 1964; Maki & Thompson, 1973). In the most general terms, these models assume that at each time point some individuals from those making up a social group possess certain information and transmit it to other individuals. Thus, the information is propagated. The deterministic and stochastic models are distinguished, and in some cases - deterministic and stochastic variants of one and the same model. In this work it is only the deterministic models that are considered.
The mechanics of the Daley-Kendall model looks as follows. At each time point, each member of the society belongs to one of the three classes: ignorants, spreaders, or stiflers. Ignorants are not yet aware about the rumor; spreaders know the rumor and propagate it, while stiflers know it but do not spread it. Initially, one member of the society is a spreader, and all the other ones – ignorants. Contacts between the individuals are described in the molecular-kinetic terms: e.g., the frequency of meetings between ignorants and spreaders is proportional to the multiplication of the current quantities of these classes (certainly this implies the homogeneity of the society). The individuals can pass from one class to another in three cases: (i) if an ignorant meets a spreader, the ignorant also becomes a spreader, (ii) if two spreaders meet, then both of them become stiflers, and (iii) if a spreader meets a stifler, the spreader becomes a stifler too. Hereinafter the spreaders passing to the class of stiflers will be called the stifling effect.
The distinction of the Maki-Thompson model prerequisites consists in only one spreader turning into a stifler when two spreaders interact (the second one remains a spreader), i.e. in a more limited character of the stifling-effect.
These early works were developed under the influence of epidemiology models (however, the influence still remains fairly strong). So early as when introducing the notions of ignorants, spreaders and stiflers, Daley and Kendall specified that the classes are analogous to classes of “susceptibles”, “infectious persons”, and “removed cases” in epidemiology. Meanwhile, it is not only the transfer of ideas from one scientific branch to another one that is in question, but so is the search of differences. So, the same authors see the difference in the fact that in epidemiology models, transition from the infectious persons class to the removed cases one (i.e. recovery or isolation) occurs merely with the course of time, without being influenced by peers in the society. Meanwhile, in the rumor model developed by them the stifling-effect takes place due to encountering another spreader or stifler.