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Coupled Ising models and interdependent discrete choices under social influence in homogeneous populations

The use of statistical physics to study problems of social sciences is motivated and its current state of the art briefly reviewed, in particular for the case of discrete choice making. The coupling of two binary choices is studied in some detail, using an Ising model for each of the decision variables (the opinion or choice moments or spins, socioeconomic equivalents to the magnetic moments or spins). Toy models for two different types of coupling are studied analytically and numerically in the mean field (infinite range) approximation. This is equivalent to considering a social influence effect proportional to the fraction of adopters or average magnetisation. In the nonlocal case, the two spin variables are coupled through a Weiss mean field type term. In a socioeconomic context, this can be useful when studying individuals of two different groups, making the same decision under social influence of their own group, when their outcome is affected by the fraction of adopters of the other group. In the local case, the two spin variables are coupled only through each individual. This accounts to considering individuals of a single group each making two different choices which affect each other. In both cases, only constant (intra- and inter-) couplings and external fields are considered, i.e., only completely homogeneous populations. Most of the results presented are for the zero field case, i.e. no externalities or private utilities. Phase diagrams and their interpretation in a socioeconomic context are discussed and compared to the uncoupled case. The two systems share many common features including the existence of both first and second order phase transitions, metastability and hysteresis. To conclude, some general remarks, pointing out the limitations of these models and suggesting further improvements are given.