UC Irvine

The distribution of opinions among people constantly evolves over time. This can be seen, for example, from the American National Election Studies (ANES) database, which contains results of surveys on public opinions that have been conducted regularly since 1948. While the statistics of the opinions can be determined from this longitudinal dataset, the laws that govern opinion spread and the driving forces of opinion change are largely unknown. In order to shed light on some of these questions, we built a class of models for opinion spread, which are based on the Kermack-McKendrick model and combine discrete-time, age-structured population dynamics with the process of social contagion. The latter process depends on the interaction matrices among different age groups and the probability of people to change their opinion state, based on the attractiveness of the opinions. We analyze the model in several cases using the Jury stability test, in order to analytically determine the long-term opinion dynamics. It turns out that, under fixed opinion attractiveness, the matrix of interactions (which defines the population structure) can change stability properties of an opinion in the population. To connect the model with real data, we adopt the communication matrix from the literature on infection spread, and fit the model to the ANES survey data, using 15 yes-or-no questions and 22 ``thermometer" questions in the database. We propose three different attractiveness models: time-dependent model (where attractiveness changes with time), cohort-dependent model (where attractiveness depends on the people's age), and a mixture of the two. Interestingly, the most powerful models for a large majority of questions either are based on an age-dependent opinion attractiveness or contain age-dependence as a major component. Such dependencies reflect cohort (internal) effects, as opposed to time-dependent attractiveness, which would reflect period (external) forces. Further, we found that in all the questions investigated, there is a significant positive correlation between age and the polarization of opinions, with at least one polarizing transition rate—from a neutral opinion to either a positive or negative stance—increasing with age. This methodology provides a quantitative way to uncover the mechanisms underlying decadal trends in opinion dynamics.