Poland’s efforts to combat COVID-19 were hindered by endemic vaccination hesitancy and the prevalence of opponents to pandemic restrictions. In this environment, the policy of a COVID-19 vaccination mandate faces strong resistance in the public debate. Exploring the discourse around this resistance could help uncover the motives and develop an understanding of vaccination hesitancy in Poland. This paper aims to conduct a social network analysis and content analysis of Twitter discussions around the intention of the Polish Ministry of Health to introduce mandatory vaccinations for COVID-19. Twitter was chosen as a platform to study because of the critical role it played during the global health crisis. Twitter data were retrieved from 26 July to 9 December 2021 through the API v2 for Academic Research, and analysed using NodeXL and Gephi. When conducting social network analysis, nodes were ranked by their betweenness centrality. Clustering analysis with the Clauset–Newman–Moore algorithm revealed two important groups of users: advocates and opponents of mandatory vaccination. The temporal trends of tweets, the most used hashtags, the sentiment expressed in the most popular tweets, and correlations with epidemiological data were also studied. The results reveal a substantial degree of polarisation, a high intensity of the discussion, and a high degree of involvement of Twitter users. Vaccination mandate advocates were consistently more numerous, but less engaged and less mobilised to “preach” their own stances. Vaccination mandate opponents were vocal and more mobilised to participate: either as original authors or as information diffusers. Our research leads to the conclusion that systematic monitoring of the public debate on vaccines is essential not only in counteracting misinformation, but also in crafting evidence-based as well as emotionally motivating narratives.

The domain of policymaking, which used to be limited to small groups of specialists, is now increasingly opening up to the participation of wide collectives, which are not only influencing government decisions, but also enhancing citizen engagement and transparency, improving service delivery and gathering the distributed wisdom of diverse participants. Although collective intelligence has become a more common approach to policymaking, the studies on this subject have not been conducted in a systematic way. Nevertheless, we hypothesized that methods and strategies specific to different types of studies in this field could be identified and analyzed. Based on a systematic literature review, as well as qualitative and statistical analyses, we identified 15 methods and revealed the dependencies between them. The review indicated the most popular approaches, and the underrepresented ones that can inspire future research.

We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We also perform some numerical analysis.

We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cramér–Lundberg risk process. We investigate this optimization problem under the constraint that the divide

We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We perform some numerical analysis as well.

We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function fulfills the Hamilton-Jacobi-Bellman equation and we identify the optimal dividend strategy.