The rapid changes in internet accessibility and the evolving ways it is used could raise doubts about whether earlier findings on selection effects in internet surveys still hold true. We address the following questions: 1) Is the selection criterion by mere internet access still a reasonable self-selection criterion? 2) If this is no longer true, how should alternative self-selection processes be modeled? 3) How can these selection processes be controlled? Are demographic control variables sufficient to establish the Missing at Random (MAR) condition, or is it possible to establish the MAR condition with more powerful control variables? 4) To what extent do the weighting procedures correct a self-selection bias? We investigate these questions in the setting of a simulation study where we assume four different selection models. These involve the length of internet use, posting behavior, and interest in politics and are based on theoretical considerations. We use the European Social Survey (ESS) as a simulation environment, which contains these variables and demographic background variables. It also includes our outcome variable, the vote in the 2017 Bundestag election in Germany. In order to judge the differences of the non-probability results and the simulated universe we compare the results of ESS estimates of the 2017 Bundestags elections the real election results.