In the mandatory health insurance market in Switzerland, a range of insurers offer policies that differ in characteristics like premium and service level while benefits are the same and regulated by law. In this paper, we give an overview of the market and analyse the relationship between insurers' characteristics and the evolution of their market shares. Indeed, in view of substantial differences between the players, the risk that policyholders change their provider is important. We develop a linear model with two-sided lognormally distributed errors and use publicly available data on the Swiss mandatory health insurance market for the years from 2002 to 2015. Thereby we identify and quantify the main drivers for the policyholders' switching behavior that reflect in changes in market shares. The results suggest that market share changes are particularly linked to the difference between an insurer's premium and the overall market premium. In addition, the difference to the previous year's premium also has an impact on the market share while the service level as well as the group affiliation of a provider turn out not be significant in explaining annual market share changes.