Most publication and citation indicators are based on datasets with multi-authored publications and thus a change in counting method will often change the value of an indicator. Therefore it is important to know why a specific counting method has been applied. I have identified arguments for counting methods in a sample of 32 bibliometric studies published in 2016 and compared the result with discussions of arguments for counting methods in three older studies. Based on the underlying logics of the arguments I have arranged the arguments in four groups. Group 1 focuses on arguments related to what an indicator measures, Group 2 on the additivity of a counting method, Group 3 on pragmatic reasons for the choice of counting method, and Group 4 on an indicator's influence on the research community or how it is perceived by researchers. This categorization can be used to describe and discuss how bibliometric studies with publication and citation indicators argue for counting methods.