Despite the immense societal importance of ethically designing artificial intelligence, little research on the public perceptions of ethical artificial intelligence principles exists. This becomes even more striking when considering that ethical artificial intelligence development has the aim to be human-centric and of benefit for the whole society. In this study, we investigate how ethical principles are weighted in comparison to each other. This is especially important, since simultaneously considering ethical principles is not only costly, but sometimes even impossible, as developers (...) must make specific trade-off decisions. In this paper, we give first answers on the relative importance of ethical principles given a specific use case—the use of artificial intelligence in tax fraud detection. The results of a large conjoint survey suggest that, by and large, German respondents evaluate the ethical principles as equally important. However, subsequent cluster analysis shows that different preference models for ethically designed systems exist among the German population. These clusters substantially differ not only in the preferred ethical principles but also in the importance levels of the principles themselves. We further describe how these groups are constituted in terms of sociodemographics as well as opinions on artificial intelligence. Societal implications, as well as design challenges, are discussed. (shrink)