The currently dominant model for moral cognition states that moral judgments of harm is driven by two processes: a fast, automatic process that leads to deontological judgment (i.e. do not harm), and a slower, deliberative process that leads to utilitarian judgment (i.e. harm is appropriate if it leads to better overall outcomes). Although the model has yielded important insights, we argue that its scope is too narrow and additional theoretical factors are needed to advance our understanding of human moral cognition. More specifically, we point out that research within this paradigm has focused exclusively on one-shot moral judgment and has thereby assumed that current moral judgments are independent of past and future judgments. However, certain normative considerations such as a fair distribution of harm only arise across multiple decisions involving the same victims. We propose a novel methodological approach to study moral cognition: sequential trolley-style dilemmas and suggest that people will display a genuine motivation to distribute harms fairly across victims besides inclinations towards deontological and utilitarian judgment. A first research line explores the incremental validity of the fairness concept we advance. In a second research line we intend to study how person-centered morality influence motivation for fairness. Finally in a third research line we intend to study this motivation for fairness on both hypothetical and real-life dilemmas.