Autonomous driving fuels an important debate on the morality of weighing negative externalities in the context of machine learning. Beyond the programming of autonomous cars, negative externalities in the analogue world are also present in other domains of algorithm-based decision making (e.g., HR recruiting). Algorithm programming is rule based. It has to be decided a priori (i.e., before an ethical dilemma occurs) which outcome variable an algorithm should maximize. This demands for an explicit commitment to an ethically preferred position. However, for some ethical dilemmas, it will be very difficult to reach consensus in societal discussions. In these cases, outcome randomization could be a way forward in programming machine-learning systems. We analyze experimentally, if decision randomization by algorithms is generally accepted as a means to address ethical dilemmas. Moral dilemmas are created by inducing decisions with real negative consequences for others as well as for the decision-makers themselves. We find that many decision makers are willing to delegate their ethical dilemmas to an algorithm for outcome randomization. This is especially true, if they are not at risk to incur the negative externality themselves. Our work contributes to the debate on algorithm aversion and its potential causes. It emphasizes that in the need to program algorithms a priori the option of randomization should be included in the societal and economic discourse.