Making morally sensitive decisions and evaluations pervade many human everyday activities. Philosophers, economists, psychologists and behavioural scientists researching such decision-making typically explore the principles, processes and predictors that constitute human moral decision-making. Crucially, very little research has explored the theoretical and methodological development (supported by empirical evidence) of utilitarian theories of moral decision-making. Accordingly, in this critical review article, we invite the reader on a moral journey from Jeremy Bentham’s utilitarianism to the veil of ignorance reasoning, via a recent theoretical proposal emphasising utilitarian moral behaviour—perspective-taking accessibility (PT accessibility). PT accessibility research revealed that providing participants with access to all situational perspectives in moral scenarios, eliminates (previously reported in the literature) inconsistency between their moral judgements and choices. Moreover, in contrast to any previous theoretical and methodological accounts, moral scenarios/tasks with full PT accessibility provide the participants with unbiased even odds (neither risk averse nor risk seeking) and impartiality. We conclude that the proposed by Martin et al. PT Accessibility (a new type of veil of ignorance with even odds that do not trigger self-interest, risk related preferences or decision biases) is necessary in order to measure humans’ prosocial utilitarian behaviour and promote its societal benefits.