How did Henry Sidgwick defend utilitarianism using common-sense morality?

In his seminal work, The Methods of Ethics, Henry Sidgwick defended utilitarianism by critically analyzing "common-sense morality"—the intuitive moral principles (such as honesty, justice, and benevolence) accepted by most people without systematic reflection.12

While some intuitionists argued these principles were self-evident, independent truths, Sidgwick rejected this view. He demonstrated that these common-sense principles are often vague and frequently conflict with one another in practice. Sidgwick argued that these rules could only form a coherent moral system if they were made subordinate to the utilitarian principle. By framing utilitarianism as the underlying foundation, he showed that the "sound" elements of common-sense morality could be explained and justified by their contribution to the general happiness, while the utilitarian principle simultaneously resolved the conflicts between them.12

Ultimately, Sidgwick believed the utilitarian principle itself rested on a self-evident axiom of rational benevolence, though he remained famously troubled by his inability to fully reconcile this universal perspective with the rational claims of egoism.12