The Roots Of Democratic Legitimacy. This is a technical article, but you can skim it to draw out the main point. We balance majority (representative) decision-making with rules that are more consistent. You could even just read the last paragraph:

This serves as a useful reminder that the majority should not be sacralized. The legitimacy of democracy is rooted in the fact that it permits relatively efficient decision-making while protecting the interests and values of everyone. When one of those two requirements cannot be satisfied by majoritarian choice, we should look for other ways to self-govern, e.g., private decision-making or expert-based (or even epistocratic) collective choices. To return to my opening example, when deciding between coal, nuclear, or wind power, simple majority rule might lead to unstable or harmful outcomes - today’s majority might choose coal, next year’s nuclear, creating costly policy whiplash. Instead, legitimate decisions emerge from established procedures: environmental impact assessments, expert consultations, and parliamentary deliberation, all operating within constitutional limits that protect minority interests.
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Majoritarianism has pragmatic value, but it’s not constitutive of political legitimacy. The latter finds its roots in the rules in which collective decision-making is embedded, rules that we all have reasons to abide by.

It’s the kind of thing Plato was all upset about when he wrote the Republic.