It's like saying "milk is only what comes from a free-range cow's teats. Nothing else is milk." As soon as you redefine it that sharply, you need to translate, not just read, everything written that came before. To fail to translate is to make equivalent two things that are not, which only leads to fallacy. Much advertising, whether it's from large corporate PR firms or Russian disinformation campaigns or written in the spirit of Lakoff, involves manipulating meanings and contexts to deceive and create fallacies that are, the manufacturers of the "frame" hope, believed.
Majoritarianism is a form of democracy. If every white person in the US voted to expel every non-white person, that would be fully democratic.
Democracy can be representative. We elect representatives and gift them our authority to decide on our behalf. A republic is a form of government in which the representatives are organized and structured in a particular kind of way.
Democracy can be "liberal" (which has a meaning other than what's found in "he's a liberal".) The first paragraph of https://en.wikipedia.org/wiki/Liberal_democracy nails it, with the caveat that the some of the components of liberalism have changed slightly over time, more in scope of application than in terms of decontextualized definition.
One recent attempted re-definition, for example, involves "minority". Like "democracy", some want to restrict its meaning to just what's politically acceptable--mostly race/ethnicity and class, where "religious minorities" and "political minorities" are properly shouted down unless they intersect in a particularly ideologically subservient way with race/ethnicity and class. Redefine words enough and anything can come to mean anything. Let me redefine 3 or 4 terms in certain ways, 3 or 4 times each, and I'll give you an unchanged Stalin under the terms of a "living" US Constitution. Balance is compromise. Liberal democracy is compromise. Majoritarianism ... dictatorship of the majority, and if the majority is proletarian, well, there ya go.
An anonymous writer, Petr Fidelius, write a samizdat monograph examining the utterances of the Czechoslovak communist party. Power was vested in the workers, the people, the population. The party leaders represented the people and were of the people. The people, therefore, elected the next rung up of the party, who were of the people and were the people. So the people selected the top leaders. The people, then, were in charge of the secret police, censorship, and all the actions of the government, as well as rewriting the laws, because the people needed to be sure that the enemies of the people (albeit a majority of the population at times) were held in check. Similarly for the USSR, where repression or not, it was really the people repressing themselves in the interest of the people. See how if you don't focus on meanings and consistency of meanings you get whatever you want? Linguistic libertinism leads to a multitude of semantic vices.
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