> > Pure majoritarianism is one means of operationalizing the concept of "democracy", but its one that's pretty much been rejected as an undesirable means of doing so for, at least, most of the modern era.
> Even in ancient Athens, with direct democracy, decisions were taken through majority-rules voting.
"Ancient Athens", you will note, significant predates the modern era, and illustrates nothing about what has been rejected in that era.
> Nor has any modern democracy (at least one operating at larger scale than your local food co-op) ever rejected "operationalizing" democracy through majoritarianism.
You dropped the word "pure"; yes, most modern democracies incorporate some majoritarian elements, and yet, they almost universally reject pure majoritarianism where policies are decided by whichever preference gains an infinitesimal degree greater than 50% support in the general public.
Indirect democracy itself its a deviation from pure majoritarianism, and most modern democracies operate largely or entirely as indirect, representative democracies.
Bicameralism in which one house has longer terms or indirectly (or un-) elected members, or staggering elections within a single house, is a further departure from pure majoritarianism within an indirect democracy (and some forms of this are quite common in modern democracies.)
The idea of fundamental limitations on the powers of government that require something more than the normal legislative process (which itself usually resembles majoritarianism, within the legislative body) -- whether it is confirmation by additional bodies, supermajority votes within the same bodies, or multiple votes within the same bodies separated by a specified time interval -- is a further departure from pure majoritarianism (and one frequently adopted by modern democracies.)
Representation models that are not strictly tied to population, such as ones where subunits are given equal representation irrespective of population, are another departure from pure majoritarianism.
Models in which officials at any level are elected by an intermediate body rather than the public at large, (and, a fortiori, those where the body itself is not apportioned strictly proportionally to population) -- such as an "electoral college" -- are further departures from pure majoritarianism.
Every modern democracy (on the national scale, at least) departs from pure majoritarianism through some degree of indirect democracy, and virtually all depart from pure majoritarianism in other ways (most adopt some of the departures previously discussed in this post, some -- e.g., the U.S., adopt all of them.)
> The only people who reject majoritarianism are a tiny number of "theory"-steeped leftist academics
This is radically untrue. Rejection of pure majoritarianism is not only not limited to either leftists or academics (much less the intersection of those groups in "leftist academics"), its probably more common and more strong among theorists of the right than of the left.