When you consider that our grouping instincts are optimized for 50-person hunter-gatherer bands where everyone knows everyone else, it begins to seem miraculous that modern-day large institutions survive at all.
Well—there are governments with specialized militaries and police, which can extract taxes. That's a non-ancestral idiom which dates back to the invention of sedentary agriculture and extractible surpluses; humanity is still struggling to deal with it.
There are corporations in which the flow of money is controlled by centralized management, a non-ancestral idiom dating back to the invention of large-scale trade and professional specialization.
And in a world with large populations and close contact, memes evolve far more virulent than the average case of the ancestral environment; memes that wield threats of damnation, promises of heaven, and professional priest classes to transmit them.
But by and large, the answer to the question "How do large institutions survive?" is "They don't!" The vast majority of large modern-day institutions—some of them extremely vital to the functioning of our complex civilization—simply fail to exist in the first place.
Science traditionally gets funded by governments, corporations, and large foundations. I've had the opportunity to discover firsthand that it's amazingly difficult to raise money for Science from individuals. Not unless it's science about a disease with gruesome victims, and maybe not even then.
Why? People are, in fact, prosocial; they give money to, say, puppy pounds. Science is one of the great social interests, and people are even widely aware of this—why not Science, then?
Any particular science project—say, studying the genetics of trypanotolerance in cattle—is not a good emotional fit for individual charity. Science has a long time horizon that requires continual support. The interim or even final press releases may not sound all that emotionally arousing. You can't volunteer; it's a job for specialists. Being shown a picture of the scientist you're supporting at or somewhat below the market price for their salary, lacks the impact of being shown the wide-eyed puppy that you helped usher to a new home. You don't get the immediate feedback and the sense of immediate accomplishment that's required to keep an individual spending their own money.
Ironically, I finally realized this, not from my own work, but from thinking "Why don't Seth Roberts's readers come together to support experimental tests of Roberts's hypothesis about obesity? Why aren't individual philanthropists paying to test Bussard's polywell fusor?" These are examples of obviously ridiculously underfunded science, with applications (if true) that would be relevant to many, many individuals. That was when it occurred to me that, in full generality, Science is not a good emotional fit for people spending their own money.
In fact very few things are, with the individuals we have now. It seems to me that this is key to understanding how the world works the way it does—why so many individual interests are poorly protected—why 200 million adult Americans have such tremendous trouble supervising the 535 members of Congress, for example.
So how does Science actually get funded? By governments that think they ought to spend some amount of money on Science, with legislatures or executives deciding to do so—it's not quite their own money they're spending. Sufficiently large corporations decide to throw some amount of money at blue-sky R&D. Large grassroots organizations built around affective death spirals may look at science that suits their ideals. Large private foundations, based on money block-allocated by wealthy individuals to their reputations, spend money on Science which promises to sound very charitable, sort of like allocating money to orchestras or modern art. And then the individual scientists (or individual scientific task-forces) fight it out for control of that pre-allocated money supply, given into the hands of grant committee members who seem like the sort of people who ought to be judging scientists.
You rarely see a scientific project making a direct bid for some portion of society's resource flow; rather, it first gets allocated to Science, and then scientists fight over who actually gets it. Even the exceptions to this rule are more likely to be driven by politicians (moonshot) or military purposes (Manhattan project) than by the appeal of scientists to the public.
Now I'm sure that if the general public were in the habit of funding particular science by individual donations, a whole lotta money would be wasted on e.g. quantum gibberish—assuming that the general public somehow acquired the habit of funding science without changing any other facts about the people or the society.
But it's still an interesting point that Science manages to survive not because it is in our collective individual interest to see Science get done, but rather, because Science has fastened itself as a parasite onto the few forms of large organization that can exist in our world. There are plenty of other projects that simply fail to exist in the first place.
It seems to me that modern humanity manages to put forth very little in the way of coordinated effort to serve collective individual interests. It's just too non-ancestral a problem when you scale to more than 50 people. There are only big taxers, big traders, supermemes, occasional individuals of great power; and a few other organizations, like Science, that can fasten parasitically onto them.