Exercise 3: "Who Is Trusted to Install Software" — Possible Solution
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WHAT DIFFERS BETWEEN THE TWO MODELS
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Per this chapter's finding-box, every Linux distribution's package manager runs as root because the OS vendor itself is treated as the installing authority - the package manager is considered part of the system, trusted with root-level access to modify the system as a whole. Homebrew's model puts that trust somewhere else: it installs into a prefix the logged-in user already owns, so ordinary installs never touch root-owned system areas and never require sudo at all. The question "who is allowed to decide what software goes on this machine, and with what privilege level" gets a different answer in each model - the OS vendor, in Linux's case; the individual logged-in user, in Homebrew's case.

WHY HOMEBREW ENDED UP WITH ITS PARTICULAR ANSWER
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The chapter explains this wasn't an arbitrary design choice so much as a consequence of Homebrew's own position: no OS vendor (Apple) had already claimed the "installing authority" role for command-line/developer tooling on macOS the way every Linux distribution's own maintainers had for their systems. Since Homebrew was built by the community, entirely outside of Apple, requiring root access the way a distribution's own official package manager does would have meant asking users to hand system-level trust to an unofficial, third-party project - so a user-owned, non-root default became the natural, lower-friction choice instead.

WHY THIS WORKS AS AN ANSWER
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It correctly identifies the OS vendor vs. the individual user as the two different answers to "who is the installing authority," and explains that Homebrew's non-root default follows naturally from its own unofficial, community-built origin rather than being an arbitrary technical decision.