What authority doesn't an HOA have?

Law above it, always

Every governance question resolves through a stack: federal and state law first, then the recorded declaration, then the bylaws, then board-adopted rules, then individual board decisions. An association's documents sit below the law, not beside it. A restriction, a rule, or a board resolution that conflicts with a statute covering the same ground does not win that conflict.

Exactly which document controls when two of an association's own documents disagree, declaration versus bylaws, for example, is set by each state's statute and can differ. Read your own declaration's stated order of precedence, or ask your association's attorney, before assuming.

A restriction that is arbitrary or against public policy

A validly recorded restriction is an enforceable equitable servitude, a use restriction binding on every current and future owner, not just the one who signed it, and a challenger carries the burden of proving it should not apply. But that presumption has an outer edge. The California Supreme Court described where a restriction crosses it:

"wholly arbitrary, violate a fundamental public policy, or impose a burden on the use of affected land that far outweighs any benefit."

Source: Nahrstedt v. Lakeside Village Condominium Assn., Supreme Court of California

An owner who simply dislikes a rule has not met that bar. This is also why a board cannot enforce a restriction against one owner and quietly skip it for another: the whole doctrine that makes CC&Rs easy to enforce rests on applying them the same way to everyone.

A decision the board never had authority to make

Courts give community association boards real latitude on maintenance and repair choices, but that latitude is not blanket deference to anything a board decides. It attaches to a board's exercise of discretion inside its own authority:

"Where a duly constituted community association board, upon reasonable investigation, in good faith and with regard for the best interests of the community association and its members, exercises discretion within the scope of its authority under relevant statutes, covenants and restrictions to select among means for discharging an obligation to maintain and repair a development's common areas, courts should defer to the board's authority and presumed expertise."

Source: Lamden v. La Jolla Shores Clubdominium Homeowners Assn., Supreme Court of California

Notice the conditions: reasonable investigation, good faith, and staying inside the board's actual authority under the statutes and the declaration. A board that decides something its documents never gave it power to decide does not earn this deference just because the vote was unanimous.

Power a master association was never given

A master association, an organization sitting above several individual community associations, often to run shared amenities or roads, has no built-in authority over the associations beneath it. Its power is a delegation, and only reaches as far as that delegation goes:

"A master association may exercise the powers... only to the extent expressly permitted in: (a) The declarations of common-interest communities which are part of the master association or expressly described in the delegations of power from those common-interest communities to the master association."

Source: Nevada Revised Statutes Chapter 116, Nevada Legislature

Exact statutory numbering differs by state, but the underlying principle, that a master association's power exists only insofar as a sub-association's own declaration actually handed it over, reflects the general common-interest ownership statute structure Nevada codifies here. If your community sits under a master association, that delegation is spelled out in your own declaration, not assumed.