The rights and powers of each member to an LLC is defined by the provisions in the LLC Operating Agreement of the particular limited liability company business. So, the answer to this question will vary widely based on what rules, powers and obligations the members have agreed upon to apply.
Having said that, the most common structure when it comes to LLC decisions is that each member’s voting power is based on his or her relative ownership in the business. Accordingly, if a member owns more than 50% of the business, this majority member will control the ultimate decision.
Given this, if there are other members who own a significant interest (albeit not a majority), such members can negotiate to require that their vote is required for all major actions or certain, identified business decisions. This becomes a negotiation between members when they are putting their business together or before a new member is admitted.
One option used is to make the limited liability company a manager managed LLC and to give all significant LLC members a manager position which cannot be taken away as long as that person is a member. In this structure, a non-majority LLC member gets more power for every day business decisions. Now, the majority member can reserve significant and strategic decisions for himself by requiring a member vote for these.
Despite the opportunity for negotiation and planning upfront, in most first time business scenarios, members are not aware enough to think through and plan for this and they do not get legal representation to handle this after LLC formation. As a result, in most cases, default provisions of the LLC laws and in most standard LLC Operating Agreements grant the majority owner final say in the event of a disagreement.
Now, when a member makes a decision on behalf of the LLC, he/she does have certain fiduciary duties to hear out the other members and to make decisions that are reasonably in the best interest of the LLC business. So, there are some laws that prevent abuse by a majority member.