If you have a Limited Liability Company that is taxed like a partnership, which is a very common setup, your decision-making authority can be specifically agreed upon in the Operating Agreement. Essentially, your partner could retain 51% of the earnings but his/her voting interests could be equal to yours. However, I suspect your partner wants to retain their 51% voting interest as well as their 51% profit interest. In this scenario, your ultimate decision making authority is limited because you can never achieve majority status.

When I represent a minority interest holder of a company I try to build certain safeguards into the Operating Agreement. For instance, I would try to include certain actions that must either have a super majority (defined as 66% or 75% depending on the size of the entity) or in your case a unanimous vote. I would try to include things like bringing on another member, distributions, taking on debt, major capital expenses, changing the Operating Agreement etc. as items that would require your consent. This will offer some protection in the decision making process. However, your partner will retain the ultimate decision making authority for anything not specifically delineated in your governing document.