Sometimes known as 'deadlock' companies, these are common among family-owned businesses, often in the first and second generation. Typical examples would be siblings setting up a business together, or a founder passing the company on to two children. It also occurs where two families, each with a cumulative shareholding amounting to 50% are in business together, and vote with 'their side' of the family.
In a 50:50 company, no-one has control of the board of directors and therefore no-one has management control of the business. Directors cannot be appointed or removed without unanimous approval. Hence it is 'deadlocked', or to put it more positively, unanimity is the key to continued success.
Some clients regard the risk of deadlock as a positive. It means that the two sides will have to find a way to work with each other. That's the basis on which you have gone into business together and the very limited alternatives to agreement, the main one being an application to court for just and equitable winding up, are too unpalatable for sensible commercial people to contemplate. In one way it's similar to the Cold War theory of Mutually Assured Destruction working - to maintain peace between countries with nuclear weapons.
The bad is that the prospect of deadlock is a negative at the same time. Where views diverge there is an immediate problem that could cause significant harm to family relationships and the family business. As human emotion will inevitably be in play, sensible, commercial solutions can be very hard to achieve as emotional responses can provoke irrational action. Back to the theory of Mutually Assured Destruction, we have less faith in it working with Kim Jong Un than Vladimir Putin. One is rational, the other possibly not (in Western terms at least).
The (imperfect) solution is to agree, ideally in a shareholders agreement, how you will work through a dispute if it arises.
First, you should have a process for trying to agree disputes between you, that provides a framework and a timescale for action. You might consider using a trusted third party to help run the process. This should help diffuse some tension and may be all that is required to get agreement.
Beyond that, where the deadlock really cannot be resolved, many shareholder agreements may resort to the option of one party buying the other out. There are many variations on the theme - one is the 'Mexican Shoot-Out', where each party fires their best price at the other and the highest wins.
The problem is that this may not provide a solution where neither party can afford to buy the other out. Also, buyout options tend to favour the side with the deepest pocket or the best access to external funds.
There are no easy solutions to draft into shareholder agreements. The successful resolution of these disputes will involve honesty, compromise and good faith - the qualities that attracted you to set up or work in the family business in the first place.