In short, boardroom mediation works because once the boardroom mediator has explained how it will provide by far the better outcomes for all parties than either litigation or doing nothing, and better than the negative outcomes that otherwise would result, all parties then want it to work. The problem for shareholders and directors is that they often do not, at first, see those benefits. It is the role of the boardroom mediator to make these benefits clear at the outset.
For example, those who hold the majority of voting shares may think that they are in control and do not need to make any changes in response to the dissatisfaction of the other shareholder(s). However, if they have dismissed a minority shareholder director and want him to take no part in the running of the company, they may not have addressed the point that, until they come to a solution that, say, involves them buying out the minority shareholder, they will either have to share dividends with them in the future proportionate to their shareholding (so the minority shareholder earns money despite doing no work) or deny themselves the significant tax benefits to themselves from issuing dividends. Over time this can accumulate to a considerable 'price' to pay for not resolving the future of the company.