Conflict is an inevitable part of human interaction. Because some occasional conflict in social settings is inevitable, the burden of conflict mitigation is a shared by everyone. The better prepared we are as individuals to handle conflict with grace, the fewer negative consequences that conflict is likely to have.
Often, conflict arises because of miscommunication or disappointment. In a group setting, there is an opportunity to manage conflict that arises in advance by taking care to manage expectations. Sometimes, this is as simple as checking in with another person about a group project or your shared plans to make sure everybody has the same expectations. If one person thinks dinner plans are at seven o'clock, for example, and the other thinks they're at seven thirty, a conflict might arise if the person sitting alone for thirty minutes gets agitated.
Other times, managing expectations might be more complicated. One person may find that there are expectations of them that they're not able to meet, which has the potential to create conflict with the person who holds those expectations. Even if the potential for conflict can't be entirely avoided, it might be lessened by an open, honest, proactive discussion about what the first person's limitations are.
If your intention is to provide opportunities to manage conflict among a group, you might take the initiative to schedule regular proactive check-ins about everyone's expectations and capabilities.
If a conflict reaches a point where mediation is necessary, the key is often compromise. To facilitate compromise, a mediator needs to open up simultaneous communication with both parties. This is true regardless of the scale of the conflict—one mediator might help two friends by sitting everyone down and having a heartfelt talk about everyone's feelings, and another might also help two companies by meeting with lawyers from both. In both cases, the mediator's job is the same: be an impartial liaison guiding the discourse toward a resolution that works for everyone.