Georg Simmel writes about the role of groups of three in social dynamics and relationships. Groups of three can facilitate reconciliation and resolution of conflicts, but can also create new conflicts. In relationships such as marriage, the presence of a third element – a child - can strengthen the bond between the two partners. In some cultures, a marriage is not considered fully established until a child is born. Groups of three have a unique dynamic that is different from groups of two or larger.

Another example of a group of three is a relationship between nations that are mediated by a third party. Here, the third element has a function in resolving conflicts and facilitating understanding within groups. This dynamic occurs in all groups of three or more; the third element serves as a mediator to resolve conflicts and promote understanding between the other two members. This process of mediation can happen in subtle ways, such as through gestures or body language, and does not always need to be explicit. The process of mediation occurs frequently and is a fundamental aspect of social life. This dynamic is important to consider in the analysis of social interactions and relationships.

The use of an arbitrator represents a higher level of trust in the objectivity of the resolution process, as both parties must willingly submit to the arbitrator's decision. The role of an arbitrator has to be distinguished from that of a mediator; the distinction between the two is often maintained in more formal contexts, such as in labor disputes or international conflicts. In everyday life, the roles of mediator and arbitrator can be difficult to distinguish and may overlap in more subtle or informal interactions within groups. It is important to be aware of these subtle and nuanced relationships in order to understand the complexity of social interactions.

The "Tertius gaudens" is the third party in a conflict between two other parties. This role can take several forms:

1. A mediator, who brings the two conflicting parties together to resolve their differences;

2. An arbitrator, who makes a decision to end the conflict;

3. A party that benefits from the conflict between the other two parties, either:

a. by taking advantage of the conflict to gain something that one of the other parties would have otherwise taken, or

b. by supporting one of the parties and gaining something in return.

The role of the third party can be complicated by the fact that it may have its own interests and conflicts with one of the other parties, leading to further complications and potential conflicts. The third party that benefits from the conflict or competition between two other parties can play various roles in mediating or arbitrating conflicts, or can simply benefit from the conflict without actively participating in it. The tertius gaudens can gain power and influence through its ability to choose which of the two conflicting parties to support or align with. The concept of the tertius gaudens is important for understanding the complexity of human social interactions and the various forms that these interactions can take.

 The tertius gaudens can also play a role in politics, specifically in the context of parliamentary systems. The Tertius can become influential in conflicts between two parties, and gain an advantage through passivity, by benefiting from the conflict between the other two parties without actively participating in it. Alternatively, the Tertius can support one of the parties in the conflict and gain an advantage that way. The Tertius can become more influential in a situation when the parties are in conflict due to economic interests; the Tertius can gain power and influence through stability and remaining uninvolved in the conflict.

Employers seek to prevent unions or collective bargaining by their employees, by the refusal to negotiate with representatives of the workers, in order to prevent the workers from strengthening their position through a representative who is not afraid of or dependent on the employer. This also hinders the ability of workers in different industries to coordinate their actions, such as through the implementation of a wage tariff. The use of neutral third parties, such as arbitrators, to mediate disputes between employers and employees, eventually developed towards collective bargaining between employers and all relevant parties in an industry.

Constitutional rulers try to prevent the formation of opposing majorities through the division of parliament through "divide and conquer," where an entity tries to pit different groups against each other in order to weaken them and prevent them from uniting against the entity. This strategy can involve manipulating people's emotions and encouraging conflict between groups, even if there is no logical basis for the conflict. Examples of this strategy are the English government's efforts to prevent the formation of uncomfortable political majorities, and the Venetian government's confiscation of the property of those involved in conflicts between different social classes. Some groups are more easily divided and conquered than others, and some groups may be more effective at fighting against each other due to their shared interests and knowledge of each other's weaknesses.