In the grand tapestry of event planning, one thread holds prominence above others - the catering service. This crucial element, often considered both an art and a science, can determine the success of your event. A harmonious blend of exquisite taste, visual appeal, and timely service, the perfect catering service can elevate your event to a whole new level.

To commence our journey towards understanding this complex process of selection, let's delve into the underlying theory of decision making. According to Herbert A. Simon's theory of 'Bounded Rationality', decision-making is often hindered by the information we have, the cognitive limitations of our minds, and the finite amount of time we have to make the decision. In the context of choosing a catering service, this theory emphasizes the need for careful planning, thorough research, and wise decision-making.

The first essential step in hiring a catering service is to clearly define your needs. This involves understanding your event type - be it a corporate meeting, wedding, or casual party. Each event type demands a unique culinary approach, and thus, different caterers specialize in different event types based on their expertise. For instance, a caterer specializing in corporate events may not be ideally suited for a wedding.

The next critical factor to consider is your budget. The Pareto principle, or the 80/20 rule, can be applied in this context. This economic principle suggests that 80% of your results come from 20% of your inputs. Here, the catering service can be considered as one of the significant inputs (20%) that will contribute considerably (80%) to the success of your event. Thus, allocating an appropriate amount in your budget for a high-quality catering service is a wise decision.

Having established your needs and budget, the selection process begins. It is crucial to remember here the Nash Equilibrium, a game theory concept. Named after mathematician John Nash, it suggests that the best outcome will come when each player in the game has chosen their strategy, and no player can benefit by changing their strategy while the other players keep theirs unchanged. When applied to the selection process, you (the host) and the catering service are the players. The 'strategy' in this context implies your requirements, budget, and their service offerings. The optimal decision, or 'Nash Equilibrium', will be a catering service that meets your needs within your budget, while also offering the best service.

Once a shortlist of potential candidates is established, delve into each caterer’s specifics. Review their menus, pricing structures, and service offerings. Also, consider their reputation and reviews. A statistical review of their ratings, or even a Gaussian distribution (bell curve), can provide insights into their overall performance – high peaks indicating consistent good performance.

One might wonder, 'Why so much emphasis on catering?' This stems from the psychological concept of 'Halo Effect'. This is a cognitive bias where the perception of one quality (such as good food) influences the perception of the overall event. Thus, a superior catering service can leave your guests with a positive impression of your event, notwithstanding other minor glitches that may occur.

The final stage in this process involves contractual agreements. It is essential here to be well versed with the 'Law of Contract' that states a contract is a legally binding agreement between two parties. Ensure that the agreement includes all your requirements, including cancellation policies, to avoid any legal disputes in the future.

As we conclude, it is evident that hiring the perfect catering service for your event is not merely a decision – it's a strategic process influenced by various theories and principles. It involves careful planning, thorough research, and wise decision-making, all while being cognizant of your needs, budget, and the caterer's capabilities. In essence, a perfect catering service is more than just food – it's a recipe for the success of your event.