Plumbing services constitute an essential sector in our society, significantly impacting the quality of our day-to-day lives. The intricacies involved in recruiting a professional plumbing service require an understanding of multiple domains including law, economics and risk assessment.

The first crucial step in hiring professional plumbing services involves comprehension of the scope of your project. The complexity of your project, whether it's a simple leaking faucet or a significant re-piping job, may dictate the level of expertise required and impact your choice of a plumber. The principle of economies of scale, derived from microeconomic theory, applies here. If your project is large and complex, you might opt for a larger company with ample human resources and a broad range of skills. However, for smaller tasks, an independent contractor might suffice.

On identifying the nature and scale of your project, you must ensure that the potential plumber is licensed and insured. Licensure indicates that the plumber has received the necessary training and possesses the knowledge to perform plumbing tasks. Insurance, on the other hand, is a safety net for both parties. Similar to a risk transfer mechanism in the insurance industry, it protects you from any potential damages or accidents that could occur during the job. It’s a nod to the principles of risk management—an integral part of finance and economics.

Price is invariably a significant determinant in the decision-making process. However, it’s important not to let it overshadow other crucial factors. Formulating a price-quality trade-off analysis, a concept widely used in consumer behavior studies, could help in this context. It involves comparing the cost of the service with the quality expected. While it's tempting to go for the lowest quote, remember that professional services come at a cost and a compromise on price could lead to subpar service and more expenses in the future.

Reputation is another aspect that should factor into your decision-making process. In an era where information is readily available, conducting research akin to a background check provides insightful details about the potential plumber's work ethic, timeliness, and experience. Websites and social media platforms can provide valuable reviews and ratings. However, be wary of the statistical bias that could be present in online reviews. For instance, the self-selection bias suggests those who leave reviews are either very satisfied or very dissatisfied with the service, thereby not providing a complete picture.

Contract negotiations form the final step. It's essential to review the details meticulously. Legal principles such as 'pacta sunt servanda' underline the necessity to abide by the agreements. Ensure that the contract includes the overall cost, detailed description of the job, materials to be used, and a timeline. Any ambiguity could lead to unnecessary disputes and additional costs, mirroring the chaos theory from mathematics where a minor change can drastically change the outcome.

It's also important to note that there exists an asymmetry of information in this process, as the plumber usually possesses more technical knowledge about the job. This can lead to moral hazards, a concept in contract theory, where one party could exploit the knowledge gap to their benefit. Clear communication and consultation can mitigate such risks.

To sum it up, hiring a professional plumbing service transcends a mere transactional process. It involves an intricate blend of decision-making, risk management, understanding economic theories, and legal agreement interpretations. It requires careful consideration of multiple aspects to ensure a satisfactory outcome. As with any employment process, due diligence, research and clear communication are key to successfully hiring a professional plumbing service. This not only guarantees a job well done but also safeguards the longevity and functionality of your plumbing system.