The decision making process for selection of a proper Big Data service platform can be complex and dynamic. The bidding process can occur multiple times, the assessment criteria vary each time and they may conflict with each other. Most existing multiple attribute decision-making (MADM) methods are unable to take into account such dynamic process. This paper presents a new dynamic decision making method for the selection of a big data service provider. The dynamic nature of such process is addressed by means of a feedback mechanism. The final decision is taken at the end of a series of exploratory processes. The ranking algorithm for the proposed method uses prospect theory to reflect the decision maker's behavior in the face of risk. A case study shows the actual bidding process and proves the proposed method is able to guide and support a decision team to efficiently aggregate their preferences dynamically.