Merit based promotion & tenure decision have always been controversial. This paper suggests an agent based model of the decision making processs using spectral graph theory, where the voting agents are the vertices of the graph, and edge weights are determined based on the extent of collaborative research between the agents, as well as their estimated levels of social interactions. The model assumes that agents with lower research productivities tend to interact more often with one another. Using the graph theoretic spectrum, the paper proposes a 2-dimensional influence diagram that maps the voting agents into points on a 2-dimensional grid, where agents that are likely to influence each other more are closely spaced. Next, a dynamic model is addressed, where votes are determined based on very small randomly assigned initial values, and the mutual interaction during the decision making process. The model is able to accurately reproduce a known promotion decision making from a department of a research oriented university which involved a sizeable number of voting agents with low research outputs.