Utility functions are often used to reflect decision makers' (DMs') preferences. They have the following two merits: one refers to the representation of the DM's utility (satisfaction) level, the other one to the measuring of the consensus level in a negotiation process. Taking the background of China's urban house demolition, a new kind of consensus model is established by using different types of multi-stage fluctuation utility functions, such as concave, convex, S-shaped, reversed S-shaped, reversed U-shaped as well as their combinations, to reveal negotiators' dynamic physiological preferences and consensus level. Moreover, the effects of the decision-making budget and the individual compensation tolerance on the consensus level are also discussed in this paper. Compared with previous research, the proposed model takes both the negotiation cost and DM's preference structure into consideration, and most importantly, it is computational less complex.