Preference elicitation to support solving synthesis problems in certain domains (e.g. automated ecological model construction) is inhibited by a severe lack of knowledge about the criteria that motivate decision making. Yet, even in these domains, humans are able to provide some partial ordering of their preferences, based on past experience and personal opinion. Working towards an efficient representation and reasoning mechanism with such partial preference information, this paper introduces a qualitative calculus of partially ordered preferences that is rooted in order of magnitude reasoning. It then integrates this calculus in a dynamic constraint satisfaction problem. A solution algorithm for the resulting dynamic preference constraint satisfaction problem is also presented. To demonstrate the ideas, the proposed techniques are applied to sample compositional modelling and configuration tasks.