arXiv:1505.02847v2 [cs.GT] 29 Mar 2019 Axioms for parametric continuity of utility when the topology is coarse ✩ Patrick H. O’Callaghan 1 School of Economics, University of Queensland Abstract In economics we often take as primitive a collection of preference orderings (on actions or alternatives) indexed by a parameter. Moreover, it is often useful to represent such preferences with a collection of utility functions that is continuous in the parameter. Existing representation theorems assume that the topology on the parameter space is metrizable. This excludes settings where the topology is coarse e.g. the weak ˚ topology on a set of probability measures or the product topology on many function spaces. Yet such spaces are often normal (disjoint closed sets can be separated). We introduce an axiom on preferences for parametric continuity when actions are countable and the parameter space is normal. Utility is jointly continuous on actions ˆ parameters when actions have the discrete topology. Keywords: parametric continuity, preferences, utility representation ✩ I thank the anonymous referees, Itzhak Gilboa, Sander Heinsalu, Atsushi Kajii, Ali Khan, Jeff Kline, Andrew McLennan, Aliandra Nasif, Wojciech Olszewski, John Quiggin, Maxwell Stinchcombe and Rabee Tourky for taking the time to read and provide feedback on earlier versions of this paper. I further thank Maxwell Stinchcombe for numerous conversations that helped to enrich my understanding of the subject matter of this paper. 1 Email: p.ocallaghan@uq.edu.au, Orcid Id: 0000-0003-0606-5465. Preprint submitted to Elsevier April 1, 2019