Theories of choice may be regarded as having two principal features: a representation of indecision and a decision rule stating the conditions which must be satisfied for a choice to occur. Three ways of representing indecision are described and evaluated. In terms of one of these representations, several theoretical models of choice are developed by considering the consequences of two kinds of decision rule. A way of determining the properties of the models is described, but is not used in more than an illustrative fashion. A detailed examination of these properties will be given elsewhere, when comparisons will be made with empirical data.