Modern robots make decisions in many ways, but rely on their designers to choose which strategies to employ and when. Adopting a perspective of bounded rationality from the cognitive sciences, we develop a definition of decision making for constructivist robots to formulate their own decisions based on their mission-specific values. Our model, extending Kirsch (2019), defines decision making with an iterative algorithm that captures a broad range of possible strategies and problem domains. Briefly, a set of decision alternatives are first assessed by a set of relevant cues. These assessments are then aggregated into a multi-dimensional evaluation of each alternative from which a preference ordering is created. Finally, based on the problem specification, a set of chosen alternatives is either accepted by a stopping rule or a new iteration is started, updating the sets of alternatives and cues. If no alternatives or cues remain after iterating, then the decision fails. Given this algorithm, we implement a toolbox of decision-making components as modules in a cognitive robot architecture and demonstrate a method of assembling them into complete decision strategies, represented as behavior trees, using an automated theorem prover. For proof of concept, we simulate three example strategies used by a domestic robot performing a search and retrieval task. We discuss new insights into designing and selecting decision-making strategies and make recommendations on how our proof of concept can be improved.