Socially Assistive Robots (SARs) are becoming very popular every day because of their effectiveness in handling social situations. However, social robots are perceived as intelligent, and thus their decision-making process might have a significant effect on how they are perceived and how effective they are. In this paper, we present the findings from a participatory design study consisting of 5 design workshops with 30 participants, focusing on several decision-making scenarios of SARs in the wild. Through the findings of the PD study, we have discussed 5 directions that could aid the design of decision-making systems of SARs in the wild.