Robotic collectives are large groups (at least 50) of locally sensing and communicating robots that encompass characteristics of swarms and colonies, whose emergent behaviors accomplish complex tasks. Future human-collective teams will extend the ability of operators to monitor, respond, and make decisions in disaster response, search and rescue, and environmental monitoring problems. This manuscript evaluates two collective best-of-n decision models for enabling collectives to identify and choose the highest valued target from a finite set of n targets. Two challenges impede the future use of human-collective shared decisions: 1) environmental bias reduces collective decision accuracy when poorer targets are easier to evaluate than higher quality targets, and 2) little is understood about shared human-collective decision making interaction strategies. The two evaluated collective best-of-n models include an existing insect colony decision model and an extended bias-reducing model that attempts to reduce environmental bias in order to improve accuracy. Collectives using these two strategies are compared independently and as members of human-collective teams. Independently, the extended model is slower than the original model, but the extended algorithm is 57% more accurate in decisions where the optimal option is more difficult to evaluate. Human-collective teams using the bias-reducing model require less operator influence and achieve 25% higher accuracy with difficult decisions, than the human-collective teams using the original model. Further, a novel human-collective interaction strategy enables operators to adjust collective autonomy while making multiple simultaneous decisions.