Proportional aggregation of preferences for sequential decision making

In various decision making settings, from recommendation systems to hiring processes, often a sequence of decisions are made by a group. A naive approach to decision-making in such scenarios is to select the alternative with the highest supporters in each round. However, this method can lead to unrepresentative outcomes, where a majority dictates all decisions, potentially disincentivizing participation from minority groups. Consider the following example where a group of friends (voters) want to hang out together weekly. They have diverse choices for the activities (alternatives) they approve of every week (round), but only one activity can be chosen as the decision (i.e., the activity which the whole group ends up pursuing even if some don't like it).