Give the chooser a real but bounded turn
Invite everyone to name firm limits before the chooser presents a title. Those limits might concern length, access features, cost or particular content. Ordinary preferences do not all need to become vetoes. The person with the turn can choose within the agreed limits without asking everyone to rank twenty titles.
Agree on what happens to objections
If tonight's chooser likes suspense and someone has ruled out horror, ask them for a mystery or another suspenseful option that respects the limit. If somebody merely preferred a comedy, record that preference for their own turn. Never require a viewer to explain a private reason for a clear refusal.
Track turns without keeping score of taste
Write down who chose last time and the next person in line. If a chooser misses the evening, move their turn instead of picking on their behalf. If the proposed film crosses a limit, ask them for a second choice.
If the same person frequently declines their turn, ask whether they want to participate as a viewer only or would prefer to pick with someone else. Write down the next chooser and the evening, not a list of who “owes” the group a film. Rotation should make starting the evening easier.