@Lily,
This happens all the time in the U.S. Senate, and it is called a filabuster.
Usually what happens is that people get together and just start talking about it, until enough people get tired or leave, so that whoever is left makes a decision.
Or ...
They start fighting about it, until there are enough casualties to allow for either an agreement or someone taking control.
Human nature is very flexible and figures out how to resolve all problems and paradoxes.
Rich