There does not appear to be any such thing as a dominant majority vote.
I want to note that this is also know in Cooperative Game Theory as an “empty core”. (In Social Choice Theory it’s studied under “majority cycling”.) See http://www.research.rmutp.ac.th/research/Game%20Theory%20and%20Economic%20Analysis.pdf#page=85 for a good explanation of how Cooperative Game Theory views the problem. Unfortunately it doesn’t look like anyone has a really good solution.
I want to note that this is also know in Cooperative Game Theory as an “empty core”. (In Social Choice Theory it’s studied under “majority cycling”.) See http://www.research.rmutp.ac.th/research/Game%20Theory%20and%20Economic%20Analysis.pdf#page=85 for a good explanation of how Cooperative Game Theory views the problem. Unfortunately it doesn’t look like anyone has a really good solution.