Floor crossing is bad because MPs are whipped. If it was not for that detail, what parties you belong to would be as politically significant as which libraries you belonged to.

"Mandate" is not a real concept in our system of government. It is merely a convention of our political culture. A person who is elected has the power. They can use that power however their conscience tells them. That is the whole basis of elected political office. Parties apply coercive pressure to people in office and influence them, but that isn't something to be encouraged. A person should ALWAYS be able to leave their party for ANY reason, without having any effect on their elected office, because otherwise it's the party that we're electing, and parties are not human beings that can hold offices with a conscience.