I think you misunderstood the concept of "minority government" (known in the UK as "hung parliament". In our system of "responsible government" (oxymoron), the executive branch requires the support of the House of Commons to remain in power. If the executive loses a vote, the entire cabinet must resign. A minority government means that the governing party holds less than half the seats in the house and can only remain in power with the support of members of other parties.
bttt!