Petition Having proportional representation with a PM (with powers of veto) voted in by electors in an election is more democratic

Proportional representation tended to give rise to a hung parliament, with minority party's interest being the powerbroker. Is ‘first past the post system' democratic? Perhaps a solution is to have proportional representation but also having a PM voted for by electors during a general election, as in the US presidential election. Such an elected PM should then be able to cast his/her vote in the House of Commons not as an ordinary MP, but as an elected PM with greater voting powers (say 30% of total potential votes of House of Commons) or powers of veto. In addition, the elected PM should be duty bound to appoint his Cabinet Ministers that reflect the proportion of the ratio of each political party's actual votes received in a general election. In short, a PM should be voted into power in a general election, not by deals done (by interest groups, mutual agreements amongst fellow MPs or hung parliaments) in the House of Commons.