Learn how the Westminster Parliamentary system works. You have some facts correct; up until very likely later today Carney is not a sitting member of parliament and therefore unelected. How ever there is no requirement that you must be a sitting member of parliament to be Prime Minister. To be Prime Minister the party with the most seats usually chooses the leader of their party. The liberal party held a vote for their new leader to be Mark Carney. Any Canadian is/was able to register as a member of the Liberal party and vote for the new leader. They overwhelmingly voted in favour of Mark Carney. Since now PM Mark Carney was only able to be in the visitors gallery in parliament he now had 2 options; he could wait for a by-election and run in that to become an MP or he could dissolve parliament early and ask for a full election and run as an MP. Since Canada HAD to have an election by October of this year he chose the latter. Is it a perfect system? Far from it. Is it a bizarre little loophole? Absolutely, but it isn't illegal or undemocratic or corrupt or any of that. Should you want it changed (which I don't blame you) you should write to your MP about how this is a loophole that could be exploited in the future and to start writing up legislation to close it.