I was responding to your comment that if the party wins the election, then they elect their leader. I still don’t understand what you’re suggesting. The parties elect their leaders well in advance of the general election, and if they win, there’s no additional leadership election; the leader who led them to government status is automatically their leader. There’s no subsequent party election.
And now I’m going to disagree with you, too. 
I must be in a disagreeable mood tonight. 
Yes, the Prime Minister is appointed by someone - the GovGen. That is a legal appointment, without which the PM has no authority. Yes, the GovGen’s power to choose is normally completely circumscribed by the party standings, but there is still a formal appointment. (He’s elected party leader by his party, but that’s separate from his position as PM.)
And yes, the GovGen has the legal authority to make appointments, such as judges, and that’s derived directly from the Constitution in some cases, from the royal prerogative in others, and from statutes in still others. Yes, it’s always done on the advice of the PM, but the PM does not have legal authority appoint. The piece of paper appointing a judge or ambassador or statutory officers needs to be signed by the GovGen, or else there is no appointment at law. The Gov Gen is the constitutional officer, appointed by the monarch and with status under the Constitution and statutes. The PM has no constitutional or statutory standing or powers.
Bagehot covedred it all in his distinction between the “dignified” parts of the Constitution, and the “efficient” parts.
And I’m going to disagree right back atcha. This strikes me as a semantic quibble rather than a substantive point, similar to saying that Parliament has no real power to enact laws, because they do not become laws until the GG gives royal assent (“GG” henceforth meaning the Governor General in Canada, or the Queen in the UK). But in reality it’s Parliament that holds lawmaking power, and this is why we refer to our country both as a democracy and as a constitutional monarchy. The GG cannot arbitrarily appoint his favorite son-in-law as PM; there are no Jared Kushners in Canadian politics. Yes, the GG invites the appropriate party leader to a formal meeting in which he is invited to form a government, and when he walks away from that meeting he has, in some technical sense, been “appointed” to the role of PM, but it was an outcome that was inevitable and basically a formality. There are very rare exceptions like the one I mentioned involving attempted coalitions, but that doesn’t change the main point.
I’m trying to make a pragmatic point rather than semantic nitpickery. It’s true, as a matter of academic interest, that the GG (the monarchy) historically holds unspecified reserve powers, but if those powers were arbitrarily exercised without strong objective non-partisan justification and long-standing constitutional conventions, that would simply be the end of constitutional monarchy in Canada or the end of the monarchy in the UK. But that’s not in the cards for the foreseeable future and I think the Westminster system with multiple parties works very well. For example, an orange doofus like Trump would have been gone within the first two weeks.
Too Late!
Like I said “In theory”. I didnt say “in* reality*”.
Yes, that is the way it occurred with Trudeau, and it is the most common way (but by no means the only way*.) I was simplifying it. In a parliamentary form of government, the people do not vote for the PM (except for as he is a MP, of course) . His party does, or a coalition.
It was short, one line answer to **installLSC **
I quickly googled “canadian campaign signs” and I noticed almost all the signs were local candidates, not the national party leaders. Do Trudeau, Scheer, and the others get their own signs? And if they don’t, why?
*Sir John Joseph Caldwell Abbott and Sir Mackenzie Bowell for example. John turners case was also unusual.