Arturo O. answered 08/10/17
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I can think of one advantage: There is no divided government. In a parliamentary democracy, the people elect the members of the parliament (somewhat equivalent to our US Congress). Whichever political party has a majority in the parliament gets to select a prime minister, somewhat equivalent to our President. Then the chief executive of the government belongs to the same party as the majority in the parliament, so the government is not divided along party lines. If the majority in parliament loses confidence in the prime minister, the majority can hold a vote of "no confidence" and declare a new election.
While there are some advantages to the parliamentary system, there are some problems too. There can be frequent "no confidence" votes during times of "ups and downs" followed by frequent repeat of elections, leading to political instability. This sort of thing has especially plagued Italy in decades past.