Some western democracies are monarchies (UK, Denmark, Spain...).
What are the advantages that this system gives to the people, when compared with a presidential system?
I want to stress that I'm asking for advantages for the people. I can easily see advantages for the powerful, and disadvantages in a democratic sense. So, I'm asking what reasons the people could have to vote for a monarchy if the possibility arose.
The arguments I found in favour of constitutional monarchy (some of them could be biased):
Whenever you agree or not with those arguments is another debate.
What are the advantages for the people of a constitutional monarchy?
The advantage to the people in countries with a tradition of constitutional monarchy is that most of them like having it.
If you wish you can analyse this answer into different sorts of liking, some of them intellectually "respectable" like a link to the past or having a head of state likely to be perceived as neutral, some of them less respectable such as pretty costumes and ceremonies, or the appeal of celebrity-watching.
However it is important to realise that "most people like it" is sufficient in itself. Giving people the government they wish to have (as far as possible in a world where not all agree) is the rock-bottom justification for democracy after all.
If people strongly don't like having a monarchy then it's up to them to vote into power a political party that has either abolition of the monarchy or a referendum on the subject in its manifesto. Until then, the status quo is justified.
In the countries, you listed, the king or queen has really become a small detail of the institutional mechanics. You could try to make some sort of argument about stability and the symbolic value of the monarchy but it's all very weak. At heart, those are simply parliamentary democracies with all the associated characteristics, positive and negative and no real “advantages for the powerful”.
If you look at Western European countries (with a few exceptions like France or Switzerland), there are roughly speaking two variants: They have either a monarch or a weak president with a minor role during government transitions. Either way, it's really difficult to see how monarchies provide any advantages or disadvantages for anybody, perhaps beyond the fact that the public usually bears the royals' living expenses.
If you would get rid of the monarch, you could simply find a way to elect a president indirectly like in Italy or Germany and keep the political system essentially intact. What could make a difference is moving towards a system like those of France or Poland, but those two countries are republics just like Italy and Germany.
Interestingly, even directly-elected presidents with extensive powers (as in Portugal) do not always take a major role in the political process. As an another example, you might consider the third French Republic (1870-1940). The regime had a powerful president, specifically so that he could be replaced at any time with a king to recreate a monarchy (a ‘real’ one, with a strong king, not a parliamentary democracy with a ceremonial monarch). Yet, the king never came and almost all the elected presidents abstained from using their powers so that France was effectively a parliamentary democracy for all this time.
Another advantage of a constitutional monarchy is that it separates the ceremonial head of state from the actual head of government. Contrast that with the United States, where the president is both. The president has to spend some amount of time hosting parties and performing other ceremonial duties (e.g. pardoning turkeys).
A monarch also has more time to prepare. The immediate heir probably knew since birth. Even alternative heirs knew of the possibility since birth. A prime minister or president is chosen much later and can't be sure. Even sure choices like Hillary Clinton can fail (twice). Was Barack Obama planning on the presidency in 2004? He didn't prepare as if he were (governor is a better stepping stone to the presidency than the Senate).
Note: I'm not arguing that time to prepare outweighs democratic advantages. I'm just pointing out that it is an advantage of hereditary monarchy.
As Aristotle said in Politics, there are three general types of rule, each with a positive potential and negative potential: Kingship-Tyrant (rule by one), Aristocracy-Oligarchy (rule by a small group), Polity-Democracy (rule by the people) (those on the left are forms of authority that may obtain the best for a particular society, those on the right are how similar forms of authority could be harmful for a society). Thus, a good King can act quickly and benevolently to his people but both a Tyrant or bad democracy can repress its people through discrimination and violence.
In the modern sense of western democracies that have royal families, these rulers typically do not govern. Instead they offer tradition and cultural values that 'the people' may morally appreciate.
If we are going to cite ancient philosophy, it's worth mentioning Plato's Republic and the 5 forms of government. Through careful argument he makes a pretty good case for an aristocracy: Plato's five regimes
Read the actual book since it relates the individual characteristic to a collective state. Its also very important to distinguish between a constitutional monarchy and a absolute monarchy, the former being a sophistication of the latter, yielding a better form of government.
The advantages of having a monarch in the traditional sense, is that he or she is incorruptible; because he or she is born with the power, and therefore does not need to grease the palms of people to gain more. Even in some kind of meritocracy, individuals will have to grease the palms of the corrupt to gain power and this is clearly articulated in The Republic.
The benefits of a constitutional monarchy is that the monarch compliments the elected head of government. One is a safeguard to the integrity of the other.
Now for some facts and empirical evidence since this will shed more light on the case for a constitutional monarchy. Take a look at the top 10 most prosperous countries in the world. 8 out of the top 10 countries are constitutional monarchy.
Secondly, give me an example of any country that has replaced a constitutional monarchy with another form of government, and come off better. Doesn't exist. Even abolishing absolute monarchies has caused more problems than it has solved e.g Afghanistan, Libya, Ethiopia, Iran. All had more prosperous, cultured and progressive societies before the monarchy was killed. Russia, arguably another example, and England during Oliver Cromwell became worse off, the latter form of government resulting in the death of millions of Irish. So IMHO it's about progressing government that is proven, not revolution or change for the sake of change.
