Simplifying Complexity, One Answer at a Time!
Rules
Not sure how you get cartel from government coalitions.
A country will have a requirement that a party need to have X number of seats to be the leading party. If you have 3 parties and none of them individually meet the requirements then 2 of them may work together to become big enough to get the required number of seats.
X is usually “more than half”
Same thing happens in the US. To win, you need more than half the votes. We just have various factions that divide into 2 parties, instead of multiple parties dividing into 2 factions.
Not always more then half, there have been instances where a government in Australia has formed with less then half of the seats. I believe those are called minority governments
Canadian here. A minority gov is one which has less than X seats (where X is 50% in Canada and I believe Australia too), and usually that requires a coalition. "Forming government" in a parliamentary system like these basically means "has a good chance of passing meaningful legislation." Since the leading party can't do so alone, they form an agreement with another party (or multiple) to help them reach that criteria.
It is entirely possible for the party with the most seats to also not form government, if they're far enough below 50% and can secure no agreement with another party to push them across the line. In these situations, another general election would soon follow.
That’s when they need a coalition
It isn't like a cartel. It is a continuation of the freedom of association.
In legislatures, the legislative body generally needs a majority to get anything done. To help with that process, parties will come together in an agreement on what will be done. The agreement can be as minor as supplying votes for certain policies to splitting up which government agencies are run by the different parties.
And Switzerland absolutely has a coalition government.
As far Switzerland has no coalition. Every subject is discussed directly in Parliament, while in opposite in Germany a lot of subjects are content of a coalition agreement. They subscribe at the beginning.
That's more a tradition within the Swiss government in how it conducts itself compared to other countries like Germany. Plenty of coalitions in other governments will allow for votes on issues where the majority government doesn't have a stance.
Also, Swiss use of direct democracy is different than other European democracies, some of which don't have direct plebiscites.
I'm an American so take what I say with a hefty grain of salt but in multi-party systems you have a wider array of political parties to align with that are typically distinct on various issues that sometimes overlap with other parties. Coalitions allow for flexibility in party choice despite some parties having policy preference overlaps and avoid devolving into a 2 party system.
Let's borrow the major alignments of the political compass just for an example and assume that the parties ideally represent the stereotypes of the political compass, let's say we have the LibLeft party, and AuthRight party each making up about 25% of the legislative body after elections (they almost never work together), and the AuthLeft and LibRight party making up about 20% each (they also almost never work together) and a true centrist party with 10% (they'll work with anyone provided its not too extreme). In order to pass a bill, you need to collect an arbitrary majority of votes to pass a piece of legislation, let's call it at 55% for our fictional parliamentary congress.
None of the parties alone have enough votes to pass legislation, they need to work with other parties to get legislation passed. So someone in LibRight (20%) has a bill they want passed they need help from other parties to make that happen. Rather than just guess what other parties want in a bill, the LibRight rep, might meet up with a Centrist (10%), a LibLeft (25%) and an AuthRight (25%l rep to try and write a bill that will satisfy each party, now you've formed a coalition. You work together to draft a bill that will include something each party wants. It won't be easy because LibLeft and AuthRight rarely align on policy. Then you bring your bill to the floor to vote and if you crafted it well enough the combined votes of LibRight, LibLeft, AuthRight and Centrists will be enough to cross that 55% requirement to pass legislation by a wide margin, assuming the entire party will vote as a united bloc (if they don't vote as a united bloc then the margin will be much closer but still likely reaching that 55%).