Is the French system a good example of a multi-party system? It currently seems to be struggling with handling three parties and it doesn't guarantee proportional representation. The presidential election is a winner-takes-all system and in the election for the Assemblée Nationale each constituency is a winner-takes-all.
I would say yes in the sense a new party can (and did) emerge and rise to power when there is demand. Even before that you had some healthy rise and fall of political parties and political alternance beyond just two main contenders.
> It currently seems to be struggling with handling three parties
There are like 6 parties with more than 10% of seats, the current government is a coalition of five parties (from two main "families") and no shutdowns or hung parliament.
> Doesn't guarantee proportional representation
That however is true, and by design. This is a property the french voting system share with eg: ranked choice and other systems that aim at resolving the compromise as part of the election rather than afterwards.
I don't mean to say that the french voting system is perfect (I quite like ranked choice), simply that it is a functioning one with interesting properties.
The left-wing coalition was about 9~10 parties, Macron's coalition was around 6~7 right leaning/centrist parties, and Le Pen's block joined by one or two smaller far right/conservative parties.
They are just spoilers; you don't see the Libertarians or Greens saying "you know what, forget the presidency, obviously we aren't going to win--let's field candidates for like mayor, city council, DA, state legislature, etc. in really swingy/purple districts and show people what we can do"
If I were to guess why third parties don't make much of a dint it'll be because successful movements gradually get incorporated into one party or the other via the primary system. Once a party has drained away the core appeal the third party or outside movement will flounder.
WTF? I didn't know UK had such a weird voting system
Here's an election in the SDP split largely from Labour; the result was ultimately the Conservatives gaining 10% more seats when their vote share went down https://en.wikipedia.org/wiki/1983_United_Kingdom_general_el...
Both of the last two elections were heavily impacted by Nigel Farage's parties in different ways; gaining very few seats but acting massively to the detriment of Labour in 2019 and even more to the Conservatives in 2024
for example the UK's most recent election had the following
- one party has 410/650 of the seats in government with a third of the popular vote - they gained 211 seats from the previous election off the back of a 1.5% swing in the popular vote - another party has 65/650 of seats with 12% of the vote, another has 5/650 seats with 14.5% of the vote