List based proportional representation is the system used by nearly all developed nations in the world, except the Anglo-Saxon nations.
There are variations and hybridised versions that meld with first-past-the-post while keeping the proportionality, but basically modern democracies have list PR.
The most equal, prosperous, democratic, environmentally friendly, politically engaged and least corrupt nations use List PR. The disadvantage is that there is less geographic link between elected representatives and where some toff has drawn some lines on a map. This also means that boundary changes have little effect on the result under list PR systems. The result cannot be gerrymandered like it is with FPTP or STV.
List PR elected parliaments contain more women, minorities and lower socio-economic groups, much more than FPTP. Even after the advent of all women shortlists, only 20% of Westminster MPs are women. In comparison, both the Scottish Parliament and the Welsh Assembly elected by List PR hybrid systems have around 50% female representation.
The so called disadvantages of List PR pale into insignificance when you look at the superior governance countries with List PR enjoy. The higher quality, better funded and better managed public services, the responsiveness and diverse representation within parliament.
Like all PR systems, List PR is likely to result in coalition government not single party rule. Contrary to Anglo-Saxon myth, this actually allows for more decisiveness demonstrated by the speed with which infrastructure projects are agreed and difficult long-term issues like keeping on top of government debt are tackled.
The UK's experience of List PR is the closed list system used for elections of our MEPS to the European Paliament. There are two criticisms that are unfair here when comparing the election of MEPs to the election of MPs to Westminster. For a start there are only 78 MEPs covering the UK compared to 650 MPs so obviously MEPs will have to cover more voters than MPs even before multi-member constituencies. Tory MPs sneer about people not being able to name two of their MEPs, but ask people to name their MP and one of their 3 local councillors and most voters will draw a blank. Also a surprising amount of MEPs are well known. Think of Nigel Farage of UKIP and Caroline Lucas of the Greens in my region - the South East (pre-May when she became an MP).
The other criticism of list PR is that only the party has a say over their elected candidate because they order the list. This is of course true for the closed list system used for the Euro parliament, but very much not true for the open list systems that are in use throughout a lot of the developed world where the voter very much chooses the candidate and not the party. There are also two further rather subtle points that need to be made.
One, because list PR unlike FPTP, gives people an effective choice of much more than just 2 parties, parties have to more democratic, open and transparent about how they choose their canddidates, so even under closed list PR, candidates tend to be more responsive to the electorate and democratically chosen. If parties are not democratic under list PR, it is easy for voters to go elsewhere and still find their vote effects the result.
Supporters of FPTP should not be smug about closed lists and remember that 80% of MPs under FPTP are chosen in safe seats by around 100 party members in a room with little chance of defeat in the general election because their party is so entrenched in that area. There is nothing more closed and chosen by 'the party' than that.
But as already said List PR does not have to be closed list. One of the easiest open list systems is the one used in Sweden, where voters first pick up the ballot paper from the party they support and then mark an X next to the party candidates they want. This way they choose both the party and candidate with just one vote. This is as easy and quick as FPTP voting in terms of both the count and for the voter, but gives completely fair and proportional results. There is none of the complexity of the vote that STV invokes.
I think you might be able to guess which electoral system I think is best after reading this.