List system

The List system is an electoral method for allocating seats to parties. Its main features are proportionality between parties, simplicity, lack of geographical links to MPs. no voter influence over which Politicians will represent a party and and the fostering of very small political parties with highly centralised party machines.

Voter experience
The voter has a ballot paper with a list of Political parties and they cast one vote for whichever party they choose to support. Few votes are wasted as the vast majority of votes are used to elect politicians in according to the voters preferences between parties.

Gender Balance
In many countries radical and progressive parties will zip their lists - alternating between male and female candidates, and even Conservative parties are shamed into fielding women. Making the List system one of if not the best system for getting a gender balance amongst MPs, and it is the system used in many of the countries with the highest proportions of female politicians.

Candidate selection and independence of MPs
Centralists and party machine hacks often like this system as it gives control of the politicians to the party machine. If a Politician has occasionally strayed and voted the wrong way the mere threat of being dropped down the list may get them in line, or they will be quietly dropped. In this system there are safe seats for parties, but not for Politicians. If people vote by ideology not personality or other qualities then this may seem the fairest system.

Liberals and others who value independent thought among politicians are uncomfortable with this aspect of the system. It can be subverted by holding member ballots to elect candidates to the party list, as is done by the Liberal Democrats in the UK.

Some centre right parties favour national list systems because they benefit from differential turnout. I.E. If Middle class right wing voters are more likely to actually vote, then in a national list system gives them an advantage over parties representing working class electorates with lower turnouts as the list system allocates seats entirely on the basis of votes cast and makes no concessions to areas with relatively low turnouts.

Variants
While in principle this is as simple as "In a Parliament of 100 MPs you get 1 MP for every one percent of the national vote". In practice there are various ways to decide whether that last seat goes as the second seat to a party with 1.3% of the vote, the only seat for a party with 0.3% of the vote or the 11th seat for a party with 10.3% of the votes.

Regional Lists
The Regional list system divides the country into different regions and holds a separate list election in each region. This has the effect of squeezing out smaller parties whose vote is widely spread. For example the UK uses a regional list system to elect its members of the European Parliament for England, Scotland and Wales. But it does so with a separate list election in each nation or English region. Little more than 1% of the vote evenly spread across the UK would have elected a member of the European Parliament under the list system, but under the Regional list system you need over 10% of the vote in even the largest region.

It also compensates somewhat for differential class turnout, as a working class region with a relatively low turnout will still elect a number of politicians based on its electorate, not its turnout.

Who uses it?
This is a widely used system but most notoriously used in some of the most diverse legislatures, Israel, the European Parliament and it used to be used in Italy.