Simply Put

Mixed Member Proportional example: Prince Edward Island, Canada

MMP is a proportional system, which means that the proportion of votes a party gets will largely reflect the number of seats it has in parliament.

Each voter gets two votes.

The first vote is for the political party the voter chooses. This is called the party vote and largely decides the total number of seats each political party gets in Parliament.

The second vote is to choose the MP the voter wants to represent the constituency they live in. This is called the constituency vote. The candidate who gets the most votes wins. They do not have to get more than half the votes.

Under usual MMP rules, a political party that wins at least one constituency seat OR 5% of the party vote gets a share of the seats in Parliament that is about the same as its share of the party vote.

For example, if a party gets 30% of the party vote in a Canadian general election it will get 101 MPs in Parliament (being 30% of 338 seats). So if that party wins 80 constituency seats it will have 21 List MPs in addition to its 80 constituency MPs. Likewise, if a party wins 20% of the vote it will get 68 MPs in parliament. If it only won 40 constituency seats it would have 28 list MPs in addition to its 40 constituency MPs.

it is easy to see from this very simple example that mixed member proportional elections pretty well guarantee that the number of seats that are party ends up with in Parliament will closely reflect (allowing for rounding errors). The percentage of vote received by that party in the general election.

Furthermore, mixed member proportional systems allow for the continuation of voters choice representation within the constituency.

The only variable is contained in the selection for the 'list' members of Parliament. That can be decided in a variety of ways. One of the most common being selecting the 'list' members from MPs who received the highest percentage of votes but were not elected in their constituencies. Although it is possible to leave the decision to the parties themselves, this would not result in a system with universality across party lines.

Coalitions or agreements between political parties are usually needed before Governments can be formed. This aspect of proportional representation election systems is widely criticized for the fact that it seldom produces a majority government. This is due to the fact that a 50+ percentage of the popular vote is required to produce a majority government in a proportional representation system and, as we can see by reviewing past Canadian elections, this is very seldom the case. In the 42 elections since Confederation, only 12 have been won by a 'true majority' of more than 50%. None since 1958. On 3 occasions the winning party had exactly 50% of the popular vote, for example, in 1984, the Progressive Conservatives won 74% of the seats with 50% of the popular vote.

Election years when a 'true majority' was obtained by the party who formed the government were 1958, 1948, 1940, 1917, 1911, 1908, 1904, 1900, 1891, 1887, 1882, 1878 and 1874. The lowest percentage of popular vote that produced an absolute majority was 38.5% in 1997 for the Liberals. The next lowest was 39.5 for the Liberals in 2015, followed closely by the Conservatives with 39.6% in 2011. In 29 of the 42 elections a majority government was elected. Since a majority government is in fact an 'elected dictatorship', in 29 of the past 42 elections Canada has had an 'elected dictatorship that was elected by fewer than 50% of the voters (Percentage of the popular vote was not available for 1940).