There are a number of different political voting systems, but too often those elected do not actually reflect the views of the population who voted - and who consequently feel they have no real representation. It looks as though it is the proportional voting systems that give a voice to the widest number of views, though even here the specific version used is important.
Mixed-Member Proportional Voting (MMP). In this electoral system, voters have two votes: one to decide the representative for their single seat constituency and the second for a political party. Seats in the legislature are filled firstly by successful constituency candidates (elected using first-past-the-post or another plurality/majoritarian system) and secondly by party candidates based on the percentage or region-wide votes that each party received (usually drawn from published party lists). On this second vote, parties may be required to achieve a minimum number of constituency candidates, a minimum percentage of the nationwide vote, or both.
MMP is used by New Zealand among others. NZ has a single-house legislature, the House of Representatives, usually with 120 members, though the number can be more due (generally) to one or two overhang seats. The 52nd Parliament (elected 2017) had 120 seats: 71 were electorate MPs, with the remaining 49 from ranked party lists.
Overhang seats. Under MMP, a party is entitled to a number of seats based on its share of the total vote. (A) If a party's share entitles it to ten seats and its candidates win seven constituencies, it will be awarded three list seats, bringing it up to the required number. This only works if the party's seat entitlement is more than the number of constituencies it has won. (E.g. If the party is entitled to five seats but wins six constituencies, the sixth constituency seat is termed an overhang seat.) (B) Individual candidates with strong local followings. A candidate may be elected with strong support in their constituency but belong to no party, or a party with very low support overall. In the case of independent candidates, their seat is guaranteed. Some countries (including NZ) have special rules that seats won by these candidates are exempted from the proportional system altogether. Dealing with overhang seats. The are four ways to deal with overhang seats. (1) Parties keep the overhang seats but then has more than its entitlement. (2) Parties winning seats over their entitlement keep them but other parties lose some of their entitlement. (3) Parties are not allowed to keep overhang seats, which requires some method to determine which seat(s) are lost. (4) Non-overhang parties are allocated bonus seats to balance the proportional representation.
[NB. Countries vary in the number of constituency MPs that make up a legislature; the NZ Parliament has just 120, with small numbers of overhang seats. The UK using a first past the post system has 650 seats (2020).]
END
