Proportional representation: the Hare system, the list system, merits, demerits and practice today

1. Meaning

Proportional representation (PR) is an electoral system in which each party or body of opinion wins seats in proportion to the votes it receives. If a party wins 30 per cent of the votes, it should win about 30 per cent of the seats. It is the fullest method of minority representation. It requires multi-member constituencies. There are two main forms: the single transferable vote (the Hare system), which is candidate-based, and the list system, which is party-based.

2. The Hare system (single transferable vote)

The system was worked out by Thomas Hare, an English barrister, in The Machinery of Representation (1857) and A Treatise on the Election of Representatives, Parliamentary and Municipal (1859). Carl Andræ had devised a similar method in Denmark in 1855. J.S. Mill championed Hare's scheme in Considerations on Representative Government, calling it among the very greatest improvements yet made in the theory and practice of government. Hare originally proposed the whole of Britain as one constituency; in practice STV uses constituencies of three to seven or so members.

The steps:

1. Multi-member constituency.
2. Preferential voting. Each voter has a single vote but marks preferences (1, 2, 3 …) against as many candidates as he likes.
3. The quota. A candidate who reaches the quota is elected. Hare's own quota was votes divided by seats. The quota now used is the Droop quota: (valid votes ÷ (seats + 1)) + 1, ignoring fractions. It is the smallest number that only as many candidates as there are seats can reach.
4. First count. First preferences are counted; anyone reaching the quota is elected.
5. Transfer of surplus. Votes an elected candidate receives above the quota are transferred to the remaining candidates according to the next preferences on that candidate's ballots, in proportion.
6. Elimination. If seats remain and no one has the quota, the lowest candidate is eliminated and his ballots are transferred by next preferences.
7. Transfers continue until all seats are filled.

3. A worked count

Problem. Three seats. Five candidates A, B, C, D, E. Valid votes 1,000. First preferences: A 502, B 150, C 140, D 120, E 88. Of A's 502 ballots, the second preferences are B 252, C 150, D 100.

Quota = (1,000 ÷ (3 + 1)) + 1 = 250 + 1 = 251.

• Count 1. A has 502, above the quota of 251: elected, with a surplus of 502 − 251 = 251.
• Count 2. The surplus of 251 is exactly half of A's 502 ballots, so each next preference is transferred at half value: B gets 252 ÷ 2 = 126, C gets 150 ÷ 2 = 75, D gets 100 ÷ 2 = 50 (126 + 75 + 50 = 251). B now has 150 + 126 = 276: elected, surplus 25. C has 215, D 170.
• Count 3. B's surplus of 25 goes by the next preferences on the transferred ballots, say 15 to C and 10 to D. C 230, D 180. No one else reaches 251.
• Count 4. E, lowest with 88, is eliminated. E's next preferences: C 30, D 50, and 8 ballots show no further preference (exhausted). C 260, D 230. C reaches the quota and is elected.

Result: A, B and C are elected. Check: every column totals 1,000. Note that C, third on first preferences, wins because more of the transferred votes favoured C than D. With three seats the Droop quota means a group of voters slightly over a quarter of the total can be sure of electing one member.

4. The list system

Each party puts up a list of candidates for a large multi-member constituency (in the Netherlands and Israel, the whole country). The voter votes for a party list. Seats are allotted to each party in proportion to its votes, and filled from its list. In a closed list the party fixes the order; in an open list voters can change it by preference votes.

Worked allocation. Five seats; votes: Party X 47,000, Party Y 31,000, Party Z 12,000; total 90,000.

Largest remainder (Hare quota): quota = 90,000 ÷ 5 = 18,000. X has 2 full quotas (remainder 11,000), Y has 1 (remainder 13,000), Z has 0 (remainder 12,000). Three seats are filled; the two left go to the largest remainders, Y (13,000) and Z (12,000). Result: X 2, Y 2, Z 1.

d'Hondt (highest average): each party's votes are divided by 1, 2, 3 … and the seats go to the five highest quotients.

The five highest are 47,000, 31,000, 23,500, 15,667 and 15,500. Result: X 3, Y 2, Z 0. The same votes give a different result: d'Hondt favours larger parties, the largest remainder method helps smaller ones.

Merits of the list system: simple for the voter; closely proportional; strengthens parties and their programmes. Demerits: the voter chooses a party, not a person; party bosses control the lists (in a closed list); many small parties; no link between member and locality.

5. Merits of proportional representation

1. Justice to all parties and minorities: seats match votes, so the legislature is a mirror of the nation.
2. No wasted votes: under STV a vote not needed by one candidate passes to the next.
3. Prevents the manufactured majority, where a party with under 40 per cent of the votes wins a majority of seats.
4. Choice for the voter (STV) among candidates of the same party.
5. Discourages gerrymandering, since constituencies are large.
6. Encourages abler and independent candidates, and the representation of women and minorities on lists.

6. Demerits

1. Complexity: STV counting is hard for voters to follow and needs literate electorates and trained officials.
2. Multiplicity of parties and unstable coalitions: Weimar Germany, Italy after 1946 and Israel are cited.
3. Large constituencies weaken the tie between member and voters.
4. Power of party machines, especially under closed lists.
5. Encourages sectional and communal parties, since a small group can win seats.
6. By-elections are difficult; a single vacancy cannot be filled proportionally.

7. The system in practice today

• STV: the Irish Dáil (since 1921), Malta, the Australian Senate and Tasmania, the Northern Ireland Assembly, and Scottish local elections.
• List PR: the Netherlands, Israel, Belgium, Spain, Sweden and most of continental Europe; also the European Parliament elections in most member states.
• Mixed systems combine single-member seats with list seats to restore proportionality: Germany and New Zealand (mixed-member proportional, adopted after a 1993 referendum).
• India uses STV only for indirect elections: the President (Article 55(3)), the Vice-President (Article 66(1)), members of the Rajya Sabha (Article 80(4)) and of Legislative Councils (Article 171(4)). In the Rajya Sabha count each first preference is valued at 100 so that transfers can be made in whole numbers, and the quota is (total value ÷ (seats + 1)) + 1. Direct elections to the Lok Sabha and Assemblies use first-past-the-post, which the Constituent Assembly preferred for its simplicity and for giving stable majorities to a largely illiterate electorate.

How this is examined

For “proportional representation system of Thomas Hare”: meaning of PR, Hare and Mill by name, the steps with the Droop quota, a short worked count, and merits and demerits. For the list system: closed and open lists, a d'Hondt or largest-remainder allocation, and merits and demerits. Always end with where each system is used, including the Indian indirect elections.