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FPTP and Proportional Representation Class 9 Elections

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Social ScienceCBSE Class 9 · Elections

Electoral Systems Class 9: FPTP, Majority and Proportional Representation

Updated 17 October 2026 · Fact-checked

An electoral system decides how votes turn into seats. First-Past-The-Post gives the seat to the candidate with the most votes even below 50 per cent; the majority system needs more than 50 per cent and uses a second round if necessary; proportional representation shares seats in proportion to the votes each party gets. India uses FPTP for the Lok Sabha and Vidhan Sabhas and proportional representation for the Rajya Sabha, President and Vice President.

FPTP picks the top vote-getter even at 40 per cent; majority needs over 50 per cent or a second round; PR gives seats in line with votes.

Illustration drawn for QuestionBuddy.

Understand Electoral Systems: FPTP, Majority and Proportional Representation

Why elections matter. Periodic elections let citizens choose who decides on their behalf and hold them accountable. They bring four things: equality (one person, one vote), representation, accountability and legitimacy (the government's right to rule comes from the people's mandate). A government cannot extend its own term, and a contest with only one party offers no real choice.

Direct and indirect elections.

  • *Direct:* citizens vote for representatives themselves. In India this covers the Lok Sabha, Vidhan Sabhas and local bodies, every five years.
  • *Indirect:* elected representatives choose the leaders: the President, Vice President and Rajya Sabha.

Three electoral systems.
1. First-Past-The-Post (FPTP, plurality). Each voter gets one vote for a candidate. The candidate with the most votes wins, even with less than 50 per cent. NCERT's example: Haritbhumi, where A gets 40 per cent, B 35 per cent and C 25 per cent, so A forms the government.
2. Majority (two-round) system. A winner needs more than 50 per cent. If nobody gets it, the top two candidates face a second round. NCERT's example: Ratnadweep, where X gets 45 per cent, Y 40 per cent, Z 15 per cent; in round two Y wins with 55 per cent.
3. Proportional representation (PR). Voters choose a party and seats are shared in proportion to votes. NCERT's example: Swarnalok with 100 seats; M gets 40 seats, N 35, O 15 and P 10, so power is shared.

India's choices. FPTP for the Lok Sabha and Vidhan Sabhas; PR for the Rajya Sabha, President and Vice President.

Single transferable vote (STV). Voters rank candidates. Anyone who reaches the quota wins. The lowest candidate is then eliminated and those votes pass to the next preference; the process repeats until all seats are filled.
Quota = (total valid votes ÷ (seats to be filled + 1)) + 1.

Bicameral States. Six States (Andhra Pradesh, Bihar, Karnataka, Maharashtra, Telangana and Uttar Pradesh) have a Vidhan Parishad, elected by Vidhan Sabha members, local bodies, graduates and teachers using STV, plus members nominated by the Governor.

Strengths and weaknesses (for evaluation answers).

  • FPTP is simple and usually produces a clear winner for each seat, but a winner can take a seat with under 50 per cent of votes, and a party's seat share can differ greatly from its vote share.
  • The majority system gives the winner wider support but needs a second round.
  • PR mirrors vote share and shares power, but it often leads to coalition governments.

Psephology is the scientific study of elections; the word comes from the Greek *psēphos*, meaning pebble.

Electoral Systems: FPTP, Majority and Proportional Representation: key facts

Direct and indirect
Direct: Lok Sabha, Vidhan Sabha, local bodies (every 5 years) | Indirect: President, Vice President, Rajya Sabha
Chapter division.
Three systems
FPTPmost votes wins
Majoritymore than 50 per cent, else run-off of top two
PRseats in proportion to party votes
With NCERT example countries.
India's use
FPTPLok Sabha, Vidhan Sabha
PRRajya Sabha, President, Vice President
STVVidhan Parishad
As in the chapter.
STV quota
Divide total valid votes by (seats + 1) | Then add 1
Quota = [total valid votes / (seats + 1)] + 1.
PR seats
Party seats = vote share x total seats | Seats of all parties add up to the house size
Always check the total.

How to answer Electoral Systems: FPTP, Majority and Proportional Representation questions

Questions ask for definitions, comparisons of systems, seat calculations under PR, STV quota calculations and judgement on which system suits a situation.

  1. 1Name the system and state its winning rule in one line (most votes; more than 50 per cent; proportional to votes).
  2. 2For a numerical, write the formula, substitute the numbers, compute and check totals (shares add to 100 per cent; seats add to the total).
  3. 3For a comparison, use rows: winning rule, vote share needed, who forms the government, India's use.
  4. 4For evaluation, give one strength and one weakness for each system.
  5. 5Finish with where India uses the system.

Electoral Systems: FPTP, Majority and Proportional Representation in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Class monitor election

Suppose a class of 90 students elects a monitor from three candidates. P gets 34 votes, Q gets 33 votes and R gets 23 votes.

Who wins under FPTP and under the two-round majority system? What changes?

Try it first, then show the solutionSolution
  1. FPTP: P has the most votes, so P wins.
  2. Majority needs more than 50 per cent, i.e. more than 45 votes. Nobody has it.
  3. Top two, P and Q, go to a second round.

Answer: Under FPTP P wins with 34 of 90 votes (about 38 per cent). Under the two-round system nobody has more than 45 votes, so P and Q face a second round and the winner will have support from more than half of the voters.

Memory hook: FPTP asks who is ahead; majority asks who has more than half.

Seats in a house

Suppose a house of 50 seats uses proportional representation and parties U, V and W get 50 per cent, 30 per cent and 20 per cent of votes.

How many seats does each party win?

Try it first, then show the solutionSolution
  1. U: 50% of 50 = 25.
  2. V: 30% of 50 = 15.
  3. W: 20% of 50 = 10.
  4. Check: 25 + 15 + 10 = 50.

Answer: U wins 25 seats, V wins 15 and W wins 10. As no party has more than 25, U falls short of a majority of 26 seats and must find a partner to form a government.

Memory hook: Seats follow shares.

Tricks to remember Electoral Systems: FPTP, Majority and Proportional Representation

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Three systems: F-M-P

    FPTP = Fastest, Most votes; Majority = More than half; PR = Proportional share.

    Use it when: Recalling the rule of each.

  • India's split

    People's house, State house: FPTP. President, Vice President, Rajya Sabha: PR.

    Use it when: Where each system is used.

  • Quota plus one

    Divide by seats plus one, then add one.

    Use it when: STV quota.

Electoral Systems: FPTP, Majority and Proportional Representation: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Which system? · 1 mark · MCQBoard level

In which system does a candidate need more than 50 per cent of votes, failing which the top two contest again?
(a) FPTP
(b) Proportional representation
(c) Majority (two-round) system
(d) Single transferable vote

Try it first, then show the solutionSolution
  1. A run-off between the top two candidates when no one has more than half is the two-round majority system (1 mark).

Answer: (c) Majority (two-round) system

Example 2: Indirect elections (2 marks) · 2 marks · Very short answerBoard level

Differentiate between direct and indirect elections with one Indian example of each. (2 marks)

Try it first, then show the solutionSolution
  1. Direct: citizens vote for representatives themselves, for example the Lok Sabha (1 mark).
  2. Indirect: elected representatives choose leaders, for example the President (1 mark).

Answer: In a direct election citizens themselves vote for their representatives, as in elections to the Lok Sabha. In an indirect election, representatives elected by the people choose the leaders, as in the election of the President.

Example 3: FPTP and PR on the same votes (3 marks) · 3 marks · Short answerHarder board level

In a house of 100 seats, three parties get these votes in a single contest: P 42 per cent, Q 33 per cent and R 25 per cent. If this were a proportional system, how many seats would each party win? Why can the same votes give P a clear majority under FPTP in each seat but not under PR? (3 marks)

Try it first, then show the solutionSolution
  1. P: 42 per cent of 100 = 42 seats; Q: 33; R: 25 (1 mark; check: 42 + 33 + 25 = 100).
  2. Under FPTP, each seat goes to the candidate with the most votes, even below 50 per cent (1 mark).
  3. So a party that is narrowly ahead in many seats can win most of them, while PR gives seats only in proportion to total votes (1 mark).

Answer: Under PR, P wins 42 seats, Q 33 and R 25, which add up to 100, and no party has a majority. Under FPTP, the winner in each seat is the candidate with the most votes, even below 50 per cent. A party that narrowly leads in many seats can therefore win most of them, but under PR it gets only its vote share.

Example 4: Assertion-reason: FPTP · 1 mark · Assertion-reasonHarder board level

Assertion (A): Under FPTP, a candidate can win with less than 50 per cent of the votes.
Reason (R): FPTP requires only that the candidate gets more votes than any other candidate.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Try it first, then show the solutionSolution
  1. In NCERT's Haritbhumi, A wins with 40 per cent. The winning rule is "most votes", which explains A (1 mark).

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Example 5: The unfair-looking result (5 marks) · 5 marks · Long answerHOTS / competency

Four constituencies each have 100 voters and three parties contest all four. In constituencies 1 to 3 the votes are: P 40, Q 35, R 25. In constituency 4 the votes are: P 10, Q 60, R 30. Under FPTP, (i) find the seats won by each party, (ii) find each party's total votes and share of all votes, and (iii) comment on the result. (5 marks)

Try it first, then show the solutionSolution
  1. Seats: P wins constituencies 1-3, Q wins constituency 4, R wins none, so P 3, Q 1, R 0 (1 mark).
  2. Total votes: P = 40 x 3 + 10 = 130; Q = 35 x 3 + 60 = 165; R = 25 x 3 + 30 = 105; total 400 (1 mark).
  3. Shares: P 130/400 = 32.5 per cent; Q 165/400 = 41.25 per cent; R 105/400 = 26.25 per cent (1 mark).
  4. Comment: Q has the most votes but only one seat; P has 3 of 4 seats on 32.5 per cent of votes (1 mark).
  5. FPTP rewards where votes fall, not just how many; R gets no representation despite more than a quarter of votes, which PR would avoid (1 mark).

Answer: (i) P wins 3 seats, Q wins 1 seat and R wins none. (ii) P has 130 votes (32.5 per cent), Q has 165 (41.25 per cent) and R has 105 (26.25 per cent) out of 400. (iii) The party with the highest total votes, Q, gets only one seat, while P holds three of the four seats with a smaller share of votes than Q. R gets no seat although a quarter of voters chose it. This happens because FPTP counts seat by seat and ignores wasted votes, whereas proportional representation would give seats in line with vote shares.

Example 6: Case: STV quota · 4 marks · Case-basedHOTS / competency

Read the case and answer the questions.

Suppose a Vidhan Parishad body elects 3 members by single transferable vote. 8,000 valid votes are cast. Voters rank candidates in order of preference.

(i) Write the formula for the quota. (1)
(ii) Calculate the quota. (1)
(iii) A candidate gets 1,500 first-preference votes. What happens next to the candidate with the fewest votes? (2)

Try it first, then show the solutionSolution
  1. (i) Quota = [total valid votes / (seats + 1)] + 1 (1 mark).
  2. (ii) 8,000 / (3 + 1) = 2,000; 2,000 + 1 = 2,001 (1 mark).
  3. (iii) 1,500 is below 2,001, so the candidate is not yet elected; the candidate with the fewest votes is eliminated and those votes pass to the next preferences on the ballots, and the count repeats until seats are filled (2 marks).

Answer: (i) Quota = (total valid votes / (seats + 1)) + 1. (ii) 8,000 / 4 = 2,000, and adding 1 gives a quota of 2,001. (iii) 1,500 first-preference votes are below the quota, so the candidate is not elected yet. The lowest candidate is eliminated and those ballots transfer to the next preference, and the count continues until all three seats are filled.

Where students lose marks in Electoral Systems: FPTP, Majority and Proportional Representation

The slips examiners see most often, and what to write instead.

  • Mistake: Wrong winning rule for FPTP

    Confusing it with majority.

    Wrong working

    FPTP needs more than 50 per cent.

    Right working

    FPTP needs only the most votes.

    Do this: Write "most votes, even below 50 per cent".

    Usually costs: 1 mark.

  • Mistake: PR seats not adding up

    Arithmetic slip.

    Wrong working

    45%, 30%, 15%, 10% of 80 gives 36, 24, 12, 10.

    Right working

    10% of 80 = 8; total must be 80.

    Do this: Add the seats to check.

    Usually costs: 1 mark.

  • Mistake: STV quota without the plus-one steps

    Half-remembered formula.

    Wrong working

    Quota = 8,000 / 3 = 2,667.

    Right working

    Quota = 8,000 / (3 + 1) + 1 = 2,001.

    Do this: Seats plus one, then add one.

    Usually costs: 1-2 marks.

  • Mistake: Mixing the Indian uses

    Learning in one list.

    Wrong working

    Rajya Sabha uses FPTP.

    Right working

    Rajya Sabha uses PR; Lok Sabha uses FPTP.

    Do this: Recall "people's houses: FPTP".

    Usually costs: 1 mark.

Exam tips

  • Always write the winning rule first and then the example; it carries the first mark.
  • Show the formula and a total check in every numerical; seat totals must equal the house size.
  • For evaluation questions give one strength and one weakness of each system.
  • Use NCERT's own country examples (Haritbhumi, Ratnadweep, Swarnalok) but do not mix up the percentages.

Practice questions on Electoral Systems: FPTP, Majority and Proportional Representation

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    Which of the following is elected indirectly in India?
    (a) Lok Sabha
    (b) Vidhan Sabha
    (c) Local bodies
    (d) President

    Hint

    Elected representatives choose.

    Answer

    (d) President

  2. Q2 · 2 marks · Very short answerBoard level

    What does proportional representation mean? (2 marks)

    Hint

    Seats and votes.

    Answer

    In proportional representation voters choose a party, and seats are shared among parties in proportion to the votes each gets. This means power is usually shared.

  3. Q3 · 3 marks · Short answerHarder board level

    In a house of 80 seats, parties A, B, C and D get 45 per cent, 30 per cent, 15 per cent and 10 per cent of votes. Find the seats of each under PR. What do you notice about a majority? (3 marks)

    Hint

    Percentage of 80.

    Answer

    A: 45% of 80 = 36; B: 30% of 80 = 24; C: 15% of 80 = 12; D: 10% of 80 = 8. Total = 36 + 24 + 12 + 8 = 80. A majority needs more than 40 seats; no party has it, so a coalition is needed to form a government.

  4. Q4 · 1 mark · Assertion-reasonHarder board level

    Assertion (A): Under the majority system, the winner always has support from more than half of the voters who vote in the final round.
    Reason (R): If no candidate gets more than 50 per cent in the first round, the top two candidates contest a second round.
    (a) Both A and R are true, and R is the correct explanation of A.
    (b) Both A and R are true, but R is not the correct explanation of A.
    (c) A is true, but R is false.
    (d) A is false, but R is true.

    Hint

    Only two remain.

    Answer

    (a) Both A and R are true, and R is the correct explanation of A.

  5. Q5 · 5 marks · Long answerHarder board level

    Compare FPTP and proportional representation on three points and state where India uses each. (5 marks)

    Hint

    Winning rule, vote share and seats, who forms the government.

    Answer

    FPTP: each voter votes for a candidate and the one with the most votes wins, even below 50 per cent; a party's seat share can differ much from its vote share; it usually gives clear winners and often a single-party government. PR: voters choose a party and seats are shared in proportion to votes; seat share mirrors vote share; power is often shared between parties in a coalition. India uses FPTP for the Lok Sabha and Vidhan Sabhas, and PR for the Rajya Sabha, President and Vice President.

  6. Q6 · 3 marks · Short answerHOTS / competency

    Suppose a town with 3 seats uses STV and 12,000 valid votes. (a) Calculate the quota. (b) Suppose candidate K gets 3,001 first-preference votes. Is K elected? Explain what this tells you about why a quota is used. (3 marks)

    Hint

    Seats plus one.

    Answer

    (a) Quota = 12,000 / (3 + 1) + 1 = 3,000 + 1 = 3,001. (b) K has exactly 3,001, which equals the quota, so K is elected. The quota is set so that no more candidates than there are seats can reach it, which guarantees that every winner has a fair, substantial share of the votes.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Which system gives the seat to the candidate with the most votes?Show answer

    First-Past-The-Post.

  2. 2.What does the majority system require?Show answer

    More than 50 per cent of votes, else a second round between the top two.

  3. 3.Which houses use FPTP in India?Show answer

    The Lok Sabha and the Vidhan Sabhas.

  4. 4.What is the STV quota formula?Show answer

    (Total valid votes / (seats + 1)) + 1.

  5. 5.What does psephology study?Show answer

    Elections.

Electoral Systems: FPTP, Majority and Proportional Representation: frequently asked questions

What is an electoral system?

The method that decides how votes are turned into seats.

What is the difference between FPTP and PR?

FPTP gives each seat to the candidate with the most votes; PR gives parties seats in proportion to their share of votes.

Which electoral system does India use for the Lok Sabha?

First-Past-The-Post.

What is single transferable vote?

A ranked-vote method in which candidates reaching the quota win and the lowest candidate's votes transfer to next preferences.