Forming a Government After the 200-Seat Election
Preliminary results for a 200-seat parliament elected under a mixed-member system: 100 single-member districts, 100 list seats, and a 5 percent legal threshold. Party-list vote shares are A 34 percent, B 28 percent, C 15 percent, D 12 percent, E 7 percent, F 4 percent. District results give A 40 seats, B 30, C 8, D 18, E 4. The electoral commission must allocate the list seats so that each qualifying party's total is proportional. Party positions on the main economic axis (0 = left, 10 = right) are A 3.0, B 6.5, C 2.0, D 7.5, E 1.0. No party has a majority; the president must nominate a prime minister who can survive an investiture vote, and the constitution does not require that the prime minister come from the largest party.
1. Compute the final seat distribution. Show the threshold step and the seat totals, including list seats.
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Step 1 - threshold. F wins 4 percent, below the 5 percent threshold, and receives no seats. Votes are therefore renormalized over the qualifying 96 percent.
Step 2 - proportional totals (200 × share/96).
- A: 34/96 × 200 = 70.8 → 71
- B: 28/96 × 200 = 58.3 → 58
- C: 15/96 × 200 = 31.3 → 31
- D: 12/96 × 200 = 25.0 → 25
- E: 7/96 × 200 = 14.6 → 15
- Sum = 200. No party's district seats exceed its proportional total, so there is no overhang and the chamber stays at 200.
Step 3 - list seats (total minus districts won).
- A: 71 − 40 = 31
- B: 58 − 30 = 28
- C: 31 − 8 = 23
- D: 25 − 18 = 7
- E: 15 − 4 = 11
- Sum = 100, matching the 100 list seats.
Majority threshold = 101. Seat shares: A 35.5 percent, B 29, C 15.5, D 12.5, E 7.5. Largest party A is far from governing alone.
The important structural fact: F's 4 percent of the vote produced zero seats while E's 7 percent produced 15. This is a manufactured majority threshold, not a natural feature of the result - remember it for the coalition question.
2. Which of the following are minimal winning coalitions, and which are merely winning: A+C; A+C+E; B+C+E; A+D+E; A+B+D; B+C+D? Define the test you are applying.
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Test: a coalition is winning if its seats are at least 101; it is minimal winning if it is winning and removing any single member makes it lose (that is, no member is surplus).
| Coalition | Seats | Winning? | Minimal? |
|---|---|---|---|
| A+C | 71+31 = 102 | Yes | Yes - 71 and 31 are each below 101 |
| A+C+E | 71+31+15 = 117 | Yes | No - A+C alone already governs at 102; E is surplus |
| B+C+E | 58+31+15 = 104 | Yes | Yes - pairwise sums 89, 73, 46 all fail |
| A+D+E | 71+25+15 = 111 | Yes | Yes - 96, 86, 40 all fail |
| A+B+D | 71+58+25 = 154 | Yes | No - A+B = 129 already wins |
| B+C+D | 58+31+25 = 114 | Yes | Yes - 89, 83, 56 all fail |
Judgment point: A+C+E is the trap. It is the coalition most people name first because E is the smallest party and 117 'looks' like a bare majority, but E adds nothing to the majority and everything to the bargaining price. Any model that predicts A+C+E is predicting a surplus coalition, which requires a separate explanation (policy payoffs, cabinet portfolios, or regional balance).
3. Using office-seeking and policy-seeking theories, which government is most likely to form, and how fragile is it? Address what happens if the threshold were 3 percent.
Read the worked answer
Prediction: A+C.
- Policy-seeking (minimal winning + ideological proximity): A+C spans 2.0 to 3.0 on the axis - a range of 1.0, the smallest of any winning pair or triple. B+C+E spans 1.0 to 6.5 (5.5) and B+C+D spans 2.0 to 7.5 (5.5). A+C is both minimal winning and maximally compact, which is where the two theories converge.
- Office-seeking (minimal winning + portfolio maximization): two parties splitting ministries beats three or four, again favoring A+C. A grand coalition A+B (129) is the office-seeking alternative if durability dominates, but it spans 3.5 points and hands B the pivotal position the whole time.
Fragility - the critical number. A+C holds 102 of 200, a margin of one seat. A single defection, expulsion, death, or by-election loss ends the government. E, though not needed, controls 15 seats and can threaten to bring the government down in coalition with the opposition, so E will extract concessions despite not being in the cabinet.
The 3 percent threshold scenario. With F included, the qualifying vote is 100 percent and totals become A 68, B 56, C 30, D 24, E 14, F 8. A+C falls to 98 seats - below the majority. The A+C government exists only because F's 4 percent was discarded and redistributed. A+C is therefore not just fragile, it is an artifact of the threshold: change the legal rule and the modal coalition changes from A+C to A+B (124) or A+C+E (112). This is the core comparative point - electoral system rules, not just votes, select governments.