Electoral system Study Guide

📖 Core Concepts Electoral system – The set of rules that decide how votes are turned into winners (candidates or parties). Single‑winner vs. Multi‑winner – One seat (e.g., president) vs. several seats (e.g., parliament). Majoritarian (winner‑take‑all) vs. Proportional Representation (PR) – Winner‑take‑all awards the whole contest to the top candidate/party; PR allocates seats roughly in proportion to vote shares. Quota – A vote total that guarantees a seat in quota‑based systems (e.g., Droop quota in STV). Highest‑average vs. Largest‑remainder – Two families of seat‑allocation formulas for PR. Strategic‑proofness – No voting system can make strategic voting impossible for all voters (Gibbard’s theorem). Arrow’s impossibility theorem – No ranked‑order system can satisfy a set of fairness criteria simultaneously. 📌 Must Remember Plurality (FPTP): candidate with the most votes wins; no majority required. Absolute majority: > 50 % + 1 vote needed. Droop quota (STV): $$Q = \left\lfloor\frac{V}{S+1}\right\rfloor + 1$$ where V = total valid votes, S = seats to fill. D’Hondt (Highest‑average): divide each party’s vote total by 1, 2, 3,…; allocate seats to the highest resulting quotients. Sainte‑Laguë (Highest‑average): same as D’Hondt but divisors are 1, 3, 5, … (more favorable to small parties). Largest‑remainder (Hare quota): quota = total votes / total seats; each party gets ⌊votes/quota⌋ seats, remaining seats go to parties with biggest leftovers. Mixed‑Member Proportional (MMP): two votes (district + list); list seats top‑up to achieve overall proportionality. Parallel (non‑compensatory) voting: district seats and list seats are allocated independently; no compensation for disproportionality. Instant‑Runoff Voting (IRV): ranked voting, eliminate lowest‑ranked candidate, transfer votes until someone has > 50 %. Two‑Round System: if no majority in round 1, a runoff (usually top‑2) decides the winner. Threshold: minimum % (often 5 %) a party must reach to qualify for seats or levelling seats. 🔄 Key Processes IRV counting Count first‑choice votes. If a candidate > 50 %, they win. Else eliminate the candidate with fewest votes, transfer their ballots to the next ranked still‑in‑play candidate. Repeat until a majority is reached. STV counting Compute Droop quota. Any candidate meeting quota is elected; surplus votes are transferred proportionally (using a transfer value = surplus / total votes for that candidate). If seats remain, eliminate the lowest‑vote candidate and transfer all their votes. Continue quota‑election → surplus transfer → elimination cycle until all seats filled. D’Hondt seat allocation (MMP list component) List each party’s vote total. Create a table dividing each total by 1, 2, 3,… up to the number of seats available. Rank all quotients; assign seats to the highest quotients until all seats are allocated. Largest‑remainder (Hare) allocation Compute quota = total votes / total seats. Initial seats = ⌊votes / quota⌋ for each party. Distribute remaining seats one‑by‑one to parties with the largest fractional remainders. 🔍 Key Comparisons FPTP vs. IRV FPTP: “most votes wins”, can elect a candidate with < 50 % and suffers vote‑splitting. IRV: requires a majority via eliminations, reduces spoiler effect. D’Hondt vs. Sainte‑Laguë D’Hondt: divisor series 1, 2, 3… → favors larger parties. Sainte‑Laguë: divisor series 1, 3, 5… → more proportional, helps small parties. MMP vs. Parallel MMP: list seats compensate for disproportionality; overall seat share ≈ vote share. Parallel: list seats are independent; disproportionality from districts remains. Closed‑list vs. Open‑list PR Closed: voters only pick a party; party determines candidate order. Open: voters can influence which candidates on the party list win seats. ⚠️ Common Misunderstandings “Plurality = majority” – Plurality only means most votes, not > 50 %. Quota confusion – Droop quota (used in STV) is lower than Hare quota; using the wrong quota changes seat outcomes. Threshold applies to all seats – In many MMP systems, a party that wins at least one district seat can bypass the national threshold for list seats. MMP always yields perfect proportionality – Overhang seats (when a party wins more district seats than its proportional share) can distort the final seat count. “Two‑round” always means a second ballot – Exhaustive ballot can involve many rounds, not just a single runoff. 🧠 Mental Models / Intuition “Seat‑share ≈ vote‑share” – Think of PR as a pie where each party’s slice is cut according to its vote percentage. “Elimination = upward pressure” – In IRV and STV, removing the weakest candidate pushes their supporters to their next preference, often consolidating around similar‑ideology candidates. “Divisor tables = competition for the next seat” – Visualize the highest‑average method as a race where each party’s next “ticket” costs more the more seats it already has. 🚩 Exceptions & Edge Cases Overhang seats – When a party wins more district seats than its proportional entitlement, the legislature may expand temporarily. Dual‑member PR – Elects two reps per constituency; one by plurality, the second to correct proportionality. Levelling seats – Compensatory seats added after the main PR allocation; can be regional or national. Electoral thresholds with “exemptions” – Some systems exempt parties that win a constituency seat from the national threshold. 📍 When to Use Which Single‑winner, low‑complexity elections → Use FPTP (quick, easy count). Desire for majority legitimacy without a second ballot → Choose IRV (ranked, instant runoff). Need for proportional representation of parties → Use Party‑list PR (closed/open) with D’Hondt or Sainte‑Laguë depending on how much you want to help small parties. Multi‑member districts with voter‑chosen candidates → Use STV (quota‑based, transfers). Combine local representation with overall proportionality → Adopt MMP (two votes, levelling seats). Simpler mixed system, no compensation → Use Parallel voting (district + list seats independent). 👀 Patterns to Recognize “Majority‑required → runoff or elimination” – Whenever a rule mentions “majority”, expect a second round, elimination, or transfer mechanism. “Quota = (Votes / (Seats + 1)) + 1” – Droop quota appears in any STV description. “Divisor series = 1, 2, 3…” – Signals a highest‑average method (D’Hondt). “Divisor series = 1, 3, 5…” – Signals Sainte‑Laguë. “Threshold + list” – Look for a minimum % before any seats are allocated. 🗂️ Exam Traps Droop vs. Hare quota – Test‑writers may give the Hare formula (V/Seats) and ask for the quota used in STV; remember the “+ 1” in Droop. Confusing “absolute majority” with “plurality” – A question may state “candidate received a majority” but give < 50 % of votes; the correct answer is that a runoff/IRV would be required. Mixing up highest‑average and largest‑remainder – A prompt about “dividing votes by a series of numbers” refers to D’Hondt/Sainte‑Laguë, not the remainder method. Overlook overhang seats – In MMP questions, total seats may exceed the “base” number; don’t assume seat count is fixed. Threshold exemption clause – If a party wins a constituency seat, it may bypass the national threshold; forgetting this leads to an incorrect “no seats” answer. --- All bullets are drawn directly from the supplied outline; no external information has been added.