AFTER THE COUNT
Instructor narration

Here is how to run After the Count. Plan for about seventy-five minutes, or divide the investigation and final comparison across two meetings. Students investigate three recent elections, change a clearly specified rule in the Rule Lab, and defend a recommendation. They finish with a new case that asks them to apply the distinctions more independently.

The question is simple: how did these votes become political power? The difficulty is working out what each number counts and which rule connects it to the result. A national vote share, a constituency victory, a valid ballot, and a seat are different objects. Much political confusion begins by giving them the same job.

The core cases are the United Kingdom in 2024, Israel in 2022, and Liberia in 2023. The transfer case is New Zealand in 2020. Each lab states its fixed inputs. The UK, Israel and New Zealand comparisons hold recorded votes fixed while changing a counting or eligibility rule. Liberia contrasts a replay of October plurality with the fresh historical November runoff. That contrast is not a controlled estimate of a rule change on the same votes.

Students can work alone or discuss in pairs. Each partner uses a separate device or browser profile for an individual saved notebook. Pairs sharing one screen keep their own plain-paper notes and prepare separate submissions. Alternate explaining and checking. Both should be able to explain a calculation and an evidence limit.

Open by saying: “Explain the result using the rule and the records. Then test a rule change. Your recommendation needs a number, a reason and a cost.” Ask for an initial representation priority. Students might value closer national vote-seat matching, a local representative, inclusion for smaller voices, or majority support for a winner. Those priorities are open to argument.

Each core case has four steps. First comes a prediction or first thought. Next comes the evidence and a short rule lesson, with structured checks. Each submitted answer and any help used are retained. Blank answers do not count as unsuccessful attempts. Then students enter the Rule Lab. Finally they make a policy choice, compare two tested settings, and name a cost or uncertainty. The compared figures stay beside the writing fields. Students confirm or revise their opening thought within the same short explanation. A first thought can be confirmed or revised using a precise figure. The existing brief makes that change in reasoning visible.

The first case is the United Kingdom. Reform received 14.3 percent nationwide and won five seats. The Liberal Democrats received 12.2 percent and won 72. Labour received 33.7 percent and won 411 of the 650 seats.

The rule was local plurality. Each constituency elected one MP. The candidate with the most votes there won, even below half. The national share summarized the local contests. Seats counted the local victories.

Use the three constituency records. Reform won Clacton with 21,225 votes. In Woking, the Liberal Democrats won with 24,019, while Reform received 4,888. In Barnsley North, Labour won with 18,610 and Reform received 10,799. Reform's Woking and Barnsley North votes added 15,687 to its national total, with no Reform seat in either place.

The second-place claim needs care. Reform finished second in 98 constituencies. That does not establish 98 narrow losses. Barnsley North's margin between Labour and Reform was 7,811 votes. Ask what a margin tells us that a ranking does not. Parliament remains remarkably unmoved by an impressive second place.

In the Rule Lab, students compare actual seats with a proportional benchmark. The calculation uses each party's exact recorded votes divided by the national valid-vote total, then multiplied by 650. Labour's benchmark is about 219.05 seats, Reform's is 92.90, and the Liberal Democrats' is 79.40. Keep the decimals. The displayed national shares are rounded. This comparison does not allocate whole seats or forecast how people would vote under a different institution.

Their recommendation can retain local plurality, explore a compensatory tier, or favor national proportional allocation. A compensatory list tier tops up parties underrepresented after local victories. Listen for the value they prioritize and what they would preserve or investigate. They can reach different conclusions with sound reasoning.

Israel introduces the entry boundary. In 2022, Meretz received 150,793 valid votes, or 3.16 percent, and no seats. Labor received 175,992, or 3.69 percent, and four seats. The threshold was 3.25 percent of all valid votes.

There were 4,764,742 valid votes. Multiply by 0.0325 and you get 154,854.115. The minimum whole-vote cutoff is therefore 154,855. Meretz fell 4,062 below that boundary with the historical denominator held fixed.

The central distinction is between an accepted ballot and a list eligible for seat allocation. Meretz's ballots were valid. Its list fell below the threshold. The threshold also does not explain every qualifying party's exact seats. Hadash-Ta'al and Labor both passed it, yet received five and four seats. Explaining that difference requires the allocation rules and the qualifying lists' vote totals.

The Rule Lab compares eligibility at two percent, three point two five percent, and five percent. At two percent, Meretz and Balad enter allocation. At five percent, Labor, Hadash-Ta'al, Ra'am and Yisrael Beitenu fall below the boundary. Fragmentation means representation across more separate lists. Students see a consequence for access, while claims about government instability require further political evidence.

The Liberian case updates the earlier activity. This is 2023, with George Weah and Joseph Boakai. On 10 October, Weah received 804,087 votes and Boakai 796,961. Weah led by 7,126. His 43.83 percent was below the required majority, so the top two advanced to a new ballot on 14 November.

Boakai won that runoff with 814,481 votes, or 50.64 percent. Weah received 793,914. Boakai's winning margin was 20,567. The result followed a new voting decision between two finalists.

Students calculate Boakai's net increase of 17,520 and Weah's decrease of 10,173. Valid votes fell by 226,121. That changing participation pool is part of the puzzle. A net increase does not identify a particular set of voters who switched. Boakai could have gained some supporters while losing others. A panel survey following the same individuals would help investigate those movements.

The Rule Lab applies plurality to the recorded October ballots, which selects Weah, then compares that with the majority requirement and the actual runoff that selected Boakai. The plurality replay holds October votes fixed; the actual runoff uses new ballots cast in November. A real plurality election could change campaigns, candidate entry and voter strategy.

The trade-off is between selecting a president with one ballot and offering another opportunity to choose between finalists and assemble a majority. Another round requires organization and participation. The table supplies actual counts. It does not supply a monetary cost estimate or a measure of popular enthusiasm.

After these three investigations, ask students to name a shared principle and a difference. They have repeatedly followed a rule from an input to an outcome, but the input has changed: local victories, eligible lists, or valid votes in a new presidential ballot.

New Zealand is the transfer case. Supply the MMP rule and raw results, then let students apply them before the worked interpretation. Voters have an electorate vote and a party vote. A party can enter proportional allocation with five percent of party votes or an electorate victory. Electorate winners fill seats first, and list seats top up the remaining entitlement.

In 2020, the Māori Party received 1.17 percent and won an electorate. It received that seat and one list seat, for two total. New Zealand First received a higher 2.60 percent, but no electorate victory and no seats. The two eligibility routes explain the apparent contradiction.

The Greens won one electorate seat and nine list seats, for ten total. For the new model check, keep the total entitlement at ten but give the party three electorate wins. Seven list seats fill the remainder. The local seats belong within the total entitlement. Labour's 46 electorate seats and 19 list seats produced 65 out of 120, a majority by itself. MMP does not make coalition government inevitable.

Rawiri Waititi won Waiariki, one of seven Māori electorates in 2020. The entry pathway can apply to any party; the Māori Party’s vote share does not measure all Māori representation. The policy question asks whether to retain that pathway into list allocation. If students remove that pathway while preserving local winners, the directly elected Māori MP keeps the seat. Ask them to weigh territorial representation against a common national threshold. They should explain the decision without inventing a complete alternative seat distribution.

Throughout the activity, let students make a serious attempt. A targeted hint follows the first unsuccessful check. After the second, the app changes representation and offers a worked visual. Ask them to explain that step, then keep moving. Repeated failure in the same box teaches very little beyond dislike of the box.

The final brief identifies the institution being designed, then asks for a priority, evidence from two cases, a recommendation, a cost, a model assumption, and a record that could change their view. Assess accurate evidence, the rule-to-result explanation, disciplined counterfactual reasoning, and a defensible trade-off. Open writing needs your judgment. The structured checks support practice. Look at the first submitted response separately from a later response completed with help.

Students complete their comparative argument at the top of the notebook. They can reopen the selected cases’ compared figures while writing, then download a TXT brief, retain a JSON process record, or print. Saving happens in their current browser. Each student submits their own exported work through your usual course process. Have them check an export before they leave.

For an optional exit, use South Africa in 2024. The ANC held 159 Assembly seats, but Ramaphosa received 283 votes when MPs elected the president. At least 124 supporters came from outside the ANC: 283 minus the maximum possible 159 ANC votes. The secret ballot establishes cross-party support without identifying individual voters.

Finish by asking: “What did you change or check more carefully after looking at the evidence?” The skill is carrying a method into the next surprising result: identify the unit, follow the rule, support the claim, and judge the trade-off.
