The Voter Turnout Puzzle
A city of 500,000 eligible voters held an election. Official figures show 275,000 ballots cast, a turnout of 55%. A journalist notices that in the three districts with the highest turnout (reported at 78%, 74%, and 71%), the sum of votes cast exceeds the number of registered voters in those districts by 4,200. The election office explains that voters can cast ballots at any polling station in the city, so district-level counts reflect where ballots were cast, not where voters live. The journalist's editor wants a story headlined "Turnout Exceeds Registered Voters - Fraud?"
1. Evaluate whether the 4,200 excess is evidence of fraud, and explain what additional data would be needed to test the fraud hypothesis.
Read the worked answer
Is the excess evidence of fraud? Not on its own. The election office's explanation - citywide voting, so district counts measure ballots cast, not registered residents - fully accounts for a district-level excess. A district can legitimately receive more ballots than it has resident registered voters if commuters or visitors from other districts vote there. The 4,200 figure is a geographic mismatch, not a count mismatch.
The citywide check: total ballots 275,000 ≤ 500,000 eligible. At the city level there is no excess, which is exactly what the portable-voting explanation predicts. Fraud would more likely show as a citywide total exceeding eligible voters, or as duplicate ballots.
Data needed to test fraud:
- Deduplicated voter records - did any individual vote more than once? (Requires matching, not district totals.)
- Ballot reconciliation - do issued ballots, spoiled ballots, and counted ballots balance citywide?
- Residency-adjusted district denominators - registered voters assigned to each district vs. ballots cast there.
- Poll-station logs - distribution of out-of-district voters by station.
Conclusion: The headline is unsupported. The excess is expected under the stated rules and the citywide total is consistent. A strong answer distinguishes an anomaly that a known mechanism explains from evidence of wrongdoing.
2. The editor argues: "Even if it's explainable, the numbers look bad - we should report the anomaly and let readers decide." Assess this position.
Read the worked answer
The editor's position has a real kernel: transparency about anomalies is legitimate. If a figure looks wrong, publishing it with context can serve the public. The problem is the framing "let readers decide" when the publication already knows the likely explanation.
Why "let readers decide" fails here:
- It presents a resolved question as open, which is a form of misleading by omission. The election office's mechanism is not a competing theory of equal standing; it is the standard explanation for portable voting.
- Readers lack the reconciliation data and cannot "decide" responsibly. Handing them a raw anomaly without the denominator correction offloads the analytical work onto people without the tools.
- The headline "Fraud?" asserts a frame the evidence does not support. A question mark does not neutralise an accusation.
Better journalism: report the anomaly and the explanation and the limits of the explanation - e.g., "District totals exceed resident registrations, which portable voting predicts; here is the citywide reconciliation and what would still need checking." That is transparent and accurate.
Model insight: The exam tests whether you can hold two things at once - the value of surfacing anomalies and the duty not to manufacture doubt. "Let readers decide" is only honest when the evidence is genuinely balanced; here it is not. A strong answer names the asymmetry between an explained anomaly and an unexplained one.