Electoral systems and political representation

Follow ballots into winners and seats. Compare plurality, ranked counts, proportional lists, mixed systems, and district boundaries while separating arithmetic from political judgments.

Prerequisite: Arithmetic and percentages. No political-science or country-specific legal knowledge required. Twelve lessons and 24 illustrated exercises distinguish single-winner selection from legislative representation. Nine interactive views use hypothetical ballots to expose counting rules, thresholds, transfers, compensation, and geographic grouping. They do not endorse a party or prescribe one universally fair system.

Lessons

1. 1

   Decide what an electoral system is choosing

   Choosing one officeholder and composing a legislature are different collective decisions.

2. 2

   Count plurality votes without inventing a majority

   The largest vote total can be well below half, and district wins do not add up like national vote shares.

3. 3

   Follow eliminations and continuing majorities

   A runoff can use a new ballot or transfer ranked ballots. The denominator matters.

4. 4

   Compare candidates head-to-head

   A candidate can beat every rival in pairwise comparisons, or majority preferences can cycle.

5. 5

   Distinguish rankings, approvals, and scores

   A ballot format determines which information is expressed, but not how honestly or comparably it is reported.

6. 6

   Turn party votes into whole seats

   Proportional representation needs a rounding rule because legislatures contain whole seats.

7. 7

   Separate legal thresholds from district magnitude

   A small party can fail to win a seat without any formal exclusion rule.

8. 8

   Follow a multi-member transferable count

   The single transferable vote fills several seats by retaining quotas, transferring surpluses, and eliminating candidates.

9. 9

   Ask whether list seats compensate for district seats

   Two ballots or two tiers do not by themselves make a system proportional.

10. 10

    Inspect geography and population before judging a map

    The same voters can elect different delegations under different equal-sized district partitions.

11. 11

    Separate a counting counterfactual from a behavioral prediction

    Voters, candidates, and parties can respond to rules, so fixed-ballot comparisons answer a limited question.

12. 12

    Evaluate an electoral-system claim

    Specify the rule and criteria, reproduce the arithmetic, then ask what evidence supports broader claims.