The complete register
Twenty-eight entries, eight sections
This is the whole roster in one place. Each entry is one rule and what it demonstrably does — stated comparatively, with the country and the period named.
Section 01
Formulas
Turning votes into seats.
- 1.1First past the postA plurality in each district, and the well-documented consequences: manufactured majorities, a squeeze toward two parties, and large numbers of votes electing nobody.
- 1.2Alternative voteRanking and elimination in a single-member seat, which changes what a rational campaign looks like without changing the number of seats.
- 1.3Largest remainderQuota then remainders, and why the choice of quota moves seats between large and small parties.
- 1.4Highest averagesSuccessive division rather than a quota, and the systematic tilt each divisor sequence introduces.
Section 02
Boundaries
Where the lines go and who draws them.
- 2.1Packing and crackingConcentrating opposing voters into few seats or splitting them across many — the two moves, and how each shows in the numbers.
- 2.2CompactnessSeveral competing mathematical definitions, none of them decisive, which is why shape alone rarely settles an argument.
- 2.3MalapportionmentDistricts of unequal population, and the difference between unequal size and deliberate shaping.
- 2.4Who draws the lineLegislature, commission or court — the institutional choice, and what each tends to produce.
Section 03
The Ballot
The paper itself.
- 3.1The secret ballotA nineteenth-century invention with a specific purpose: an official paper, a screened booth, and the end of a public show of hands.
- 3.2Ballot designLayout, column breaks and instruction wording measurably changing how many papers are spoiled or misread.
- 3.3Order effectsPosition on the paper carries a small but repeatable advantage, and the remedies used against it.
Section 04
The Count
What happens after the polls close.
- 4.1Counting rulesWhat makes a mark valid, who adjudicates it, and why the rule has to be written before anyone knows it matters.
- 4.2TransfersMoving a surplus or an eliminated candidate's papers, and the different methods for deciding which papers move.
- 4.3RecountsThresholds, who may request one, and why a second count is not simply the first count repeated.
- 4.4Spoiled papersDeliberate and accidental spoiling, and what the rate is usually measuring.
Section 05
The Roll
Who is on the list.
- 5.1RegistrationOpt-in against automatic enrolment, and what each does to who ends up on the list.
- 5.2EnumerationDoor-to-door compilation, its cost, and why some systems abandoned it.
- 5.3The census behind itCounting the population is the input to almost everything downstream, including how many seats a place gets.
Section 06
Procedure
Where the quiet power sits.
- 6.1QuorumThe number that decides whether anything can be decided, and what happens when it is set too high or deliberately broken.
- 6.2CommitteesWhere bills are actually shaped, and why control of a committee is worth more than a speech.
- 6.3Debate and delayProcedural delay as a minority instrument, and the closure devices built to answer it.
- 6.4ConfidenceThe mechanism that ends a government, and the constructive variant that requires a replacement first.
Section 07
Paradoxes
Where the arithmetic misbehaves.
- 7.1The Condorcet cycleMajorities that go round in a circle, so that no option beats all others and the agenda order decides the winner.
- 7.2Arrow's resultA short list of reasonable-looking conditions that no ranked method can satisfy at once, and what it does and does not prove.
- 7.3The Alabama paradoxAdding a seat to the total and watching a place lose one — the discovery that ended a whole family of apportionment methods.
Section 08
Apportionment
Dividing seats between places.
- 8.1Divisor methodsChoosing a divisor and rounding, and how the rounding rule quietly favours larger or smaller places.
- 8.2RemaindersQuota plus leftovers: simple, intuitive, and the source of the paradoxes.
- 8.3Seats and placesGuaranteed minimums, fixed chamber sizes, and what has to give when both are required.