# Electoral Systems

Political Science I · Political Science I · https://tryals.app/learn/political-science-i/electoral-systems

## The Conversion Problem

An electoral system converts votes into seats. It determines how public preferences become power.

Three components do most of the work:

| Component | What it fixes | Effect |
|---|---|---|
| **District magnitude** | Seats per constituency | The strongest determinant of proportionality |
| **Electoral formula** | How votes become seats | Majoritarian, proportional, or mixed |
| **Threshold** | Minimum support to qualify | Excludes small parties |

**District magnitude is the decisive one**. A single-seat district cannot divide its seat. Therefore, it cannot be proportional under any formula. Proportionality rises as magnitude increases.

### The Three Families

- **Majoritarian.** The winner takes the seat. These systems routinely award a party with 40% of the vote an absolute majority of seats.
- **Proportional.** Multi-member districts allocate seats by vote share using divisor methods like **D'Hondt** or **Sainte-Laguë**. **D'Hondt** favours larger parties, while **Sainte-Laguë** is more neutral.
- **Mixed.** Voters elect members from both districts and lists. In **mixed-member proportional** systems, list seats compensate to ensure proportional totals. In **parallel** systems, they do not.

Spain uses closed lists with **D'Hondt** and a **3%** district **threshold**. However, small rural districts keep its overall result far less proportional than expected.

### Effects on Party Systems

**Duverger's law** states that single-member plurality favours two-party systems, whereas proportional representation favours multiparty systems.

This outcome occurs through two distinct mechanisms:

- **Mechanical**: the seat allocation rules directly deny seats to smaller parties.
- **Psychological**: voters abandon uncompetitive parties to avoid wasting votes.

Plurality systems often maintain more than two parties nationally when minor parties concentrate their support regionally.

### Measuring Electoral Results

- The **effective number of parties** weights parties by their seat or vote share. For example, a 40/40/10/10 split yields an effective count of roughly 2.6.
- The **Gallagher index** measures the disproportionality between vote shares and seat shares. Scores in the low single digits represent proportional outcomes.

> **Common pitfall:** treating proportional representation as a single, uniform system. Variations in magnitude, thresholds, and formulas mean two proportional systems can function entirely differently.

## Practice questions

9 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. Two countries both use list PR with the same formula, but one has districts of three seats and the other of fifteen. Why will the first be substantially less proportional?

A. Smaller constituencies inherently create a psychological bias reducing turnout
B. District magnitude dictates proportionality, and three seats cannot divide finely
C. The D'Hondt divisor formula alters its internal mathematical logic at low counts
D. Three-seat constituencies legally require higher formal thresholds for every list

**Answer:** B. District magnitude dictates proportionality, and three seats cannot divide finely

**Why:** Because **magnitude** dominates. Three seats cannot represent a party with ten per cent of the vote; fifteen can. This is why the label "PR" tells you much less than people assume, and why Spain's nominally proportional system behaves far less proportionally than Netherlands-style national-list PR.

Page: https://tryals.app/practice/political-science-i/electoral-systems/two-countries-both-use-list-pr-with-the-same-formula-but-one-has

### 2. What percentage threshold applies at constituency level in Spanish general elections?

**Answer:** 3

**Why:** **3%**, applied per constituency. In most Spanish provinces this is not the binding constraint at all, with district magnitudes of three or four, the effective threshold imposed by magnitude alone is far higher than three per cent, which is a good illustration of why the legal threshold is often the least important of the three components.

Page: https://tryals.app/practice/political-science-i/electoral-systems/what-percentage-threshold-applies-at-constituency-level-in-spanish

### 3. Duverger's law holds more reliably at district level than at national level.

**Answer:** True

**Why:** **True.** The mechanical and psychological effects operate within each district, so a party concentrated in one region can win seats comfortably while polling a few per cent nationally. That is why plurality systems reliably contain more than two parties at national level while approximating two-party competition constituency by constituency.

Page: https://tryals.app/practice/political-science-i/electoral-systems/duvergers-law-holds-more-reliably-at-district-level-than-at-national

### 4. Which are true of the mechanisms behind Duverger's law?

A. The law predicts exactly two parties nationally in every plurality system
B. The psychological effect is that voters abandon parties they expect to lose
C. Candidates and donors also respond to expected outcomes
D. The mechanical effect is that the rules deny small parties seats

**Answer:** B. The psychological effect is that voters abandon parties they expect to lose; C. Candidates and donors also respond to expected outcomes; D. The mechanical effect is that the rules deny small parties seats

**Why:** The fourth is the overstatement that gets the law dismissed. It is a tendency operating district by district, and it coexists with several national parties whenever support is geographically concentrated. Canada and the United Kingdom being the standing examples.

Page: https://tryals.app/practice/political-science-i/electoral-systems/which-are-true-of-the-mechanisms-behind-duvergers-law

### 5. Sort each system by its family.

**Answer:**

- Majoritarian: First past the post, Two-round system
- Proportional: Closed-list PR with D'Hondt, Single transferable vote
- Mixed: Mixed-member proportional, Parallel voting with non-compensatory list seats

**Why:** The two mixed systems land in the same column and behave very differently: compensatory list seats produce an overall proportional result, while parallel list seats simply add a proportional tier to a majoritarian one. The family name tells you the ingredients, not the outcome.

Page: https://tryals.app/practice/political-science-i/electoral-systems/sort-each-system-by-its-family

### 6. Complete the account of electoral systems.

**Answer:** The single strongest determinant of proportionality is district **magnitude**. The divisor formula that systematically favours larger parties is **D'Hondt**. Duverger held that plurality single-member districts tend towards **two**-party competition. Disproportionality is commonly measured by the **Gallagher** index.

**Why:** The first and second blanks together explain most of Spain's results: D'Hondt favours larger parties and small district magnitudes amplify that further, so a system correctly described as proportional delivers outcomes much closer to a majoritarian one in the smaller provinces.

Page: https://tryals.app/practice/political-science-i/electoral-systems/complete-the-account-of-electoral-systems

### 7. Arrange these steps in analysing an electoral system's effects, in order.

**Answer:**

1. Identify the district magnitude
2. Identify the formula and any legal threshold
3. Compute the effective threshold that magnitude alone imposes
4. Compare vote shares with seat shares
5. Compute the disproportionality index

**Why:** Beginning with magnitude rather than the formula is the habit worth building. The effective threshold imposed by a three-seat district is far above any legal threshold a country is likely to write down, so an analysis that starts with the legal rules will systematically misread the system.

Page: https://tryals.app/practice/political-science-i/electoral-systems/arrange-these-steps-in-analysing-an-electoral-systems-effects-in

### 8. Both mixed-member proportional and parallel systems combine local single-member districts with party lists. Why does this structural similarity fail to produce comparable degrees of proportionality?

A. Mixed systems abandon constituency representation to ensure parity
B. Mixed systems apply majoritarian seat thresholds to national list tiers
C. Parallel allocation relies entirely on single-member plurality formulas
D. Parallel systems do not use party lists to correct district imbalances

**Answer:** D. Parallel systems do not use party lists to correct district imbalances

**Why:** Students frequently assume adding party lists automatically guarantees proportionality. In parallel systems, list seats operate independently alongside district races rather than compensating for seat-vote distortions.

Page: https://tryals.app/practice/political-science-i/electoral-systems/both-mixed-member-proportional-and-parallel-systems-combine-local

### 9. A party winning 40 per cent of the vote under first past the post typically receives about 40 per cent of the seats.

**Answer:** False

**Why:** **False**, and the gap is the system working as intended rather than failing. Plurality systems routinely convert around 40 per cent of votes into a comfortable majority of seats. Whether that is a virtue, decisive government, or a defect is exactly the argument between the two families.

Page: https://tryals.app/practice/political-science-i/electoral-systems/a-party-winning-40-per-cent-of-the-vote-under-first-past-the-post