Elections and Electoral Systems Notes

Elections and Electoral Systems

Democracies are often categorized by their electoral system, which consists of laws governing electoral competition between candidates and/or parties.

Elections and Electoral Integrity

Elections are increasingly common for filling legislative and executive positions worldwide, with most independent states employing direct elections for their lower house of parliament.

Election Statistics

Legislative and Presidential Elections by Decade:

• 1950s: Approximately 125 elections (Legislative), Approximately 75 elections (Presidential)

• 1960s: Approximately 150 elections (Legislative), Approximately 100 elections (Presidential)

• 1970s: Approximately 175 elections (Legislative), Approximately 125 elections (Presidential)

• 1980s: Approximately 225 elections (Legislative), Approximately 100 elections (Presidential)

• 1990s: Approximately 325 elections (Legislative), Approximately 125 elections (Presidential)

• 2000s: Approximately 325 elections (Legislative), Approximately 150 elections (Presidential)

• 2010s: Approximately 300 elections (Legislative), Approximately 150 elections (Presidential)

Electoral Integrity

Electoral integrity is the degree to which elections adhere to international standards and global norms for 'good' elections, often outlined in treaties, conventions, and guidelines from international and regional organizations.

Violations of electoral integrity are termed electoral malpractice.

Electoral Integrity levels include:
*Very High
*High
*Moderate
*Low
*Very Low
*Not Assessed

Factors Influencing Electoral Integrity

• Domestic structural constraints

• The role of the international community

• Institutional design

• Electoral management bodies

Democracies generally exhibit higher electoral integrity than dictatorships, though variations exist within both.

Strategies to Identify Election Fraud

1. Election monitoring

2. Election forensics

Benford’s Law

Benford’s Law describes the frequency distribution of digits in numerical data. It posits that lower digits (1, 2, 3) appear as the first digit more often than higher digits (7, 8, 9). For example, a number starting with 1 is more likely than one starting with 9. Fabricated numbers tend to be uniformly distributed, allowing comparison of digit frequencies against Benford's Law to detect anomalies.

The probability that the first digit in a number will be a 3 is 0.125, and the probability that it will be a 6 is 0.067. Similarly, the probability that the second digit in a number will be a 0 is 0.120, and the probability that it will be a 6 is 0.093. The mean or expected value of the first digit is 3.441, whereas it’s 4.187 for the second digit.

Walter Mebane (2013) examined electoral returns from 45692 ballot boxes in the 2009 presidential election in Iran.

Benford’s Law: Frequency Distribution of First and Second Digits

Electoral Systems

Political scientists classify electoral systems based on their electoral formula. These include:

1. Majoritarian

2. Proportional

3. Mixed

The electoral formula dictates how votes are converted into seats.

Electoral System Families

Consists of: Majoritarian, Proportional, and Mixed systems.

Majoritarian

Includes:

• Plurality: e.g., Single-Member District Plurality, Single Nontransferable Vote, Block Vote, Party Block Vote

• Absolute Majority: e.g., Alternative Vote, TRS (Majority-Runoff)

Proportional

Includes:

• Quota

• Divisor

• Single Transferable Vote

• List PR

Mixed

Can be:

• Independent

• Dependent

• Coexistence

• Supposition

• Fusion

• Correction

• Conditional

Majoritarian Electoral Systems

These systems award victory to candidates or parties with the most votes.

Single-Member District Plurality (SMDP)

Voters cast one vote for a candidate in a single-member district; the candidate with the most votes wins.

Example: Bedford Constituency, UK Legislative Elections, 2019

Mohammad Yasin (Labour) won with 20,491 votes (43.3%).
Ryan Henson (Conservative) received 20,346 votes (43.0%).
Henry Vann (Liberal Democrat) got 4,608 votes (9.7%).
Adrian Spurrell (Green) secured 960 votes (2.0%).
Charles Bunker (Brexit) obtained 896 votes (1.9%).

A candidate can win with as few as two votes if all other candidates receive only one vote each.

Strengths of SMDP Systems

• Simplicity: Easy for voters to understand and inexpensive to administer.

• Clear Accountability: Each district has one representative, making it easy to assign responsibility for policies.

Single Nontransferable Vote (SNTV)

Voters cast a single candidate-centered vote in a multimember district; candidates with the highest number of votes are elected.

Alternative Vote (AV)

An 'absolute majority' majoritarian system is also known as the instant-runoff vote is candidate-centered preference voting system used in single-member districts where voters rank order the candidates.

If a candidate wins an absolute majority of first-preference votes, they’re immediately elected. If no candidate wins an absolute majority, the candidate with the fewest first-preference votes is eliminated, and their votes are reallocated among the remaining candidates based on the designated second preferences. This process is repeated until one candidate has obtained an absolute majority of the votes cast (full preferential system) or an absolute majority of the valid votes remaining (optional preferential system).

Example: Richmond Constituency, New South Wales, Australia 1990

• Neville Newell ultimately won with 34,664 votes (50.5%) after multiple counts and reallocations.

• Charles Blunt finished with 33,980 votes (49.5%) after the seventh count.

Majority-Runoff Two-Round System (TRS)

Another 'absolute majority' majoritarian electoral system.

Voters cast a single candidate-centered vote in a single-member district. A candidate with an absolute majority in the first round is elected. Otherwise, the top two candidates compete in a second-round runoff election.

Example: Burundi Presidential Elections, 2020

Évariste Ndayishimiye (CNDD-FDD) won the first round with 71.45% of the vote.
Agathon Rwasa (National Congress for Liberty) received 25.15% of the vote.

Example: Uruguay Presidential Elections, 2019

In the first round, Daniel Martinez (Broad Front) received 40.49%, and Luis Alberto Lacalle Pou (National Party) got 29.70%.
In the second round, Luis Alberto Lacalle Pou (National Party) won with 50.79%.

Strengths of Majority-Runoff TRS

Gives voters more choice compared to SMDP systems.

Proportional Electoral Systems

These systems employ quota- or divisor-based methods in multimember districts to translate votes into seats proportionally.

Types of Proportional Representation (PR) Systems

1. List Proportional Representation systems (List PR)

2. Single Transferable Vote (STV)

List PR System

Each party presents a list of candidates in multimember districts. Parties gain seats in proportion to their overall vote share, and seats are allocated among candidates on their list.

List PR systems vary by:

1. Formula for allocating seats

2. District magnitude

3. Electoral thresholds

4. Type of party list

Quota Systems

A quota determines the 'price' (votes) a party must pay to guarantee a seat in a district.

Q(n) = \frac{Vd}{Md + n}

• V_d is the number of valid votes in district d.

• M_d is the district magnitude.

• n is the modifier of the quota.

Types of Quotas

• Hare quota: n = 0

• Hagenbach-Bischoff quota: n = 1

• Imperiali quota: n = 2

• Reinforced imperiali quota: n = 3

• The Droop quota is the Hagenbach-Bischoff quota plus 1.

Allocating Seats Using the Hare Quota

Example:

The most common method for allocating the remainder seats is the largest remainder method.

Divisor (Highest Average) Systems

These systems divide the total votes for each party by a series of numbers (divisors) to obtain quotients. Seats are allocated based on which parties have the highest quotients.

Common Divisor Systems

• D’Hondt: 1, 2, 3, 4, . . .

• Sainte-Lagu¨e: 1, 3, 5, 7, . . .

• Modified Sainte-Lagu¨e: 1.4, 3, 5, 7, . . .

District Magnitude

The number of representatives elected in a district. A larger district magnitude leads to greater proportionality.

District Magnitude Examples

• Ukraine (2006/2007): 450

• Serbia (current): 250

• Chile (historical): 2

Electoral Threshold

The minimum level of support required for a party to gain representation. It can be:

• Natural: A mathematical byproduct of the system.

• Formal: Explicitly written into the electoral law.

High electoral thresholds decrease electoral system proportionality.

Negative Side-Effects of Electoral Thresholds

• Turkey 2002: 46% of votes were wasted because parties failed to surpass the 10% threshold.

• Poland 1993: 34% of votes were wasted, enabling former Communists to regain power.

Party Lists

• Closed: The party determines the order of elected candidates.

• Open: Voters can indicate their preferred party and candidate.

• Free: Voters have multiple votes to allocate within or across party lists.

Single Transferable Vote (STV)

The only proportional electoral system that doesn’t employ a party list. It uses a candidate-centered preferential voting system in multimember districts.

Candidates surpassing a quota of first-preference votes are immediately elected. Surplus votes from elected candidates and votes from eliminated candidates are reallocated until all seats are filled.

STV Example

• District magnitude: 3

• Voters: 20

• Candidates: Bruce, Shane, Sheila, Glen, Ella

• Droop quota: [20 / (3 + 1)] + 1 = 6

Mixed Electoral Systems

These systems combine majoritarian and proportional elements.

Most mixed systems use multiple electoral tiers. The district or constituency level is the lowest tier. Upper tiers group lower-tier constituencies, typically at regional or national levels.

Majoritarian systems are typically used in the lowest tier, and proportional systems are used in the upper tier.

Types of Mixed Systems

1. Independent Mixed Electoral System:

The majoritarian and proportional components operate independently.

2. Dependent Mixed Electoral System:

The application of the proportional formula depends on the distribution of seats or votes from the majoritarian formula.

In most dependent mixed systems, voters cast two votes:

• One for the district-level representative (candidate vote).

• One for the party list in the higher electoral tier (party vote).