Elections and Electoral Systems

Electoral Systems

An electoral system is a set of laws regulating electoral competition between candidates and/or parties.
Democracies are classified based on their electoral system.

Elections and Electoral Integrity

Elections are used to fill legislative and executive offices globally.
Most independent states use direct elections for their lower house of parliament.

Electoral Integrity

Electoral integrity is the degree to which elections meet international standards and global norms for 'good' elections.
These standards are in treaties, conventions, and guidelines from international and regional organizations.
Violations of electoral integrity are called electoral malpractice.
Democracies tend to have higher electoral integrity than dictatorships, but there's variation within both.

Factors Influencing Electoral Integrity

Domestic structural constraints.
The role of the international community.
Institutional design.
Electoral management bodies.

Strategies to Identify Election Fraud

Election monitoring.
Election forensics.

Benford’s Law

Benford's Law describes the frequency distribution of digits in numerical data.
It states that lower digits are more common as the first digit in a number than higher digits; numbers starting with 1 are most frequent, and those starting with 9 are least frequent.
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.
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.
Mean value of the first digit: 3.441, Second digit: 4.187
Used to detect financial and accounting fraud, it compares the frequencies of digits in financial accounts with expected probabilities.
Significant deviations indicate suspicious numbers and potential fraud.
It has been applied to identify electoral fraud in voting returns, focusing on the distribution of the second digit.
Walter Mebane (2013) examined electoral returns from 45692 ballot boxes in the 2009 presidential election in Iran.

Electoral Formulas

Political scientists distinguish electoral systems based on their electoral formula:
1. Majoritarian.
2. Proportional.
3. Mixed.
An electoral formula determines how votes are translated into seats.

Majoritarian Electoral Systems

Majoritarian electoral system: candidates or parties with the most votes win.

Single-Member District Plurality (SMDP)

SMDP: voters cast a single vote for a candidate in a single-member district; the candidate with the most votes wins.
Example: Mohammad Yasin of the Labour Party won the most votes in the Bedford Constituency, UK Legislative Elections, 2019.
Strengths: Simplicity and single representative per constituency.
Weaknesses: Can win with as few as two votes if all the other candidates win only one vote each.

Single Nontransferable Vote (SNTV)

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

Alternative Vote (AV)

AV, or instant-runoff vote: candidate-centered preference voting system in single-member districts where voters rank order candidates.
If a candidate wins an absolute majority of first-preference votes, they are immediately elected.
If no candidate wins an absolute majority, the candidate with the fewest first-preference votes is eliminated, and their votes are reallocated based on second preferences.
This process is repeated until a candidate obtains an absolute majority (full preferential system) or an absolute majority of the valid votes remaining (optional preferential system).

Majority-Runoff Two-Round System (TRS)

TRS: voters cast a single candidate-centered vote in a single-member district.
If a candidate obtains an absolute majority in the first round, they are elected.
If no one obtains an absolute majority, the top two vote winners compete in a runoff election in the second round.
Strengths: Gives voters more choice than SMDP systems.

Proportional Electoral Systems

Proportional Representation (PR) system: quota- or divisor-based system in multimember districts to produce a proportional translation of votes into seats.

List PR Systems

List PR: each party presents a list of candidates to voters in each multimember district. Parties receive seats in proportion to their overall share of the votes, allocated among candidates on their list.
List PR systems differ in:
1. Formula for allocating seats to parties.
2. District magnitude.
3. Use of electoral thresholds.
4. Type of party list employed.
PR systems use either quotas or divisors to allocate seats.

Quotas

Quota: the 'price' in votes a party must pay to guarantee a seat in a district.
Quota, Q(n), is calculated as Q(n) = rac{Vd}{Md + n}
- V_d: valid votes in district d.
- M_d: district magnitude or number of available seats in district d.
- n: modifier of the quota.
Hare quota: n = 0.
Hagenbach-Bischoff quota: n = 1.
Imperiali quota: n = 2.
Reinforced Imperiali quota: n = 3.
Droop quota: Hagenbach-Bischoff quota plus 1.

Hare Quota with Largest Remainders

A list PR system that doesn’t employ quotas to allocate seats to parties is known as a divisor or highest average system
Remainder seats are allocated using the largest remainder method: the party with the largest remainder gets the seat.

Divisor Systems

Divisor, or highest average, system: divides the total votes won by each party by a series of numbers (divisors) to obtain quotients. District seats are allocated according to 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.
The larger the district magnitude, the greater the degree of proportionality.

Electoral Threshold

Electoral threshold: the minimum level of support a party needs to obtain representation.
Natural threshold: a mathematical by-product of the electoral system.
Formal threshold: explicitly written into the electoral law.
Electoral system proportionality is low when the electoral threshold is high.
Negative side-effects:
- Turkey 2002: 46% of votes were wasted.
- Poland 1993: 34% of votes were wasted.

Party Lists

Closed party list: the order of candidates elected is determined by the party.
Open party list: voters can indicate their preferred party and their favored candidate within that party.
Free party list: voters have multiple votes they can allocate either within a single party list or across different party lists.

Single Transferable Vote (STV)

STV: candidate-centered preferential voting system in multimember districts without a party list.
Candidates surpassing a quota of first-preference votes are immediately elected. In successive counts, votes from eliminated candidates and surplus votes from elected candidates are reallocated until all seats are filled.
Example: District magnitude is 3, 20 voters, 5 candidates: Bruce, Shane, Sheila, Glen, and Ella.
Droop quota: [20 / (3 + 1)] + 1 = 6

Mixed Electoral Systems

Mixed electoral system: voters elect representatives through two different systems, one majoritarian and one proportional.
Most mixed systems employ multiple electoral tiers.
Electoral tier: a level at which votes are translated into seats. The lowest is the district level; higher tiers are regional or national.
In a mixed system, a majoritarian system is used in the lowest tier (district level), and a proportional system is used in the upper tier (regional or national level).

Types of Mixed Systems

Independent mixed electoral system: majoritarian and proportional components are implemented independently.
Dependent mixed electoral system: the application of the proportional formula depends on the distribution of seats/votes produced by the majoritarian formula.

In most dependent mixed systems, individuals have two votes:
- One vote for the representative at the district level (candidate vote).
- One vote for the party list in the higher electoral tier (party vote). Dependent mixed systems are more proportional.