Electoral Formulas Flashcards
What are Electoral Formulas?
The mathematical method for coverting votes into seats
The formulas is the main method used to distinguish and classify the types of electoral systems
What is the most common criterian used for classifying electoral sysstmes?
Electoral formula
it is basically classifying electoral systems by their proportionality
What are the 3 families of electoral systems?
Majoritarian, Proportional, and Mixed
Which electoral systems are in the Majoritarian family?
FPTP, TRS, AV, BV, PBV
Refered to as the Plurality/Majoritarian family - Uses SMDs (not MMDs)
Plurality
Majority - First Past the Post
Alternative Vote
Two Round System
Block Vote
Party Block Vote
Which electoral systems are in the Proportional Representation family?
List PR (Open/Ordered/Closed) and STV
List System, PR formulas
Single Transferable Vote
Which electoral systems are in the Mixed family?
Parallel and MMP
Mixed-member proportional
Parallel system
Which electoral systems are not in the 3 main families?
the others
SNTV, LV, BC
Single Non-transferable Vote
Borda Count
Which electoral system is used most by democracies?
Proportional Representations (53%)
FPTP
First Past the Post / The Plurality
the simpliest form of the majoritarian system (in SMD)
- Uses SMD (single member districts) and candidate centered voting.
- The winner is the candidates witht he most votes (not necessarily and absolute majority of votes)
- USA/Canada/UK/India/Ethiopia/Nigeria/Kenya etc
AV
or IRV (instant run-off voting)
Alternative Vote: enables voters to express their preferences btw candidates rather than jsut thier first choice
a majoritarian electoral system in SMD
- candidate needs to win an absolute majority
- Used in SMD (single member districts)
- voters rank the candidates in the order of their choice -> if a candidate immedialty has the absolute majority they are elected, but if none do than the canddiates w/ the lowest # of 1st preferences is eliminated and their ballors are transfered to the cadidate that has the highest preference -> this is repeated until 1 candidate has the absolue majority
- Australia, Ireland, Papua New Guinea
TR
Two-Round System
a majoritarian electoral system in SMD - most common way to elect Prs/PM
- the winning candidate needs the absolute majority
- most commonly the 1st round is done FPTP -> if 1 candidate reaches and absolute majority they are immediatly elected… if not then the 2nd round is held
- 2 kinds of 2nd rounds in TR systems:
1- Majority run-off/Majority-Majority: the 2 most voted access the 2nd round (most common)
2- Majority-Plurality: mutliple candidates may access the 2nd the round (only a plurality is required for the 2nd round)
Majoritarian System in MMD
Block Vote (BV) and Party Block Vote (PBV)
Block Vote: FPTP applied to multi-member districts. Voters have as many votes as there are seats to be filled, and the highest-polling candidates fill positions regardless of the % of the vote they get
Party Block Vote: Voters have a single vote and the party (list) which wins the most votes takes alll of the seats in the district (winner takes all)
Party Block Vote (PBV)
Similar to block vote, with the change that voters vote for party lists instead of individual candidates. Voters have a single vote and the party (list) which wins msot votes takes all the seats in the district.
Block Vote (BV)
FPTP applied to MMD
Voters have as many votes as there are seats to be filled, and the highest-polling candidates fill the positions regardless of the percentage of the vote they acheive.
Proportional Systems Overview
Goal = to decrease the difference btw a party’s share of the national vote and its share of the parliamentary seats
- party lists: where political parties present lists of candidates to voters on a national or regional basis
- preferential in PR is doen thru STV (Single-transferable vote) where voters rank-order candidates in MMDs (Multi-member districs)
List PR
In MMDs, each party constructs a part list, voters vote for a party, parties receive seats in proportion to their overall share fo the vote in the electoral district. Winning candidates are taken from the lists in order of their positions on the lists.
The choice of List PR doesn’t completely specify the electoral system
What are the 2 main categories of PR Formulas?
- Highest Average Formulae (divisor)
- Largest Remainders (quota)
- Highest Average Formulae (divisor): allocate seats sequentially -> awading each seat to the party that presents the highest ‘average’ (average = the # of votes it won divided by a # reflecting the # of seats it has already been awarded)
- Largest Remainders: calculating a quota based on the # of votes cast and the # of seats to be awarded -> each aprty is then awarded as many seats as it has full quotas -> if this leaves some seats unallocated, the remaining seats fo to the parties with the most votes left over.
Highest Average Formulae (divisor)
Allocates seats sequentially.
A process of awarding each seat to the party that presents the highest ‘average’.
‘Average’ = the # of votes it won / a # reflecting the # of seats it has been already awarded
1 out of 2 main categories of seat allocation formulae in List PR
Danish (1,4,7,10,…)
St. Lague (1,3,5,….)
Modified St. Lague (1.33,3,5,…)
D’Hondt (1,2,3,…)
Imperial HA (1, 1.5, 2, 2.5, 3, 3.5, ….)
Largest Remainders
- 1st calculate a quota based on the # of votes cast and the # of seats to be awarded.
- Each oarty is then awarded as amnt seats as it has full quotas.
- If this leaves seats unallocated, the remaining seats go to the parties with the most votes left over
1 out of 2 main categories of seat allocation formulae in List PR
Hare (V/M)
Droop (V/M+1)
Imperiali (LR) (V/M+2)
Seat allocation formulaes of PR ranked in order of proportionality
- Danish
- LR-Hare/Sainte-Lague
- Modified Sainte-Lague
- LR-Droop
- D’Hondt
- LR-Imperiali
- Imperiali highest averages
Perfect proportionailty is impossible
STV
Single Transferable Vote
a type of proportional electoral formula in MMD
In MMD voters rank candidates in order of preference (like AV).
Quota = (votes/(seats+1))+1
Result determined thru a series of counts: 1- the total # of 1st preference votes for each candidate (any candidate with a # of 1st preferences > or = Quota is immediatly elected 2- the surplus votes of elected cadidates (votes above the quota) are redistributed according to the 2nd preferences on the ballot papers 3- after any count, if no candidate has surplus votes over the quota, the candidate with the lowest total of votes is eliinated and their votes are then redistributed in the next count ot the candidates left in the race according to the 2nd and then lower preferences shown.
The Irish System
STV
CALCULATE THE QUOTA: quota = threshold # of votes that if reached secures the election of a candidates. {Q = total # of valid ballots / (total # of seats to be filled +1) + 1}
1ST COUNT: andy candidates with 1st preferences = or > than the quota is elected.
2ND COUNT & SUBSEQUENT COUNTS: either the distribution of the surplis of an elected candidate or the exlusion of the lowest candidate(s) and the distribution of their votes
Mixed Systems
Integrates 2 distinct principles of representation (proportional/Majoritarian)
Parallel systems and Mixed Member Proportional (MMP) systems
MMP
Mixed Member Proportional System
A type of mixed electoral system -more proportional than parallel system
- Uses a PR seats to compensate for any disproportionality arising under the plurality/majority
- much country to country variance
- Usually voters have 2 votes: 1 for party 1 for local rep
- Germany, South Korea, Bolivia, New Zealand
- proportionality benefits of PR systems + ensures that elected representatives are linked to geographical districts
The German Electoral System
Mixed Member System of PR with a 2 tier districting system
- Each voter casts 2 votes (1 for a candidate in a SMD 1 for the 16 closed party lists for their region)
- Once the pary votes are known -> 4 stage process to determine composition of the Bundestag
- 1- any party that doesn’y meet 5% threshold is eleminated
- 2- LR St.Lague method is used to calculate how many seats the parties are entitled to overal (based on 2nd votes/list votes)
- 3- LR-St.Lague used to determine how many candidates for each party are drawn from each land
- 4- Winners of the district races are decucted from the # of seats accruing to each party in each Land and proportionality is established by drawing the appropriate # of cadidates from the Land party lists startinf at the top of the list.
- 5- A party can then win more plurality/majority seats in a Land than its party bote in the reion would entitle it. To deal with this the size of the legislature is increaed: the extra seats are claled overhang mandates or Uberhangsmandaten
Überhangmandate
Overhang Seats in the German Budenstag
- The 2 reasons for overhang seats: 1- High # of constituences won 2- Low # of party votes
- Overhang seats happen in elections in which a party is entitles to less seats according to party vote than it has won constituencies. These “overhanging seats” remain with the party.
- Can result from an unproportional distribtion of constituencies or a strong region-based support or the existanc eof regional parties
- The overhang seats are outside of proportionality, enlarge the # of seats and change the proportional composition of parliament
Borda Count
Prefential system used is SMD and MMD
Used to elect the UN Secretary General
- Voters rank each candidate based on their preferences
- The formula assigns points to voters’ preferences: with x candidates, x points are given to 1st preferences -> x-1 points to 2nd prefernces -> ect
- Candidates are ranked by the total # of points theyy receive and the candidate w/ the most points wins
SNTV
Single Non-Transferable Vote
- MMD (multi-memeber districts) but voting for candidates and not party lists
- The seats go to the candidates with the most votes
- not widely used
- even candidates from the same party are competing against themselves in this sustem -> strange stratefies
- each candidate is competing against every other candidate
- wasted votes
Limited Vote
Like SNTV, but gives voters more than 1 vote. Unlike block vote, not as many as there are seats to be filled
Thresholds
The minimum level of support which a aprty needs to gain representation
Legal Thresholds (explicit)
Legally imposed thresholds writrten into the constitutional or legal provisions requited for representation in the legislature
A high threshold -> likely to exclude smaller parties
….Turkey at 10%
A low threshold -> may promote smaller party representation
…. Israel at 1.5%
Threshold may also be different for coalition of parties
Effective Thresholds
Exist as a mathematical property of the electoral system ( bc of district magnitude’s important role)
or implicit thresholds or natural thresholds
- In smaller districts -> the effective threshold is higher (if there are only 3 seats avaiable then you must get 25% +1 of the vote to get a seat as a threshold)
- other factors: seat allocation formula, the # of contestant political parties, and the size of assembly
- effective threshold = [total # of votes / (# of seats+1)]+ the smallest possible # of votes
- or Effective threshold = [ V / (M+1) ] + E
Majoritarian Systems (in general)
The winning candidate must recieve an absolute majority: Uses 2nd preferences to get a winner with an absolute majority if none have one on the 1st round.
Alternative Vote & Two Round System(Majority run-off+Majority Plurality)
- Alternative Vote (Instant run-off): No 2nd round. IN SMDs voters rank candidates. The candidate with absolute majority is immediatly elected, if there is none than the one with the lowest # of 1st prefs is eleinated and each ballot is transferred to whichever remianing candidate has the highest preferences… repeat till a candidate has an absolute majority -> they are elected.
- Two Rounds System: 1st round uses FPTP. If a candidate recieves a specified proportion of votes, they are elected immediatley- if not then a 2nd rounf of voting happens
- Majority run-off (Majority-Majority): the 2 most voted access the 2nd round (most common)
- Majority-Plurality: multiple candidates may access the 2nd round, and only a plurality is required for the 2nd round.
Is it possible to use a proportional system to elect a single winner to a unique position?
NO!
(you can’t divide 1 president proportionally)
