Electoral Formulas

Question 1

What are Electoral Formulas?

Answer 1

The mathematical method for coverting votes into seats

The formulas is the main method used to distinguish and classify the types of electoral systems

Question 2

What is the most common criterian used for classifying electoral sysstmes?

Answer 2

Electoral formula

it is basically classifying electoral systems by their proportionality

Question 3

What are the 3 families of electoral systems?

Answer 3

Majoritarian, Proportional, and Mixed

Question 4

Which electoral systems are in the Majoritarian family?

Answer 4

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

Question 5

Which electoral systems are in the Proportional Representation family?

Answer 5

List PR (Open/Ordered/Closed) and STV

List System, PR formulas
Single Transferable Vote

Question 6

Which electoral systems are in the Mixed family?

Answer 6

Parallel and MMP

Mixed-member proportional
Parallel system

Question 7

Which electoral systems are not in the 3 main families?

the others

Answer 7

SNTV, LV, BC

Single Non-transferable Vote
Borda Count

Question 8

Which electoral system is used most by democracies?

Answer 8

Proportional Representations (53%)

Question 9

FPTP

Answer 9

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

Question 10

AV

or IRV (instant run-off voting)

Answer 10

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

Question 11

TR

Answer 11

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)

Question 12

Majoritarian System in MMD

Answer 12

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)

Question 13

Party Block Vote (PBV)

Answer 13

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.

Question 14

Block Vote (BV)

Answer 14

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.

Question 15

Proportional Systems Overview

Answer 15

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)

Question 16

List PR

Answer 16

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

Question 17

What are the 2 main categories of PR Formulas?

Answer 17

1. Highest Average Formulae (divisor)
2. Largest Remainders (quota)

1. 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)
2. 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.

Question 18

Highest Average Formulae (divisor)

Answer 18

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, ….)

Question 19

Largest Remainders

Answer 19

• 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)

Question 20

Seat allocation formulaes of PR ranked in order of proportionality

Answer 20

1. Danish
2. LR-Hare/Sainte-Lague
3. Modified Sainte-Lague
4. LR-Droop
5. D’Hondt
6. LR-Imperiali
7. Imperiali highest averages

Perfect proportionailty is impossible

Question 21

STV

Answer 21

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.

Question 22

The Irish System

Answer 22

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

Question 23

Mixed Systems

Answer 23

Integrates 2 distinct principles of representation (proportional/Majoritarian)

Parallel systems and Mixed Member Proportional (MMP) systems

Question 24

MMP

Answer 24

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

Question 25

The German Electoral System

Answer 25

Mixed Member System of PR with a 2 tier districting system ## Footnote - 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

Question 26

Überhangmandate

Answer 26

Overhang Seats in the German Budenstag ## Footnote - 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

Question 27

Borda Count

Answer 27

Prefential system used is SMD and MMD | Used to elect the UN Secretary General ## Footnote 1. Voters rank each candidate based on their preferences 2. The formula assigns points to voters' preferences: with x candidates, x points are given to 1st preferences -> x-1 points to 2nd prefernces -> ect 3. Candidates are ranked by the total # of points theyy receive and the candidate w/ the most points wins

Question 28

SNTV

Answer 28

Single Non-Transferable Vote ## Footnote - 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

Question 29

Limited Vote

Answer 29

Like SNTV, but gives voters more than 1 vote. Unlike block vote, not as many as there are seats to be filled

Question 30

Thresholds

Answer 30

The minimum level of support which a aprty needs to gain representation

Question 31

Legal Thresholds (explicit)

Answer 31

Legally imposed thresholds writrten into the constitutional or legal provisions requited for representation in the legislature ## Footnote 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

Question 32

Effective Thresholds

Answer 32

Exist as a mathematical property of the electoral system ( bc of district magnitude's important role) | or implicit thresholds or natural thresholds ## Footnote - 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

Question 33

Majoritarian Systems (in general)

Answer 33

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) ## Footnote - 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.

Question 34

Is it possible to use a proportional system to elect a single winner to a unique position?

Answer 34

NO! | (you can't divide 1 president proportionally)