1. Computation of Local and Regional Elections
In the local and regional electoral system in Denmark every single municipality (98 in total) or region (5 in total) constitutes an independent unit.
2. Number of Seats
In municipalities, seats must be an odd number between 9 and 31, except in Copenhagen whose City Council consists of 55 members. In regions, the number of seats is 41. The number of seats in local council elections depends on any prior resolution of the sitting local council for the coming election period. The number of local council members is laid down in the local statute.
If the local council wants to change the number of its members, such amendment must be adopted not later than 1 August in the election year, to take effect from the next election period. The local council must make known the number of members to be elected by public announcement printed in the local media not later than 13 weeks before the election day.
3. Lists of Candidates in Local and Regional Elections
A person intending to stand for government in local and regional elections must be entered in a list of candidates. A list of candidates may be submitted to the election committee by a political party, a group of local voters (local list) or a single individual, without any distinction being made between different types of list of candidates. A list of candidates must not state more than four names in excess of the number of members to be elected in the municipality or region.
In order to register a list of candidates in local or regional elections the list of candidates must be recommended by a number of voters resident in the municipality, known as supporters. This means that a list of candidates in local council elections must be signed by at least 25 voters in the municipality as supporters. The number of supporters required for the City of Aarhus, Odense and Aalborg is 50 and 150 for the City of Copenhagen. The number of supporters signing the list of candidates must not exceed the equivalent of twice the minimum number of supporters in the municipality, i.e. between 50 and 100 I Aarhus, Odense and Aalborg, between 150 and 300 supporters in Copenhagen, and between 25 and 50 in the other municipalities. A list of candidates in regional council elections must be signed by at least 50 voters in the region as supporters. The lists of candidates must be signed by a number of supporters not exceeding the equivalent of the minimum number of supporters in the region by more than 50 per cent, i.e. 75 supporters.
A list of candidates which was elected at the latest local or regional election and is still represented in the local or regional council can by request be released from the requirement of signatures from a number of supporters.
The election committee approves the lists of candidates and assigns letters to the approved lists of candidates. Lists of candidates for a party that on 1 August in the election year is entitled to stand for Parliament must as list designation use the party’s name in general elections, or a designation of which this name forms a part. These parties are allotted the party letter that they were allocated in connection with general elections. No other list of candidates may as list designation use the name of any of the above parties, or a designation of which this name forms a part, or which may cause the list of candidates to be indistinguishable from lists of candidates for one of these parties. Single letters (A, B, C, etc.) or a combination of letters that does not form a word (RV, CD, SF, KRF, etc.) cannot be used as designation for a list.
4. Election and List Coalitions
Seats are allocated among the registered lists of candidates according to the d’Hondt formula. Lists of candidates that have been assigned the same letter may form list coalitions to support each other. Lists of candidates with different letters may form election coalitions. A list coalition may also form an election coalition.
The d’Hondt formula favours the big lists of candidates, however only to a limited extent and particularly when one party is comparatively much larger than the others. This tends systematically to give major parties a larger share of seats, with a lesser share being available for minor parties if compared with other methods of distribution. The lists of candidates may counteract the tendency to favour the big lists by forming election or list coalitions. Establishing the largest possible ”units” reduces the waste of votes in connection with the allocation of seats and diminishes the tendency to overrepresentation by major lists. Even major local lists may sometimes form election and/or list coalitions in order to secure the largest possible number of seats.
5. Allocating Seats Among Lists of Candidates
Seats are allocated among the registered lists of candidates according to the d’Hondt formula, whereby the aggregate number of votes for each election coalition, list coalition (not having formed election coalitions) and each list of candidates which has not formed a list coalition or an election coalition, is divided by 1, 2, 3 and so on. Divisions continue until all seats have been distributed. The size of the established quotients then determines the number of seats for each party. The size of the established quotients also determines the order of priority, thus allocating the first seat in the local council or the regional council to the election coalition, list coalition or the list of candidates that has the largest of the established quotients. The second largest quotient authorizes the second seat, and this procedure is applied repetitively until all seats in the local council or the regional council have been allocated. If the quotients are equal, seats are allocated by drawing lots.
If an election coalition, a list coalition or a list of candidates is attributed more seats than nominated in the list of candidates and list coalitions included in the election coalition, list coalition or the list of candidates, the remaining seat or seats are transferred to the election coalition, list coalition or list of candidates next in line to qualify according to the d’Hondt formula, i e the election coalition, list coalition or list of candidates that has the second largest quotient.
5.1. Example of Seat Allocation
Suppose nine lists of candidates are registered in an election, and 11 candidates are to be elected. Lists O1 and O2 have formed a list coalition (O), and lists P1, P2 and P3 have also formed a list coalition (P).
List coalitions O and P have formed an election coalition. Furthermore, lists T1 and T2 (T) have formed a list coalition, and list coalitions T and U have formed an election coalition.
List coalitions (O: O1 + O2, P: P1 + P2 + P3, T: T1 + T2)
Election coalitions (O + P, T + U)
First, the votes are distributed among lists of candidates, list coalitions and election coalitions. Then the 11 seats are allocated among lists of candidates, list coalitions and election coalitions based on the d’Hondt formula.
List of candidates

N

O1

O2

P1

P2

P3

T1

T2

U

Number of votes

444

57

73

28

38

27

54

129

70

List coalition


130

93

183


Election coalition


223

253

Divided by 1

444 (1)

223 (3)

253 (2)

Divided by 2

222 (4)

111.5 (7)

126.5 (6)

Divided by 3

148 (5)

74.333 (11)

84.333 (10)

Divided by 4

111 (8)

55.75

63.25

Divided by 5

88.8 (9)



Divided by 6

74



Number of seats

5

3

3

When the votes have been distributed among the lists of candidates, list coalitions and election coalitions, the seats are allocated to the list coalitions, election coalitions or lists of candidates participating in the election and not having formed a coalition. The numbers in parenthesis indicate the order in which seats are allocated. The 11 largest quotients trigger seats to the lists. The list of candidates N is credited with the first seat for being the list that has obtained the largest quotient. The second seat goes to the election coalition between list coalitions T and U for having obtained the second largest quotient after the first division and so on.
Election coalition O and P has obtained three seats, no 3, no 7 and no 11, and has to split these between them by number of votes, based on the same formula. This means that the seats are allocated to the list coalition that by priority has obtained the largest number of votes.
List coalition

O

P

Number of votes

130

93

Div 1

130 ^{(3)}

93 ^{(7)}

Div 2

65 ^{(11)}

46.5

Div 3

43.333

Number of seats

2

1

The list coalition O1 and O2 has obtained two seats, no 3 and no 11, and has to split these between them by number of votes, based on the same formula.
List of candidates

O1

O2

Number of votes

57

73

Div 1

57 ^{(11)}

73 ^{(3)}

Div 2

36.5


Number of seats

1

1

The list coalition P1, P2 and P3 has obtained one seat, which is allocated to the list having obtained the largest number of votes, i e list P2.
The election coalition T and U has obtained three seats, no 2, no 6 and no 10.
List of candidates

T

U

Number of votes

183

70

Div 1

183 (2)

70 (10)

Div 2

91.5 (6)

35

Div 3

61

Number of seats

2

1

The list coalition T1 and T2 has received two seats, no 2 and no 6.
List of candidates

T1

T2

Number of votes

54

129

Div 1

54

129 (2)

Div 2

64.5 (6)

Number of seats

0

2

Hence, the result is:
List of candidates N

5 seats

(no’s 1, 4, 5, 8 and 9)

List of candidates O1

1 seat

(no 11)

List of candidates O2

1 seat

(no 3)

List of candidates P2

1 seat

(no 7)

List of candidates T2

2 seats

(no’s 2 and 6)

List of candidates U

1 seat

(no 10)

6. Selection of Candidates
Once it is established how many seats each of the registered lists is to fill in the local council, an equivalent number of individuals has to be picked from the eligible lists of candidates. The procedure for the selection of candidates depends on the form of list organization registered by the list of candidates. The list of candidates can be put up as a party list or a ”parallel” form of list organization. Both the form of list organization and the number of the candidates’ personal votes influence the selection.
6.1. Party List Organization
When a list of candidates has registered a party list, it means that the candidates are nominated in a fixed order. In this case the returns of the candidates are computed according to the following procedure:
 The total number of votes for the list of candidates is divided by an integer of one higher than the number of seats allocated to the list of candidates.
 The established number is increased to the next integer, even if it is itself an integer.
 This number hence constitutes the distributional number for the list of candidates (Droop’s quota).
 Candidates who have obtained a number of personal votes equal to or larger than the distributional number are elected.
 Candidates who have obtained fewer personal votes than the distributional number are allocated seats by order of appearance in the party list, by adding as many of the list votes to the number of the relevant candidates’ personal votes to make them arrive exactly at the distributional number. The aggregate of personal votes and list votes thus constitutes the distributional number. Candidates that in this way obtain a number of votes equal to the distributional number are elected.
 If, after allocation of seats to the list of candidates, seats are still left vacant, the other candidates are elected by priority of the size of the number of their votes (personal and list votes combined). If two or more candidates hold an equal number of votes, the candidate or candidates higher on the party list are elected.
By choosing a party list, the party organization maximizes its influence as to which candidate is elected.
6.2. Example of Selection of Candidates and Determination of Order of Party List Substitutes
A list of candidates with 11 candidates has received a total of 444 votes, of which 272 are personal votes and 172 are list votes. The list is allocated five seats, and the distributional number for the list is 444:(5+1)=444:6=74, increased to 75. The personal votes cast for each individual candidate and the allocation of list votes are as stated below:
Candidate:

Personal votes

List votes

Total

Elected

Substitutes

no 1

30

45

75

no 1

no 2

10

65

75

no 2

no 3

18

57

75

no 3

no 4

14

5

19

no 3

no 5

17

17

no 4

no 6

7

7

no 6

no 7

79

79

no 4

no 8

20

20

no 2

no 9

43

43

no 5

no 10

23

23

no 1

no 11

11

11

no 5

Aggregated

272

172

444

5

6

Candidates having obtained the distributional number or above are elected first, i.e. no’s 1, 2, 3 and 7. These are elected by order of appearance in the list of candidates. Candidate no 9 is elected for being the candidate who among the candidates failing to obtain the distributional number has the largest number of votes. Nonelected candidates become substitutes. The numbering of substitutes reflects the return by priority of the size of the number of their votes, regardless of ballot paper position. Hence, the six nonelected candidates become substitutes in the following order: no’s 10, 8, 4, 5, 11 and 6.
6.3. Standing in Parallel
If standing in parallel, a candidate is elected on the exact size of the number of his personal votes. This means that the seats of the list of candidates are allocated to the candidates in priority of the size of the number of their personal votes. In the event of a tie, the election committee draws lots.
Since access to standing in parallel was introduced in connection with the amendment of the local government act in 1985, its popularity has steadily increased. Increasing its use from 48 per cent in 1985 to 74 per cent in 2001, standing in parallel suddenly dropped to 70 per cent in 2005. As there are only two forms of list organization in local and regional council elections, the share of party list organization has taken the opposite course.
7. Actual Thresholds
It sometimes happens that a party is allocated a number of seats in the local council or the regional council that represents a higher seat/vote ratio than the seat/vote ratio obtained by the party in question. There are several explanations why such lopsided results may appear. One of the reasons is that a certain type of threshold exists even in local and regional elections, though the Local and Regional Government Elections Act does not mention it. The explanation for these thresholds not being mentioned in the Local and Regional Government Elections Act is that there are no compensatory seats at the lowertier level, and all seats can and must be directly allocated as described above. Nevertheless there are some ”natural” electoral thresholds setting a lower limit for representation of small parties in local councils.
In reality, there are two thresholds to consider:
 Exclusion threshold: a list of candidates risks exclusion from representation if the vote share of the list of candidates is below this value. The exclusion threshold is calculated using the d’Hondt formula as 2/(m+1), where m represents the number of seats to be distributed.
 Representation threshold: a list has a possibility of representation, in theory, if its vote share lies above this value, whereas it has no chance of representation if its vote share lies below this value. The calculation is based on the d’Hondt formula as 1/m+n1), where m represents the number of seats to be distributed and n represents the number of units, i e the sum of independent lists of candidates, and election and list coalitions included in the distribution at a given level.
The actual sizes of the two threshold values depend largely on the number of seats to be distributed in the constituency. This number must therefore be known before the two threshold values are calculable for specific municipalities and in specific elections. The representation threshold also depends on how many ”units” are included in the calculations, and this number must also be known before the value can be calculated. Usually the threshold values can be calculated only after expiry of the last day of registration.
The exclusion threshold and the representation threshold vary according to combinations of number of seats and number of registered parties, lists and election coalitions in local and regional elections. It is also possible to calculate the threshold values for an election coalition. For an election coalition that receives three seats, one quarter of the total number of party votes in the election coalition is required to secure a seat.
The threshold values may become very important if e g prior to an election a local council decides to cut the number of local council seats, which the law allows them to do. This will increase the two threshold values, to imply that parties that after the amendment find themselves below the increased threshold values (though previously above), are excluded and vice versa.
The larger the number of seats to be distributed, the lesser the share of votes required to secure representation. The grey area between the representation threshold and the exclusion threshold, i e between the possibility, in theory, of being represented (the absolute threshold) and the value that secures representation of a party or a list, diminishes the more seats that have to be distributed.
There is a slightly higher probability of representation, at least in theory, in case of more parties, as this will widen the spread of votes and the scope for distribution of seats.
* J. Grønnegård Christensen, E. Damgaard and J. Elklit: Valg, parlamentarisme og forvaltning, Academica, 2007, pp 61.