The Norwegian Storting electoral system, as amended for the September 12, 2005 election, provided for a two-tier allocation of parliamentary seats by proportional representation. The process consisted of three steps, namely:

• Distribution of Storting Constituency Seats
• Nationwide Allocation of Storting At-Large Seats
• Distribution of At-Large Seats by Constituency

Distribution of Storting Constituency Seats

The distribution of Storting seats in the 2005 election began with the allocation of seats in each one of Norway's nineteen multi-member constituencies. To calculate the number of seats a party list was entitled to receive in a given constituency, the votes polled by each of these were divided by an adjusted sequence of odd numbers starting with 1.4 and continuing with 3 (1.4, 3, 5, 7, 9 and so on - that is, the sequence 0.7, 1.5, 2.5, 3.5, 4.5 and so on, multiplied by two in order to obtain whole numbers from the second divisor onwards), until enough quotients had been found to allocate all constituency seats. This procedure is known as the modified Sainte-Laguë method. Unlike the pure Sainte-Laguë method, the modified procedure features a larger initial divisor (1.4 instead of 1), in order to make it more difficult for smaller parties to initially win seats; otherwise, both methods are identical.

There was no statutory threshold for participation in the allocation of constituency seats, but the application of the modified Sainte-Laguë rule introduced a de facto threshold at the county level.

For example, Østfold county - located in southeastern Norway - was allocated eight constituency seats, which were distributed by the modified Sainte-Laguë method in the following manner (votes in parentheses; results for minor parties not shown):

Seats were then awarded to the parties obtaining the largest quotients, shown in bold. The distribution of constituency seats could also be obtained by dividing the votes for each party by the smallest quotient used to allocate seats, multiplied by two; if the integer part of the division was greater than or equal to one, remainders larger than or equal to 0.5 were rounded up to the next whole number, but if the integer part of the division was equal to zero, only remainders larger than or equal to 0.7 were rounded up to one. In Østfold county, the votes obtained by each party would be divided by the 15th largest quotient times two - 7,657.857 x 2 = 15,315.714, truncated to 15,315 - with the following results:

The eighth largest quotient times two was equal to the eighth largest quotient resulting from successive division of party list votes by 0.7, 1.5, 2.5, 3.5, 4.5 and so on. In turn, this number multiplied by 0.7 was the effective representation threshold: the number of votes necessary to secure one constituency seat. For Østfold county, this threshold was equal to 7.2% of the vote.

For the 2005 legislative election, the allocation of Storting constituency seats by the modified Sainte-Laguë method produced the following effective thresholds:

Each constituency returned an average of eight seats, and the effective representation threshold - the number of votes needed to secure a seat according to the application of the modified Sainte-Laguë rule - emerged as a significant barrier for participation in the proportional allocation of constituency mandates. As such, the lack of a statutory threshold became completely irrelevant.

In fact, the modified Sainte-Laguë method tends to favor large and middle-sized parties, particularly as the constituency size diminishes: generally speaking, the effective representation threshold, as a percentage of the total vote, increases as the number of seats to be allocated decreases. In turn, this pattern is amplified by the cumulative effect of the application of the modified Sainte-Laguë rule over mostly small-to-medium-sized constituencies.

The result of the 2005 Storting election after the distribution of all 150 constituency mandates in the counties was as follows:

Had the allocation of Storting mandates concluded at this point, there would have been significant differences between the distribution of votes and seats: most notably, the Labour Party would have emerged significantly over-represented (40.7% of the seats with 32.7% of the vote), while the Christian Democratic Party, despite outpolling both the Center Party and the Liberal Party, would have obtained fewer seats than either of the these parties and would have come up clearly under-represented (just 2.7% of the seats with 6.8% of the vote).

However, since 1989 the Storting also includes a number of additional seats, whose purpose is to bring about a more proportional allocation of parliamentary mandates. These seats - increased in 2005 from eight to nineteen - are known as at-large seats because, unlike constituency seats, they are initially apportioned at the national level.

Nationwide Allocation of Storting At-Large Seats

Once all constituency mandates were allocated, the following step was to distribute all 169 Storting seats among qualifying parties on a nationwide basis. The seven parties that had already secured representation at the constituency level had all polled at least four percent of all valid votes cast, and were entitled to participate in the proportional distribution of seats at the national level. None of the other parties that ran in the election reached the four percent threshold; consequently, these were excluded from the apportionment process.

The number of seats each one of the seven qualifying parties was entitled to receive was also determined the modified Sainte-Laguë method, as shown below:

Then, the total number of constituency seats obtained by each party was subtracted from the number of seats allocated to the party on a nationwide basis:

As it was, the Labour Party won more constituency seats than the total number of seats it was entitled to at the national level. Labour kept the additional seats, but the 61 constituency seats won by the party were subtracted from the total number of Storting seats, and the distribution of the remaining 108 Storting seats was repeated among the other qualifying parties. However, the new distribution gave the Progress Party a total of 37 seats - one seat below its constituency seat total. Consequently, that party kept the extra seat as well, but its 38 constituency seats seats were also subtracted from the nationwide total, and the remaining 70 Storting seats were apportioned among the other parties, as shown below:

This time, no party won fewer seats at the national level than constituency seats. The number of at-large seats allocated to each party was then obtained by deducting the constituency seats won by the party from its corresponding nationwide seat total:

Consequently, the definitive outcome of the 2005 Storting election was as follows:

Labour ended up slightly over-represented in the Storting, but all the other parties secured representation in close proportion to their actual voting strength.

Distribution of At-Large Seats by Constituency

Having allocated all nineteen at-large seats on a nationwide basis, all that remained was to distribute these seats among constituency party lists. To that end, for each constituency a ratio of votes to seats was calculated by dividing the total number of valid votes cast by the corresponding number of constituency seats. Then, for each list in the constituency belonging to a party that received at-large mandates, a seat quotient was calculated by dividing the list's first unused Sainte-Laguë quotient (if it had at least one constituency seat) or the total number of votes obtained by the list (if it had no constituency seats) by the ratio of votes to seats.

For example, in Østfold county a total of 148,243 valid votes were cast in the election, so the constituency's ratio of valid votes to seats was:

And the Østfold county party seat quotients were as follows:

As previously noted, the Conservative Party and the Socialist Left Party had each won one seat in the constituency, so their first unused Sainte-Laguë quotients were 5,899 and 3,573.7, respectively. The Christian Democratic Party, the Center Party and the Liberal Party won no seats in the constituency, so their respective party vote totals were used to calculate their corresponding party seat quotients.

The seat quotients from all constituencies were then sorted in descending order, and the largest quotients were allocated to their corresponding constituency party lists, but in a manner such that each constituency received exactly one at-large seat, and each party obtained exactly the number of at-large seats it had been allocated on a nationwide basis. Thus, once an at-large seat was assigned to a constituency, the seat quotients for the remaining parties in that constituency were disregarded and could not be used to obtain further seats. Likewise, once a party filled its quota of at-large seats, its unused seat quotients in other constituencies were discarded.

After at-large seats were allocated to higher-placed seat quotients in Akershus (for the Center Party), Oslo (for the Christian Democratic Party) and Hedmark (for the Conservative Party), Østfold county's at-large seat was also awarded to the Christian Democrats: the party's seat quotient was used to fill the seat because the constituency's at-large seat had not been previously allocated, and up to this point the party had filled only one of its seven at-large seats. Therefore, the definitive allocation of Storting seats for Østfold was as follows:

In most constituencies, at-large seats went to the parties with the highest seat quotients. However, the Liberal Party was awarded all of its four at-large mandates in constituencies where other parties had obtained higher seat quotients, but could not use them as they had already filled all of their at-large seats elsewhere. The most extreme example of this situation took place in Finnmark county (located in northeastern Norway), where the Liberals received the last at-large mandate to be allocated with a seat quotient of 0.08918 - the lowest figure in the constituency and in the entire country.