2003 Icelandic parliamentary election

The available constituency seats are first distributed to each party according to the D'Hondt method, so that proportional representation is ensured within each of the constituencies. The next step is to apportion these party distributed seats to the candidates within the party having the highest "vote score", after counting both direct candidate votes and their share of party votes in the constituency. In Iceland the "candidate vote system" is that, for each constituency, each party provides a pre-ranked list of candidates beneath each party name (listed according to the preferred order decided by the party), but where the voters voting for the party can alter this pre-ranked order by renumbering the individual candidates and/or crossing out those candidates they do not like, so that such candidates will not get a share of the voter's "personal vote" for the party.[6][7]

As a restriction on the possibility of re-ranking candidates, it is however only possible to alter the first several candidates on the list. The borderline for alterations is drawn for the first three candidates if the party only win one of the total seats in the constituency, or if more than one seat is won the borderline shall be drawn at the pre-ranked number equal to two times the total number of seats being won by the party in the constituency. So if a party has won two seats in a constituency, then the voter is only allowed to re-rank the top four ranked candidates on the list, with any rank altering by voters below this line simply being ignored when subsequently calculating the candidate vote shares within each party. Final calculation of the candidate vote shares is always done according to the Borda method, where all candidates above the previously described borderline in the ranking are granted voting fraction values according to the voters noted rank. If the number of considered candidates consist of four (as in the given example), then the first ranked candidate is assigned a value of 1 (a so-called full personal vote), the next one get the value 0.75 (1/4 less), followed likewise by 0.50 and 0.25 respectively for the two last candidates. If the number of considered candidates instead had been six (due to winning 3 seats), then the first ranked candidate in a similar way would be assigned a value of 1 (a so-called full personal vote), with the following five candidates receiving respectively 5/6, 4/6, 3/6, 2/6 and 1/6. As mentioned above, crossed out names will always be allocated a 0.00 value. The accumulated total score of the candidates voting fractions, will be used in determining which candidates receive the seats won by their party. Note that candidate vote scores are not directly comparable to candidates from other parties, as how many seats are being won in a constituency by a particular party will effect how their candidates receive voting fractions (like in the above examples, where a candidate ranked number four for a party winning two seats would receive a voting fraction of 0.25, compared to 0.50 for an equally ranked candidate belonging to a party winning 3 seats)[6][7]

After the initial apportionment of constituency seats, all the parties that exceed the election threshold of 5% nationally will also qualify to potentially be granted the extra leveling seats, which seek to adjust the result towards seat proportionality at the national level.

The calculation procedure for the distribution of leveling seats is, first, for each party having exceeded the national threshold of 5%, to calculate the ratio of its total number of votes at the national level divided by the sum of one extra seat added to the number of seats the party have so far won. The first leveling seat will go to the party with the highest ratio of votes per seat. The same calculation process is then repeated, until all 9 leveling seats have been allocated to specific parties. A party's "votes per seat" ratio will change during this calculation process, after each additional leveling seat being won. The second and final step is for each party being granted a leveling seat to pin point, across all constituencies, which of its runner-up candidates (candidates that came short of winning direct election through a constituency seat) should then win this additional seat. This selection is made by first identifying the constituency having the strongest "relative constituency vote shares for this additional seat of the party", which is decided by another proportional calculation, where the "relative vote share for the party list in each constituency", is divided with the sum of "one extra seat added to the number of already won constituency seats by the party list in the constituency". When this strongest constituency has been identified, the leveling seat will be automatically granted to the highest placed unelected runner-up candidate on the party list in this constituency, who among the remaining candidates have the highest personal vote score (the same figure as the one used when ranking candidates for constituency seats).[6][7]

The above described method is used for apportionment of all the party allocated leveling seats. Note that when selecting which of a party's constituencies shall receive its apportioned leveling seat, this identification may only happen in exactly the same numerical order as the leveling seats were calculated at the party level. This is important because the number of available leveling seats are limited per constituency, meaning that the last calculated leveling seats in all circumstances can never be granted to candidates who belong to constituencies where the available leveling seats already were granted to other parties.[6][7]