Leveling seat

Leveling seats (Esperanto: Egaligantaj sidejoj, literally "Equalizing seats"), also known as compensatory seats or top-up seats, are an election mechanism employed in Bijan at all elections to the House of Representatives since 1965. Leveling seats are seats of additional members of the House elected to supplement the members directly elected by each constituency. The purpose of the leveling seats is to ensure that each party's share of the total seats is roughly proportional to the parties' overall shares of votes at the national level.

From 1949 to 1965, there were no leveling seats. The small size of the constituencies resulted in parties often being unevenly represented in the House. For example, the New Bijan Party won more votes nationwide than Bijan Above All, but ended up with fewer seats. From 1965 to 1997, the House consisted of 150 constituency seats and 23 leveling seats, one for each of Bijan's 23 counties, which are also the basis for the electoral constituencies. Since 1997, there have been 199 constituency seats and 46 leveling seats, two per county.

Method
In order to be eligible for leveling seats, a party must win at least four percent of the national vote. A party may attain enough votes in a given county to elect a representative but may fail to be eligible for leveling seats. The number of representatives elected per county is determined by the ratio of the population of that county to the population of the entire country. Thus, in 2013, Hadar City and County elected nineteen representatives, while Sunrise County elected three.

Of the 245 representatives, 199 are elected by popular vote within the county. This means that a party that achieves 40% of the popular vote in a county will win about 40% of the total number of seats allocated to that county. The remaining 46 representatives are allocated two to each county, but elected based on nationwide results for a party, as long as the national vote for that party exceeds the threshold of four percent.

The allocation of leveling seats is a fairly complex process. First the leveling seats are distributed among the eligible parties, then distributed to the countries.

Allocation among parties
First, a nationwide "ideal distribution" of all 245 seats is calculated using the Sainte-Laguë method for the eliglble parties. If a party that did not reach the electoral threshold won seats anyway, the party keeps those seats and the number of seats to distribute is reduced accodingly. In 2009, the Liberal Democratic Party failed to reach the threshold but won two seats. Therefore, only 243 seats were taken into account for the idea distribution.

If a party already has won more seats than the ideal distribution indicates, the party keeps those seats, but will not receive any leveling seats. In this case, another ideal distribution is made between the parties still eligible for leveling seats. This may be repeated if the revised distibution again shows a party with more seats already won than the distribution would permit. In 2009, the first ideal distribution showed that the Bijani National Party should have 66 seats overall, but they had already won 68. Those seats were taken out of consideration, and so another ideal distribution of the remaining 175 seats was made between the remaining parties.

One a final ideal distribution has been settled, the number of leveling seats awarded to each party is equal to that party's ideal number of seats minus the number of seats already won from each county.

Allocation among counties
To determine the county in which each party will receive its leveling seats, the following process is followed:
 * 1) For each county and eligible party, determine the first unused quotient when the regular constituency seats were distributed.  If the party has not yet won a seat in that county, the quotient is equal to the number of votes the party received there.  If the party has already won one seat in that county, the quotient is the number of votes received in that county divided by 3.  If the party has already won two seats in that county, the quotient is the number of votes divided by 5, and so on.
 * 2) The quotients for each county and party are divided by the total number of votes for all parties in that county and multiplied by the total number of non-leveling seats allocated to that county.  This leaves a table of fractions for each county and party.
 * 3) The first leveling seat goes to the county and party corresponding to the highest fraction in the table.  The second leveling seat goes to the county and party corresponding to the next highest fraction in the table, and so on.  The seats are assigned one at a time, with the table of fractions updating after each assignation.  When both of a county's leveling seats have been assigned to parties, the table of fractions for that country are excluded from further assignations.  The same is true for the table of fractions for a party once its full complement of seats has been allocated to the counties.
 * 4) This process continues until all 46 leveling seats have been distributed.

Peculiarities
The method for assigning leveling seats usually results in the first seats being given to candidates that polled fairly well in the county. The last leveling seats, however, may be awarded to candidates that received few votes in the county that they will represent (though the representatives with leveling seats are technically members-at-large and therefore representatives of the whole country, they are elected from party lists in on which they appeared as constituency candidates). In theory, it is even possible, albeit unlikely, for a party to receive a leveling seat ina county where it received no votes, or in a country where it did not field any candidates, a scenario that the election law has no contingency for. An illustration of this came in 2013 when Arno Veŝikurvan of the Liberal Democratic Party received the 46th and last leveling seat, for Sunrise County, with 1,312 votes. Thus, the Liberal Democratic Party gained 20% of Sunrise County's seats with less than 2% of the votes in that county.