The Irish Single Transferable Voting (STV) system functions similarly to the regional list system of Norway, in that representatives are elected in multimember districts, but it does not have any compensatory layer. In addition, the STV system is an individualized system that does not rely on the notion of party affiliation in assigning votes. Rather, voters use ranked ballots in which they indicate their preferences between the various candidates. During the counting process, individual ballots are initially assigned to the top-ranked candidate on each ballot. If a candidate receives more votes than the ‘quota’ required to be elected, that candidate is elected and the surplus fraction of each ballot currently assigned to that candidate is transferred to the next-named candidate on the ballot who remains in the running. After all surpluses have been dealt with, the lowest-ranked candidate is removed and the ballots currently assigned to that candidate are transferred as described above. The process repeats until the required number of candidates have been elected.
In principle, we would calculate the Legislative Power Share scores on a ballot-by-ballot basis and include the effect of fractional ballot allocations.
Unfortunately, however, ballot-level data is not publicly available. We have therefore introduced a simplification in which we consider the total number of ballot-equivalents received by elected representatives. In the counting process, most candidates accumulate a total number of ballots equal to the quota required to be elected, with any surplus ballot fractions being transferred to other candidates. In the final rounds of the count, the final candidate to be elected has typically received less than a full quota’s worth of votes, and other candidates may have received slightly more (if surplus transfers are not required to determine the final outcome, they are not carried out). A given voter may have their ballot allocated in part to more than one candidate, but since we cannot track this fractionation process, we treat each ballot-equivalent that an elected candidate receives as representing one distinct voter.^{1}
Within each region, then, we calculate the LPS for a given elected candidate c as LPSc = Q / Vc, where Q is the national quota, as defined earlier for Norway and New Zealand, and Vc is the equivalent number of votes received by candidate c. For example, in the 2020 Irish election, 2.2 million voters cast votes for 160 elected representatives, which gives an average quota, Q, of 13,647 votes per seat. To calculate the Legislative Power Share score for a voter who helped elect a representative, we divide this number by the total number of votes that the elected representative received. For example, in Carlow-Kilkenny, Kathleen Funchion was elected with 12,274 votes, so these voters are assigned an LPS score of 13,647/12,274 = 111.2%.^{2}
The net effect of this simplification on our calculation of the LPS scores is likely negligible - since most candidates win with approximately one quota’s worth of votes, the LPS contribution of each elected representative to a given voter’s LPS score will be very close to the fractional portion of the voter’s ballot applied to each elected representative, so there will be negligible differences if a ballot is treated as distributed or unitary. Some voters will, in practice, have slightly lower LPS scores than we calculate because some fraction of their ballot value may not have been fully used up, while we treat them as having used their whole ballot. For example, suppose 100 voters exist who in actuality have each used 80% of their ballot weight towards elected representatives. We will end up approximating this group of voters as 80 voters who used their ballots up entirely, and 20 voters who did not contribute to electing a representative. The net effect of our approximation will be to slightly exaggerate the overall disparity present in the actual election. Since we are trying to demonstrate that proportional voting systems exhibit lower disparity than First Past the Post, an error that slightly exaggerates the disparity in a proportional voting system will tend to understate any differences we do find. ↩︎
We also make one small adjustment in one particular electoral district in each election to accommodate a special convention under the Irish system in which the out-going chair of the legislature is automatically re-elected and so does not stand for election. This has the effect of reducing the number of seats up for election in the chair’s electoral district. For example, in the 2020 election, the district of Kildare South, which normally elects four representatives, only elected three for this reason. We handle this by treating the district as one with only three seats. This has the net effect of reducing the LPS scores for the voters in that district as the effective number of voters per seat being contested in the district is larger than one might otherwise expect. ↩︎