With First Past the Post, a voter is said to have a share in a representative’s legislative power if their vote was counted for that representative (MP). To determine the legislative power share of a voter who voted for their MP, we first divide the average number of votes cast in that voter’s riding by the number of votes received by the elected MP. We then apply a weighting factor based on the relative size of that riding to adjust the share of each voter’s legislative power (since voters in ridings with fewer voters have more impact on the election of an MP than voters in ridings with more voters). Because the number of seats per province is set by federal law, we perform these calculations at a provincial level and do not include disparities arising from differences in the average number of voters per riding across provinces.

More specifically, we calculate the LPS score for an individual voter as follows:

1. Calculate the provincial quota, Qp = Vp / Sp, where Vp = the total number of votes cast in a particular province, and Sp = the total number of seats in that province.1

2. In a particular riding i, we calculate a local relative influence value as Ii = Vti/Vi, where Vti = the total number of votes cast in riding i and Vi = the number of votes cast for the winning candidate. Ii = 0 for voters who did not vote for the winning candidate. For example, if a candidate receives 20,000 votes out of 40,000 cast, then the local relative influence of the voters who supported that candidate will be I = 40,000/20,000 = 2, or twice the influence voters would have if all their votes had equal influence on the makeup of parliament.

3. We then apply a weighting factor, Wi, to that riding to reflect any deviation from the average riding size in the province. We define Wi as Wi = Qp/Vti.2 For example, if 50,000 votes are cast in an average riding, and 40,000 votes are cast in riding i, then Wi = 50,000/40,000 = 1.25, which reflects the fact that voters in that riding have greater legislative influence due to the fact that a smaller number of voters than average share in the legislative influence of the elected MP there.

4. We multiply these two factors together to calculate the LPS score in riding i for those voters who voted for the winning candidate3: LPSi = Ii * Wi.4 In the example above, we would say that the 20,000 voters who voted for the winning candidate in a riding of 40,000 people would have a Legislative Power Share of 2 x 1.25 = 2.5, or two and a half times as much influence as parity would warrant.

5. For a single election, we place each voter’s LPS into one of nine bins: a bin for LPS scores of 0, a bin for scores in the range (0.00, 0.50]5, and so on. Graphing the percentage of values in each bin yields the following graph:

## Legislative Power Share scores across time

By stacking each of the bars on top of each other, left to right, we can represent all of the elections since Confederation:

The following summary statistics show that the number of voters no Legislative Power has been increasing over time. This has been at the expense of the voters in the green range (LPS in 0.75 - 1.25) or the green + yellow range (LPS in 0.50 - 1.50).