The Goldilocks Assembly: What number of seats is “just right” for provincial legislatures?

Legislative Assembly of Ontario. Photo retrieved from CBC Ottawa.

Electoral boundary redistributions can be contentious, even when administered by independent commissions. In addition to the tense nature of deciding where to draw lines around communities, these debates are often defined by a more profound philosophical question: just how many lines should be drawn in the first place?

There is no consensus on how many seats a legislature should have. Supporters of larger assemblies argue that additional seats promote direct democracy by having fewer voters per district. The downside of larger assemblies is that they require additional resources to administer elections and pay MLA salaries.

On the other side of this argument, smaller legislatures are less costly to taxpayers but they clump voters into fewer districts. While less expensive, smaller assemblies risk being less diverse or representative of local needs. An infamous example of this debate emerged during the Ontario government’s 2018 redrawing of Toronto City Council boundaries from 44 seats to 25. The Ford government defended the move as an effort to improve municipal government efficiency while city councillors argued that it undermined local democracy.

In most developed countries, legislatures (both national and regional) are responsible for setting boundary redistribution rules. Typically, lawmakers delegate this task to independent bodies composed of professors, civic leaders, and the occasional retired judge; however, elected politicians often set guiding rules for boundary commissions. For example, the Electoral Boundaries Readjustment Act provides Canadian federal commissions with high levels of autonomy but set strict parameters on the number of seats in the following parliament. The maximum number of MPs for each province is established by the Chief Electoral Officer based on population size and Section 51 of the Constitution Act, 1867.

Given all the factors that contribute to redistricting debates, the question must be asked of whether any guiding principles could help a boundary commission (or chief electoral officer) decide what number of seats is “just right.” Although there is no hard rule to determine the appropriate number of seats in a legislature, Estonian political scientist Rein Taagerpera discovered an interesting trend in 1972. When looking at the sizes of parliaments in a handful of countries, he noted that the number of seats in a country’s lower house is approximate to the cube root of the country’s population.

Nearly a half-century later, Taagerpera’s discovery holds true. When examining OECD member states, the Cube Root Rule appears to offer policymakers a Goldilocks number of legislature seats (i.e., not too many, not too few) that is indirectly proportional population.

Relationship between the cube root of population and lower house size across the OECD. Canada is denoted by the red dot and the United States is denoted by the blue dot.

Within the OECD, there is a strong positive relationship between the cube root of a country’s population and the number of seats in its lower house. The two variables are strongly associated across the entire membership of the organization (N = 37, r =.0.789, p<0.01)*. Table 1 shows how closely the legislature sizes of some countries reflect population cube roots. Canada, Denmark, Mexico, and Switzerland receive honourable mentions in this regard, but Lithuania is the winner with a perfect net-zero score.

Table 1: Data from OECD countries with the smallest discrepancies between their legislature size and population cube root.

The United States had the biggest discrepancy between its population cube root and lower house seat count. The House of Representatives has not added new seats since 1929, and as a result has a seat deficit of 255. This discrepancy has led the New York Times Editorial Board to endorse the Cube Root Rule as a means for increasing the size of the House. Similarly, a Fordham University study recommends increasing the size of the House from 425 seats to 623 over the next twenty years. The authors argue that such an increase can strengthen local representation, mitigate partisan gerrymandering, and improve lawmaker diversity.

Although it is clear that Canada has better legislative representation than voters south of the border, there is value in examining whether the Cube Root Rule can apply to provincial legislature.

Table 2: Cube Root Rule in Canadian provincial legislatures

The findings in Table 2 suggest that provincial legislatures do not follow the Cube Root Rule like the lower houses of the OECD; however, the picture is much clearer in Table 3 when the cube root of each province’s population is halved.

Table 3: Modified Cube Root Rule in Canadian provincial legislatures

Table 3 reveals that provincial legislature only have an average 4 more seats than the cube root of their population divided by 2. For six of Canada’s ten provinces, this discrepancy is either 0 or 1. When depicted visually, the relationship is highly significant (N = 10, r = .982, p<0.01)*.

Relationship between the cube root of population (divided by 2) and legislature size across Canadian provinces

These results provide some interesting observations about the Cube Root Rule in provincial settings. First, the population cube roots are not the sole determinant of legislature sizes. Provincial boundary commissions often conduct their studies with a pre-set number of seats or an alternative counting method. For example, PEI pegs its legislature size to the number of electors in a district rather than the broader population.

Second, some provinces seek to add representation in for remote areas. Ontario often draws its boundaries based on federal commission reports, but increases representation in northern communities. Additionally, there are also costs associated with paying for additional district elections and MLA salaries. These considerations make provincial boundary commissions more likely to prioritize geography over direct/indirect proportionality.

Despite these limitations, a modified version of the Cube Root Rule predicts legislature sizes with near perfect accuracy. This equation can provide subnational policymakers with reference points for legislature sizes that would make Goldilocks proud. By adopting empirical measure for their studies, boundary commissions can recommend seat numbers that are “just right” for their electorates.

*For a full breakdown of how these findings were obtained, click here.

MSc graduate from the London School of Economics and Political Science (LSE) | Interests include Canadian and UK politics, transit, and health policy

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