Proportional Seat Distribution
PSD Flavours:
Opportunities for Customization
The Proportional Seat Distribution (PSD) system can be tailored to better meet the needs of the country (or state, or province...) where it is implemented. When adapting the PSD system for use in a specific place one can customize the level of its application, choose whether or not to factor local voter-turnout into candidates' results, select the type of proportionality, pick the method for counting party seats, set a minimum level of support for a party to be eligible to earn a seat and even increase ballot options.
Level of Application
To quantify a candidate’s success, vote results must be compared from multiple electoral districts. There are different ways to group electoral districts for the purpose of determining candidates’ success and producing party proportional results within the grouping. That is, PSD can be applied across the whole region where an election is being held, or it can be applied separately to sub-regions. So, in the case of a federal election, PSD can be applied across the entire country altogether or separately to individual provinces/territories..., or to groupings of provinces/territories..., or to much smaller groupings of electoral districts within each province/territory... The level of application affects results in two ways: it determines the resolution at which results are proportional, and it influences geographical clustering of elected party representatives.
When applied separately to small sub-regions, there are fewer seats to distribute among the parties in each sub-region, whereas there are more seats involved when PSD is applied to larger sub-regions or even to the whole region altogether. More seats in a multi-district group improve the degree to which results are proportional. For instance, in a sub-region with four seats each seat represents about 25% of the votes so the degree to which party representatives can be distributed is relatively limited. In contrast, in a region with 338 seats, every 0.3% of votes gets a representative. Even though the resolution of proportionality in election results depends on the number of seats in the regions where PSD is applied, PSD guarantees representation is as proportional as physically possible in each grouping.
When applied separately to small sub-regions, PSD ensures that representation in each sub-region is proportional to party support, preventing any of the sub-regions from being disproportionately dominated by a party. When applied to large sub-regions, or to the whole region together, a party's representatives can cluster in geographical areas.
Voter Turnout Factor
PSD is unique among voting systems in permitting voter turnout to influence results. Though the number of seats distributed to each party depends exclusively on those votes that are cast, every candidate's success ratio can be modified by those votes that are not cast by multiplication of each success ratio with the voter turnout percentage in the candidate's district. In this way, candidates running in districts with good turnout receive higher success exceptionality measures and rank higher in the seat distribution process, while those in districts with poor turnout rank lower and thus have a decreased chance to receive one of their party's seats. This turnout-modified version of the success ratio thus incentivizes candidates to increase voter turnout in their riding.
Type of Proportionality
PSD aims to make representation for each political party proportional to the party’s support. There are two ways to do this. First, PSD can give each party a proportional share of all the seats by comparing the number of votes cast for the party with the total number of votes in all electoral districts. This type of proportionality is used in the examples in the Technical Details section of the website as well as in the report written for Canada's 2016 Special Committee on Electoral Reform. Alternatively, PSD can give each party a proportional share of the seats in those electoral districts where the party ran by comparing the number of votes cast for the party with the total number of votes in the electoral districts where it had candidates.
While these two ways of conceptualizing party proportionality commonly produce the same results, they occasionally differ. Consider the vote result for the Bloc Québécois party in Canada’s 2015 federal election. The Bloc Québécois received 19.5% of votes cast in the 78 ridings in which it had candidates and 4.7% of all votes cast in all 338 ridings. So, the Bloc Québécois would receive about 15.2 seats (i.e. 19.5% X 78) if PSD gives each party a proportional share of seats where it ran, or about 15.9 seats (i.e. 4.7% X 338) if PSD gives each party a proportional share of all the seats (the difference here is because the electoral districts where the Bloc Québécois ran generally had more voters voting than the other ridings). Check out the PSD simulator spreadsheet to see the effect that these two types of proportionality would have on the PSD results for the 2015 Canada federal election.*
*Spoilers: The effect is minor: when PSD is applied separately to Canada’s regions there is no difference; when PSD is applied to the whole nation at once, if parties get a proportional share of seats in electoral districts where they ran, then the Conservative party gains an additional seat at the expense of the Bloc Québécois.
Method of Counting Party Seats
To minimize the degree that each party’s share of seats is overrepresented and underrepresented, PSD uses the Webster/Sainte-Laguë method of highest averages. This involves calculating how undervalued and overvalued each party is without and with additional seats or rounding each party’s modified ideal seat count to the nearest whole number. If desired, other methods of counting party seats can be used: if it is deemed beneficial to minimize just the overrepresentation of parties, without regard for parties’ underrepresentation, the Jefferson/D'Hondt method of highest averages can be used by omitting any calculations of how undervalued each party is without an additional seat or by rounding down each party’s modified ideal seat count.
Minimum Support Requirement
The number of districts in a region produces a natural minimum level of support which each party must meet in order to earn a seat. In general, this minimum level is the inverse of the number of districts: e.x. for 338 districts a party must receive about 1/338 % (i.e. 0.3%) of votes to get a seat. If desired, a higher level of support can be chosen to keep parties with relatively low support (though greater than the natural minimum) out of governance.
Ballot Options
If desired, ballots used in a PSD election can be augmented to provide greater choice to voters. In its simplest form, a PSD ballot requires voters to check off a single box to indicate their preferred candidate for their district, the PSD procedure then uses this information to determine the number of seats for each party and to distribute seats among party candidates according to their success ratios. Alternatively, PSD ballots can be designed to allow voters two distinct choices: first, voters can choose their preferred candidate in their district; and second, they can indicate which party they prefer among those running in their district (here independent candidates are not considered their own party). Voters' choice of specific candidate is then used to see whether any independent candidates represent their district and to determine the party candidates' success ratios, while their choice of party is used to determine the number of seats for each party. To prevent voters who elect an independent candidate in their district from doubling their effect on the election results, ballots cast for independent candidates who successfully get their district's seat will not contribute to the calculation of party seat count (of course, for any ballot with a vote for an independent candidate who does not go on to receive the local seat, the party vote portion will be used in calculating party seat counts). With a two-check ballot, PSD provides the opportunity for voters to express their preference for local candidate and for party separately.