Overview of Simulations

Party Proportionality

Over/Under RepresentationParty Disproportionality Indices
IDYearRiding DesignBallot StyleCounting Algorithm#Local MPs#Reg MPsCon%Lib%Lbr%QC%Pop%Env%Oth%Gallagher IndexComposite Gallagher IndexLoosemore Hanby IndexLijphart IndexAvg RepEq Index
11867ca-sglMbr-001smpfptp134020%11%-32%27.829.134.633.644.69
21872ca-sglMbr-002smpfptp14809%14%0%-23%19.920.324.422.245.36
31874ca-sglMbr-003smpfptp15104%21%-0%-25%22.523.925.023.945.96
41878ca-sglMbr-003smpfptp195022%-2%-21%18.719.622.820.548.89
51882ca-sglMbr-005smpfptp186020%7%-27%21.722.027.325.545.41
61887ca-sglMbr-006smpfptp20709%-6%-4%7.16.710.86.446.63
71891ca-sglMbr-006smpfptp20705%-3%-3%4.07.16.23.647.90
81896ca-sglMbr-008smpfptp2090-4%11%-6%10.011.614.310.548.17
91900ca-sglMbr-008smpfptp2080-9%9%-0%0%10.116.511.510.548.17
101904ca-sglMbr-010smpfptp2100-10%13%-0%-2%12.014.513.612.746.67
111908ca-sglMbr-011smpfptp2180-8%11%-1%-2%9.813.011.511.446.87
121911ca-sglMbr-011smpfptp217012%-8%-1%-3%10.215.612.311.848.81
131917ca-sglMbr-013smpfptp203012%-9%-2%-1%9.821.711.511.545.29
141921ca-sglMbr-014smpfptp2350-9%9%-1%1%9.617.713.59.148.77
151925ca-sglMbr-015smpfptp24501%0%-1%-0%1.522.33.21.247.97
161926ca-sglMbr-015smpfptp2440-9%5%3%1%7.118.79.28.345.30
171930ca-sglMbr-015smpfptp24307%-8%1%-1%7.713.09.57.648.21
181935ca-sglMbr-018smpfptp2450-14%25%-7%-6%1%22.224.230.226.050.94
191940ca-sglMbr-018smpfptp2450-14%19%-6%1%-1%19.019.824.221.949.08
201945ca-sglMbr-018smpfptp2450-1%10%-6%-1%-2%7.316.911.88.452.43
211949ca-sglMbr-021smpfptp2630-14%24%-10%1%-1%20.521.125.623.948.61
221953ca-sglMbr-022smpfptp2630-12%15%-3%0%0%13.615.915.915.146.95
231957ca-sglMbr-023smpfptp26403%-2%-1%0%-0%2.818.24.13.250.73
241958ca-sglMbr-023smpfptp265025%-15%-6%-3%-0%21.221.525.024.848.47
251962ca-sglMbr-025smpfptp26507%0%-6%-0%-0%6.514.77.16.654.01
261963ca-sglMbr-025smpfptp26503%7%-7%-3%-0%7.515.910.07.253.85
271965ca-sglMbr-025smpfptp26504%9%-10%-3%-0%10.319.113.610.054.72
281968ca-sglMbr-028smpfptp2640-4%13%-8%0%-0%11.420.313.213.048.45
291972ca-sglMbr-029smpfptp26406%3%-6%-2%-0%6.315.88.46.149.50
301974ca-sglMbr-030smpfptp26401%10%-10%-1%-0%9.918.110.810.348.64
311979ca-sglMbr-031smpfptp282012%0%-9%-3%-1%10.819.312.712.345.50
321980ca-sglMbr-031smpfptp28204%8%-9%-2%-1%8.718.811.98.444.77
331984ca-sglMbr-033smpfptp282024%-14%-8%-1%-0%-0%-1%20.920.524.824.846.71
341988ca-sglMbr-034smpfptp295013%-4%-6%-2%-0%-1%11.317.314.314.347.03
351993ca-sglMbr-035smpfptp2950-16%19%-4%5%-1%-0%-3%17.727.223.518.746.46
361997ca-sglMbr-036smpfptp3010-12%13%-4%4%0%-0%-0%13.325.817.613.046.57
372000ca-sglMbr-037smpfptp3010-12%16%-4%2%-0%-1%-1%13.622.518.216.344.18
382004ca-sglMbr-038smpfptp30802%7%-10%5%-0%-4%-0%9.820.914.89.545.43
392006ca-sglMbr-039smpfptp30804%3%-8%6%-0%-4%-0%8.615.513.38.145.65
402008ca-sglMbr-039smpfptp30809%-1%-6%6%-0%-7%-0%9.915.714.78.846.37
412011ca-sglMbr-039smpfptp308014%-8%3%-5%-0%-4%-1%12.421.517.114.346.40
422015ca-sglMbr-042smpfptp3380-3%15%-7%-2%-0%-3%-0%12.015.915.015.047.26
432019ca-sglMbr-042smpfptp33801%13%-9%2%-2%-6%-0%12.217.016.513.447.06

Legislative Power Scores: FPTP

Canadian elections since Confederation

Percent of voters who voted for their MP

Decisive, Surplus and Unrepresented Votes

Legislative Power Functions

At least during this exploratory phase, Legislative Power is being measured in a variety of ways. The following graphs show 4 different approaches.

FptpLPS

A voter's base legislative power score (LPS) is 1 if the candidate they voted for was electd MP and 0 if the candidate was not elected.

The base LPS is adjusted by V/v where V is total number of votes cast in their district and v is the number of votes the elected candidate received. For example, if there were 100,000 votes cast in the district and the winner received 50,000 then the LPS is doubled (100,000/50,000 = 2) for those who voted for the elected candidate. That extra legislative power comes at the expense of those who did not vote for the elected candidate and have 0 legislative power.

The base LPS is further adjusted according to the malapportionment or deviation in riding size. The malapportionment factor is W = A/s where A is the average size (number of voters) of all electoral districts in the province and s is the size (number of voters) in the voter's district. For example, if the average district has 100,000 voters but the voter's district has only 80,000 then the voter has 100,000/80,000 = 1.25 times the legislative power of someone in an average sized district.

The voter's Legislative Power Score is then V/v * W if they voted for the elected candidate and 0 if they did not.

Legislative Power Score Distribution over time

Legislative Power held by voters over time

Legislative Power Index (Gini) over time

Top 6 Preferences w/ declining wt

A voter's legislative power is derived from their top 6 preferences. The first preference has a weight of 1.0; each subsequent preference has a weight that is 1/j less where j is the minimum of 6 and the number of preferences on the ballot. Any preference that isn't elected receives a weight of 0.

The weight contributed by each candidate is adjusted by comparing the number of votes they received to the provincial average. If the average MP in the province received 50,000 votes but this candidate won with only 40,000 votes, then the people who voted for this MP have a greater than average legislative power (50,000/40,000 = 1.25).

Finally, all Legislative Power scores are normalized by province so the average is 1.

In an FPTP election there is only one preference and thus voters who voted for the elected MP have an LPS of 1 and 0 otherwise.

Legislative Power Score Distribution over time

Legislative Power held by voters over time

Legislative Power Index (Gini) over time

Riding Size Inequity

Some of the inequities in voting can be attributed to disparities in riding sizes. Voters in larger than average ridings will have less legislative power than voters in smaller than average ridings.

This utility function gives a weight of 1 to every voter. The resulting legislative power index varies only according to the number of voters in the riding relative to the average riding in the province.

Legislative Power Score Distribution over time

Legislative Power held by voters over time

Legislative Power Index (Gini) over time

Same party ranked equal

In a party leader driven culture, as Canada has, the local candidate often is less important than the party they are affiliated with. This utility function gives the same weight to next prefences provided they belong to the same party. If a party switch is involved the score decreases by a parameterized amount (0.5 in this simulation).

For example, suppose the voter votes for A, B, C, D, and E. Candidates A, B, C, and D all belong to the same party while E belongs to a different party. Assume that B, C, and E are elected.

Candidate A starts with a weight of 1 (but wasn't elected and so contributes nothing). B is from the same party as A and so has the same weight. B was elected and thus contributes 1.0. C was elected and is from the same party as B and thus also contributes 1.0. E involves a party switch and thus contributes 1-0.5=0.5 to the score.

Legislative Power Score Distribution over time

Legislative Power held by voters over time

Legislative Power Index (Gini) over time

Legislative Power Disparity Index over time -- Canada + Regions

Note: This is only for the 1st LPS function (FptpLPS).

Legislative Power Scores: Alternative Vote

Top K Analysis

Number of voters who helped elect at least one candidate with one of their top k preferences.

IDYearRiding DesignBallot StyleCounting Algorithm12345
11867ca-sglMbr-001smpfptp57.7%57.7%57.7%57.7%57.7%
21872ca-sglMbr-002smpfptp57.4%57.4%57.4%57.4%57.4%
31874ca-sglMbr-003smpfptp58.0%58.0%58.0%58.0%58.0%
41878ca-sglMbr-003smpfptp55.9%55.9%55.9%55.9%55.9%
51882ca-sglMbr-005smpfptp54.4%54.4%54.4%54.4%54.4%
61887ca-sglMbr-006smpfptp54.3%54.3%54.3%54.3%54.3%
71891ca-sglMbr-006smpfptp54.6%54.6%54.6%54.6%54.6%
81896ca-sglMbr-008smpfptp52.8%52.8%52.8%52.8%52.8%
91900ca-sglMbr-008smpfptp54.1%54.1%54.1%54.1%54.1%
101904ca-sglMbr-010smpfptp54.9%54.9%54.9%54.9%54.9%
111908ca-sglMbr-011smpfptp54.6%54.6%54.6%54.6%54.6%
121911ca-sglMbr-011smpfptp55.8%55.8%55.8%55.8%55.8%
131917ca-sglMbr-013smpfptp66.9%66.9%66.9%66.9%66.9%
141921ca-sglMbr-014smpfptp56.5%56.5%56.5%56.5%56.5%
151925ca-sglMbr-015smpfptp56.9%56.9%56.9%56.9%56.9%
161926ca-sglMbr-015smpfptp58.4%58.4%58.4%58.4%58.4%
171930ca-sglMbr-015smpfptp55.8%55.8%55.8%55.8%55.8%
181935ca-sglMbr-018smpfptp48.9%48.9%48.9%48.9%48.9%
191940ca-sglMbr-018smpfptp53.8%53.8%53.8%53.8%53.8%
201945ca-sglMbr-018smpfptp47.6%47.6%47.6%47.6%47.6%
211949ca-sglMbr-021smpfptp52.3%52.3%52.3%52.3%52.3%
221953ca-sglMbr-022smpfptp53.1%53.1%53.1%53.1%53.1%
231957ca-sglMbr-023smpfptp51.7%51.7%51.7%51.7%51.7%
241958ca-sglMbr-023smpfptp55.5%55.5%55.5%55.5%55.5%
251962ca-sglMbr-025smpfptp46.9%46.9%46.9%46.9%46.9%
261963ca-sglMbr-025smpfptp48.5%48.5%48.5%48.5%48.5%
271965ca-sglMbr-025smpfptp47.9%47.9%47.9%47.9%47.9%
281968ca-sglMbr-028smpfptp50.4%50.4%50.4%50.4%50.4%
291972ca-sglMbr-029smpfptp48.9%48.9%48.9%48.9%48.9%
301974ca-sglMbr-030smpfptp51.2%51.2%51.2%51.2%51.2%
311979ca-sglMbr-031smpfptp53.3%53.3%53.3%53.3%53.3%
321980ca-sglMbr-031smpfptp53.8%53.8%53.8%53.8%53.8%
331984ca-sglMbr-033smpfptp52.2%52.2%52.2%52.2%52.2%
341988ca-sglMbr-034smpfptp48.5%48.5%48.5%48.5%48.5%
351993ca-sglMbr-035smpfptp51.7%51.7%51.7%51.7%51.7%
361997ca-sglMbr-036smpfptp48.1%48.1%48.1%48.1%48.1%
372000ca-sglMbr-037smpfptp51.7%51.7%51.7%51.7%51.7%
382004ca-sglMbr-038smpfptp49.8%49.8%49.8%49.8%49.8%
392006ca-sglMbr-039smpfptp48.8%48.8%48.8%48.8%48.8%
402008ca-sglMbr-039smpfptp49.1%49.1%49.1%49.1%49.1%
412011ca-sglMbr-039smpfptp50.4%50.4%50.4%50.4%50.4%
422015ca-sglMbr-042smpfptp48.2%48.2%48.2%48.2%48.2%
432019ca-sglMbr-042smpfptp49.1%49.1%49.1%49.1%49.1%

Top 2 parties

Share of the vote earned by the top two "parties" (nationally) across time.Each actual party is mapped to an "ideology" since parties have come and gone throughout Canada's history.

Top 2 Parties Vote Share vs. Seat Share

For each election, show the percentage of votes earned vs. the percentage of seats awarded for the party winning the most votes (first chart) and the party winning the second most votes (second chart).

Parties were not firmly established for the first five elections, causing some odd results by this measure. Those elections are shown in gray.

Key:

Party earning the most votes

Party earning second most votes

Parties earning first and second most votes