Dandelion Sprout Electoral System

I haven’t been a particularly active blog writer in the past couple years, but I figured I wanted to write down something I thought about and invented in my late teens: An easy calculation method to convert first-past-the-post election results, into the amount of seats parties would’ve got if there had been somewhat proportional representation.

The calculations below are based on the 2019 United Kingdom House of Commons election, British constituencies.

1. Ensure you have a list of election results where the vote share is down to at least 1 decimal for each party. This would typically be found on Wikipedia. Copy the vote shares for each party to a text editor.
2. Determine on your own what the electoral cutoff would be. I recommend 2.0%.
3. For each party, detract the electoral cutoff from each vote share. (e.g. 47.2 – 2.0 = 45.2).
4. Calculate how many combined vote share points that remain after step 3. (e.g. 45.2 + 32.0 + 10.4 + 1.0 = 88.6).
5. Divide the number of seats that are up for grabs, with the sum from step 4 (533 : 88.6 = 6,0158). Feel free to round down to 4 decimals for simplicity.
6. For each party, multiply the vote share points from step 3, with the seat factor from step 5. (e.g. 45.2 • 6.0158 = 271.91), down to 2 decimals. This will show the number of seats for each party.
7. There will usually be 1~3 seats left to align. Those will be given to the parties with the highest decimals (e.g., x.91% would usually get a seat, while x.04% usually wouldn’t). This will be the final tally.

For the Wikipedia article above, this would result in:

• Conservatives: 272 (↓24 from the official results)
• Labour: 192 (↓35)
• Liberal Democrats: 63 (↑55)
• Greens: 6 (↑5)

I have also applied the calculations with success to Canada’s House of Commons (albeit on a national basis without a separate count for Québec), and I expect it to work for e.g. the French National Assembly as well. I hope the system will provide some nice thinking exercises out there, or could even be considered for real-life applications.

Note: I acknowledge that the cutoff is handled a bit differently from most European proportional representation parliaments (e.g. the Norwegian parliament). Whereas a party above the cutoff who has 2.3% of the votes would get approx. 1 seat in Dandelion Sprout Electoral System, they’d get circa 2.3% of the seats in the parliaments in question.