How Voting Systems Penalize or Encourage ‘Third Parties’

by John Johnson

In the United Kingdom’s elections last year, the Conservative Party received 36.8% of the vote, while Labour (the next largest party) won 30.4%. However, the Conservatives got over half the seats in the House of Commons and thus the right to install their own chief executive and cabinet. Essentially, achieving less than 37% of the popular vote won them 100% of the power. Two of the more prominent minor parties—the UK Independence Party (UKIP) and the Liberal Democrats—collectively won over a fifth of the vote. Yet combined they received less than 2% of the seats in Parliament. Conversely, the Scottish National Party (SNP) turned their 4.8% of the national vote into 8.6% of the total number of seats.

Sweden held their own national parliamentary elections in 2014. The results could hardly be more different. Compare the two tables below. In each the yellow bars represent that party’s share of the popular vote, while the corresponding blue bars depict the resulting share of seats.

United Kingdom 2015 Elections[i]

Uk 2015 chart

Sweden 2014 Elections

Sweden 2014 Chart

There are two main differences between these two graphs. First, the difference between votes received and seats received for each party is much greater in the UK. Second, some parties in the UK receive more than their fair share of votes at the expense of other parties which receive less. Conversely, nearly all parties receiving seats in Sweden actually receive a slightly higher share of seats than their portion of the popular vote would suggest. The reasons for this are actually quite simple. It all comes down to the two countries’ different methods of counting votes.

The United Kingdom uses the same system as the United States. It’s called “First-Past-the-Post” (a horseracing reference). Candidates all run in districts. Whichever candidate gets the most votes in each district wins.

Sweden uses a form of proportional representation. Of the 349 seats in the Riksdag, 310 are awarded in constituency-based races—meaning that they represent specific districts of the country. However, they are not “single-member districts” as in the US and UK. Rather, each constituency has a number of associated seats ranging from 2-39, depending on its population. After these constituency-based seats have been apportioned, the remaining 39 seats are used to adjust for any deviations that may have arisen between a party’s share of the vote and its share of the seats. To enter the Riksdag, a party must have received at least 4% of the national vote or 12% in a single constituency. All those votes which went to parties failing to meet the threshold are shown in the “Other” column. This explains why most of the parties received slightly more than their expected share of seats in the parliament.

I completed the same analysis for Canada’s 2015 elections, Germany in 2013, the U.S. in 2014, Israel in 2015, and Brazil’s 2014 elections to the Chamber of Deputies (lower house). In each case I calculated a measure of the total discrepancy between the achieved and actual representation of each party. I found the difference between each seat-winning party’s portion of seats and portion of the popular vote and then added these absolute values together. The results are below.

Size of Discrepancy between Share of Vote and Share of Seats

Discrepancy table

Blue indicates FPTP voting; orange states vote proportionally; Germany uses a mixed system. As always, by clicking on the chart you can use the tooltip to see detailed results.

The graphs to the U.S. House and Senate, Israel’s Knesset, Canada’s House of Commons, and Germany’s Bundestag are below.

United States 2014


US House 2014 Chart


US Senate 2014 Chart

Germany 2013

Germany 2013 Chart.PNG

Canada 2015

Canada 2015 chart.PNG

Israel 2015

Israel 2015 Chart


[i] For simplicity’s sake, I’ve eliminated the following minor parties: Plaid Cymru, Democratic Unionist, Sein Fein, and the Social Democratic Labour Party. The first is Welsh and the latter three operate only in Northern Ireland. Also, I have not included the single successful independent candidate or the race of the Speaker. Traditionally, the Speaker of the House of Commons runs on an independent ticket, regardless of his previous party affiliation. If you click on the graph, you’ll be treated to a full version in all its absurd complexity.