How Voting Systems Change Election Results

In the United Kingdom's 2024 general election, the Labour Party won about 34 percent of the votes and about 63 percent of the seats in the House of Commons. Reform UK won about 14 percent of the votes and fewer than 1 percent of the seats. Neither result involved anything improper. They are simply what the British counting rule does with a vote spread across many parties.

Every electoral system has to answer two questions: what area does each representative stand for, and how do votes in that area become seats? Answer them differently and the arithmetic changes, and so, over time, does the behaviour of parties and voters who learn to work within it.

The country is divided into districts, each electing one representative, and whoever gets the most votes in a district wins it, even without a majority. Britain, the United States, Canada and India all use this for their main legislative chambers. It is simple to understand, produces a clear local representative, and tends to hand one party a working majority even on a minority of the vote.

The cost is that votes for losing candidates and surplus votes for winning ones count for nothing, and a party whose support is spread thinly across the country can win millions of votes and almost no seats. Voters respond by voting tactically for the candidate most likely to beat the one they dislike, and the system drifts towards two large parties, a pattern political scientists call Duverger's law.

Proportional systems aim to match a party's share of seats to its share of votes. In the party-list version used in the Netherlands, Israel and much of Europe, voters choose a party, and seats in large multi-member districts are allocated in proportion. A party with 20 percent of the vote gets close to 20 percent of the seats.

Most countries add a threshold to keep tiny parties out: Germany requires 5 percent of the national vote, Turkey 7 percent. Coalition government is the norm, because a single party rarely wins half the vote. Supporters see that as a truer picture of what the country voted for; critics point out that the coalition deal is negotiated after the election by politicians, not chosen by voters, and that a small party holding the balance can gain influence out of proportion to its support.

Germany and New Zealand use mixed-member proportional systems, in which each voter casts two votes: one for a local candidate elected by first past the post, and one for a party. The party vote decides the overall share of seats, and extra members are added from party lists to top each party up to its proportional share. The result keeps a local representative for every district while making the total outcome proportional.

Ranked systems ask voters to number candidates in order. The alternative vote, used for Australia's lower house, eliminates the last-placed candidate and transfers those ballots to their next choice until someone has a majority, which removes the need for tactical voting but is not proportional. The single transferable vote, used in Ireland and Malta, does the same in multi-member districts and is proportional as a result. Britain rejected the alternative vote in a 2011 referendum by two to one.

No system scores well on everything, which is why the argument never ends. First past the post gives decisive governments and clear local accountability but wastes votes and can exaggerate or invert the national result. Proportional systems reflect the vote faithfully but produce coalitions and weaken the link between a voter and a single representative. Mixed systems get most of both at the price of complexity and two classes of member.

When you read an election result, or a proposal to change the rules, the useful questions are the same every time:

• •How many representatives does each district elect?
• •Does a candidate need a majority, or only the most votes?
• •Is there a national threshold, and what does it exclude?
• •Can a party win a majority of seats on a minority of votes?
• •Who chooses the government if no party has a majority: voters or negotiators?

A small invented example shows the effect clearly. Imagine 100 voters and three candidates. Forty voters rank A first, then C, then B. Thirty-five rank B first, then C, then A. Twenty-five rank C first, then B, then A. Under first past the post, only first choices count, so A wins with 40. Under the alternative vote, nobody has a majority, so C is eliminated and those 25 ballots move to their second choice, B, who now has 60 and wins. Nothing about the voters has changed, only the rule used to read their ballots.

Now compare each pair head to head. C beats A, because the 35 B voters and the 25 C voters prefer C to A, giving 60 against 40. C also beats B, since the 40 A voters and the 25 C voters prefer C, giving 65 against 35. So C, the candidate eliminated first under the alternative vote and third under first past the post, is the one a majority prefers to every rival. The economist Kenneth Arrow later proved that no ranked voting rule can satisfy every reasonable fairness condition at once, which is why examples like this cannot be engineered away.

Proportional systems still need a rule for turning vote shares into whole seats, and the rule matters. One of the most widely used, the D'Hondt method, divides each party's votes by 1, then 2, then 3 and so on, and hands out seats one at a time to the largest numbers on the resulting list. Take a district electing seven members, with party A on 42,000 votes, B on 31,000, C on 18,000 and D on 9,000. The seven largest quotients give A four seats, B two, C one and D none, so A wins 57 percent of the seats on 42 percent of the vote.

The Sainte-Lague method uses the divisors 1, 3, 5 and so on instead, which makes each additional seat harder for a big party to win. Run the same votes through it and A gets three seats, B two, C one and D one, much closer to each party's share. That is why D'Hondt is said to favour larger parties and Sainte-Lague to treat them more evenly. Spain uses D'Hondt in small provincial districts, which magnifies the effect, while New Zealand and Germany use versions of Sainte-Lague. Two countries can both call themselves proportional and still reward big parties quite differently.

Wherever representatives are elected from single-member districts, whoever draws the boundaries can shape the result. Take a town of 50 voters, 30 for party A and 20 for party B, split into five districts of ten. Spread them evenly, six A and four B in each, and A wins all five seats on 60 percent of the vote. Now redraw the lines: put nine A voters and one B voter into each of two districts, and fill the other three with four A and six B. Party B now wins three seats out of five on 40 percent of the vote, and not a single voter has changed their mind.

The two techniques are called packing, crowding an opponent's supporters into a few districts they win by huge margins, and cracking, spreading them thinly so they fall just short everywhere else. The practice is named after Elbridge Gerry, governor of Massachusetts, who in 1812 signed a map with one district so contorted that a newspaper likened it to a salamander. Britain hands boundary drawing to independent Boundary Commissions, while in many American states the legislature itself still draws the lines, which is why redistricting fights there are so bitter. Proportional systems with large districts are far less exposed, since moving a boundary barely changes any party's share.

Electoral systems decide how votes become seats, and the choice between district winners, proportional lists, mixed systems and ranked ballots trades local representation and decisive majorities against a faithful match to the national vote. A result that looks unfair under one rule is often exactly what that rule was designed to produce.