How frequently is the winner of the election not the person/party that received the most votes?

Question

Most modern democracies select the government somewhat indirectly.

The UK votes in 650 (currently, the number changes over time) separate constituencies each selecting a single MP by a first past the post method. Those MPs then select a government. The USA votes for the next president not directly but via an electoral college which usually allocates all the electoral college votes to the candidate with a majority of votes in the state.

Both the UK and USA can, therefore, have a winner who did not win the aggregate popular vote across the whole country (for example, Trump won the electoral college with ~3m fewer votes overall than Clinton). This is an inherent quirk in indirect systems of selecting governments (or presidents).

Is this quirk common? How often in long standing representative democracies does the "winner" not also win the popular vote?

Note: There are many voting systems where the question may be meaningless. For example, countries like Ireland who use STV give people multiple votes (so it may be impossible to say who "won" the vote. Others have proportional parliamentary systems where the quirk in systems like the UK is designed out. The scope of the question, therefore, excludes those countries where it doesn't make sense. So answers should explain the nature of the electoral system they refer to. I'm not restricting it to specific countries as I don't know enough about every system to be sure I've picked the ones where it does apply. So consider it in two parts: which systems have the quirk and how common is it in practice.

Answer 1

In the UK this has happened 7 times since the introduction of the secret ballot: 1852, 1874, January 1910, December 1910, 1929, 1951 and February 1974. However the UK did not offer universal suffrage until 1928, so only the last three apply to a democratic system as we would understand the term today.

For example in 1974, Labour won 11,645,616 votes, compared to the Conservative 11,872,180. However Labour a plurality of the seats (301 compared to the Conservative 297)

In 1951, although the Labour party won slightly more votes than the Conservatives, the Conservatives actually gained a slim majority in the House of Commons. In both cases the reason was the same: votes "wasted" in large majorities in safe constituencies.

In the US the President has lost the popular vote 4 or 5 times,1876, 1888, (1960 depending on how you count the unpledged elector vote), 2000, and 2016. However, the system was not democratic (by current standards) in 1876, 1960 or 1888.

In systems with proportional representation, the winners of a plurality may not be able to form a majority coalition. For example in the Netherlands in 1982, the Labour party won a plurality (with 30.4% of the popular vote), but the government was formed by a coalition of the second and third place parties (The Christian Democrats and the Liberal Democrats) So the party of the Prime Minister was not the party that won the most votes.

Answer 2

This has happened in the United States five times in it's nearly 250 year history with the Electoral College (there is a possible sixth related to some funny counts in one state that would have flipped the 1960 election but it was ultimately conceded without any recounting). What's more, the Founding Fathers had intended that the U.S. citizens only vote for exactly one office in national government directly (their member to the House of Representatives) and it wasn't until the 17th Amendment that direct election of Senators was possible (they were indirectly elected by each state's legislature, but many states weren't able to send full delegations because infighting in the state legislatures held up the selection of a Senator.). The U.S. has exactly one President that was never elected at all to office, either directly or indirectly (President Gerald Ford, who was nominated by Nixon under compromise with Democrats in the House to fill the gap of Vice President Spiro Agnew resigning from office over a matter wholly unrelated to Watergate, which would doom Nixon to resignation to avoid impeachment.).

Given the nature of the delegation of electoral college members as it is today, it boils down to the president winning the popular vote in 48 races (Nebraska and Maine are not winner take all states) plus D.C. If you need an analogy, the electoral college is a lot like winning the World series- it's not the points that get you the Win, but the number of games won.

Switzerland also has an interesting indirect system as their technically is no one head of state/government but rather a 7 member executive board. Each member represents one cabinet head and the most senior member is the chair of the board in a "First among equals" situation and will serve the functions of a typical singular "President" when a singular person is needed (The Swiss government is structured more like the U.S. than the UK or France in terms of authority and separation of powers and they pretty much copied the U.S. constitution when making their own). Members of the board serve a single 7 year term with the seats being allocated to parties based on political strength. Presently, the big four parties split the seats with the big 3 getting two seats each and the fourth getting a single seat.

Answer 3

I will assume that winning an election means the ability to form a government and I will present a little frame challenger:

Others have proportional parliamentary systems where the quirk in systems like the UK is designed out.

(West) Germany has always used a proportional parliament system on a federal level and state level as far as I am aware. Votes can be tallied for the individual parties rather easily and it is probably reasonable to say that the party whose candidate is elected chancellor/minister president can be considered the election winner. Despite your underlying assumption it is not always the party with the most votes that wins the executive position. Here are two examples:

• in 1969 after the end of the first post-war German grand coalition of CDU/CSU and SPD, the former parties (which should be considered a single party for election purposes as there is no place in Germany where there is a choice between the two) won 1.1 million votes more than the SPD yet SPD and FDP entered into a social-liberal coalition under chancellor Brandt (SPD).

• in 2011 in the state of Baden-Württemberg, the CDU gained 39 % over the Greens’ 24 % yet the latter formed a coalition with the SPD (23 %) resulting in Kretschmann being elected minister president.

Arguably, in a proportional representation scenario where coalitions are often required to form a government, this type of situation should be more common than in FPTP or similar systems which often produce stable majorities. While one might have assumed (in Germany) that there were essentially two coalitions competing for the largest vote tally, that picture has fallen apart now that mostly a two-party coalition is no longer possible in German parliaments and there are typically 5 or more parties represented.

Answer 4

I don't see this happen in countries that use the D'Hondt method

https://en.wikipedia.org/wiki/D%27Hondt_method

And I think this is the most common way countries avoid this issue