If so, then why the focus on electoral reform? Is the absence of exact
proportional representation really what is keeping countries like the
US and the UK from a multi-party system, or is it just more of a
cultural stable state that is hard to escape from?
The two party system in the U.S., and the two party system in some regions of the U.K., is almost entirely a product of the electoral system and has almost nothing to do with cultural stability.
The scenario proposed in the question was one that was expected to be common by the drafters of the U.S. Constitution (although keep in mind that in the scenario in which no candidate receives a majority of the electoral vote, states vote by state and not by member, and even then, a state only votes at all if a majority of the members from that state support the candidate; this is by all accounts, a horrible way to elect a President).
Their expectations were understandably incorrect, because there was very little history of democratic national government on a large scale anywhere in the world except the U.K. at the time, and the U.K. system had some structural differences from the U.S. system they were adopting. In fact, this provision of the U.S. Constitution has been invoked only once, in the Presidential election of 1824.
It didn't happen because a two party system emerged in the U.S.
Duverger's law provides that two party systems emerge naturally in political systems were politicians are elected in single member districts on a single round plurality vote basis (often called "First Past The Post" or "FPTP"), subject to the exception that geographically concentrated third-parties such as regional nationalist parties, can still emerge. This is the predominant means by which elected officials at the state and federal levels are elected in the United States and has been since the current constitution took effect in 1789.
Apart from brief episodes where one of the two major parties collapses and is replaced by a new party (drawn, in part, from existing elected officials who defect to the new party), which is how the current Republican Party was born, the U.S. has had a predominantly two party system since it had political parties at all. And, so long as there is a two party system, the scenario imagined in the question is unlikely to happen on a regular basis.
Reforms have been hard to achieve because almost all U.S. elected officials come from one of two major parties and have a vested interest in maintaining the status quo.
Note also that the U.S. isn't a pure two party system. There have been notable independent Presidential campaigns (these probably played a significant role in both of President Clinton's elections), and there have often been a small number of Representatives in the U.S. House and Senators in the U.S. Senate (typically 1-3% or less), who caucus with, but are not members of, one of the two major political parties. Similar levels of third-party and independent candidate participation have been seen in partisan races at the state and local level in the U.S.
Two of the fifty Senators who, together with the Democratic Party's Vice President make up the U.S. Senate majority, are not currently members of the Democratic Party. The current U.S. Senate majority is already a multi-party coalition.
A similar analysis in a previous answer at Politics.SE heavily overlaps with this one, but pays more attention to the roles played by legislative rules (especially in the U.S. Senate) and lightly examines some constitutional amendment based options.
How Could It Be Done?
It would be easy (procedurally, not politically), without a constitutional amendment, to mandate (1) that states with more than one seat in the U.S. House of Representatives elect their representatives by proportional representation, and (2) that states elect U.S. Senators (and representatives, in states with one member in the House of Representatives) through instant runoff voting (or actual runoff voting).
Ending Spoiler Effects That Discourage Third-Parties In Single Member District Races
Instant runoff voting (or a requirement that a plurality supported candidate receive a majority of the vote to avoid a runoff election, which some U.S. states have right now) eliminates the spoiler effects of voting for third-party candidates in single member district plurality elections (like those held in most, but not all, U.S. states).
This spoiler effect is an important reason that the U.S. developed the two party system that is has now. Systemically, this spoiler effect discourages the development of "moderate" political parties and instead encourages a two party political system with one liberal and one conservative political system at any one time.
But, any single member district system still discourages the formation of political parties that have diffusely spread support that is sub-majority almost everywhere, in contrast to proportional representation systems which don't penalize such parties in terms of electoral results if the party meets the minimum percentage threshold to get legislative representation (which can be imposed by statute or flow from the number of seats in each electoral region).
The pertinent constitutional and statutory authorities
This kind of regulation is authorized by Article I, Section 4, Clause 1 of the U.S. Constitution which states:
The Times, Places and Manner of holding Elections for Senators and
Representatives, shall be prescribed in each State by the Legislature
thereof; but the Congress may at any time by Law make or alter such
Regulations, except as to the Places of chusing Senators.
This authority currently mandates that members of the U.S. House be elected from single member districts, which effectively ruled out proportional representation. See 2 U.S.C. §2c. This statute passed on December 14, 1967 says:
In each State entitled in the Ninety-first Congress or in any
subsequent Congress thereafter to more than one Representative under
an apportionment made pursuant to the provisions of section 2a(a) of
this title, there shall be established by law a number of districts
equal to the number of Representatives to which such State is so
entitled, and Representatives shall be elected only from districts so
established, no district to elect more than one Representative
(except that a State which is entitled to more than one Representative
and which has in all previous elections elected its Representatives at
Large may elect its Representatives at Large to the Ninety-first
Congress).
(The 91st Congress was the one elected in 1968.)
This statute was enacted with a goal of preventing states from electing all of their U.S. House members in a single statewide vote that would tend to give all of the U.S. House seats in the state to the party with the most voters in the state, much like the electoral college does today (which was done primarily to marginalize the effectiveness of black voters in the South).
The likely impact
This would, almost inevitably, lead to a multiparty system. I am not aware of any country with a proportional representation system of electing its national legislature of some kind that does not have more than two major political parties.
The most likely path to these reforms
Politically, the most likely path to these kinds of reforms would be to first implement them at the state level to show that it is a viable option and then to use that success build support for the system in other states, before attempting to make the change at the federal level through an amendment to 2 U.S.C. § 2c.
Five states have already adopted instant runoff voting, or a requirement to secured a majority of the vote or face an actual runoff election, for single member districts, in part, to prevent a major party candidate from being unseated by a third-party spoiler candidate in single member district races. So, this reform could conceivably be widely adopted without too much opposition.
Georgia, Mississippi, and Louisiana — require runoff
elections in a general election when no candidate receives a majority
of the vote. In every other state, a candidate can win a general
election with a plurality of the vote.
(Source).
Maine and Alaska use some form of instant runoff elections in federal elections.
Jungle primaries
Another way to remove institutional reinforcement of a two party system would be to eliminate political parties from the process of nominating candidates for elected offices entirely.
In this reform, sometimes known as a "jungle primary" and more formally described as a nonpartisan blanket primary, there are low barriers to entry to a first round election, which includes all candidates from all parties, that are narrowed down in that round to finalists who face off in a general election (often with two, four, or five finalists). Per the Wikipedia link in this paragraph:
This system theoretically elects more moderate candidates, since
winning might require appealing to voters of both parties in a
two-party system. However, all primaries use plurality voting and are
susceptible to vote-splitting: the more candidates from the same party
that run in the primary, the more likely that party is to lose.
Research on California's primaries have shown no increase in moderate
candidates, and no increase in turnout among nonpartisan voters. Some
have proposed using other voting systems in the primary to alleviate
this problem, such as the unified primary based on approval voting for
its first round.
The top-two system is used for all primaries in Washington and
California except presidential primaries, and Alaska began using a
top-four primary system in the 2022 Alaska's at-large congressional
district special election using ranked-choice voting.
The so-called Louisiana primary is similar, with a first round to pick
the top two candidates and a second round to choose between these two.
The difference is that the first election is the general election,
whereas the second is a later "runoff" election that is held if no
candidate wins more than half of the vote in the first round.
This system has produced more moderates in Alaska since it was adopted, and historically did so in Louisiana, although hardening partisan divisions with a shrinking pool of moderate voters in Louisiana have obscured this fact.
Of course, weakening political parties generally does not, in and of itself, lead to third parties. It can also lead to more independent candidates and elected officials not affiliated with any particular political party.
Footnote Re Federalism
One of the more subtle features of Duverger's law is that the U.S. has the same two parties in all 50 state and the District of Columbia because these political jurisdictions are coupled institutionally to the federal political system that elects the President and Congress (re-emphasized by the Supremacy Clause and direct taxation powers of the federal government). State political systems are really just one sub-part of a single complicated mega-political system, rather than 51 truly separate political systems.
This used to be even more true.
This Presidential election of 1824 giving rise to the only contingent election in U.S. history, notably, took place at a time when some states selected electors legislatively, while other states selected electors by popular vote. Soon after that, all states directly elected Presidential electors, but it was a very different kind of federal electoral system at the time.
Similarly, it is worth recalling that prior to 1914, U.S. Senators were selected by state legislatures, rather than by popular vote established by the 17th Amendment to the U.S. Constitution in 1913, and that prior to the U.S. Civil War, it was common for Senators to resign to seek other offices without finishing their terms, in part, because the U.S. federal government was much smaller and less significant in the pre-Civil War era. Before then, Senatorial appointments reflected the partisan make up of state legislatures.
Legislative elections of electors and U.S. Senators in the early U.S. was one of the important factors that aligned federal political parties with state political parties at the outset, making it a status quo that any new federal or state political parties would have to overcome.
When a political jurisdiction's politics are not institutionally coupled to the national political system, as is the case in the Commonwealth of Puerto Rico, that political jurisdiction develops its own political parties. You see something similar in Northern Ireland and in Scotland, which have significant local self-government, in the U.K.
If we had the same state election laws in every state that we have today, but they were not linked together through Congress and the Presidential election system, almost every U.S. state would still have a two party system, but the two parties would be different in every U.S. state or region, coming up with different portfolios of policies and different coalitions in each state, so that each state would be almost equally divided between two competitive local political parties.
But, because U.S. states and the District of Columbia are all intimately tied into the federal political system, instead, the U.S. has the same two political parties (or close analogs to them) in every state, causing either the Democratic party or the Republican party, to be dominant and have "trifecta" control of state government in the lion's share of U.S. states.
In the wake of the 2023 general election in the U.S., for example, there were 22 Republican trifectas (plus Nebraska where Republicans elected on a non-partisan basis to the unicameral legislature controlled it and the Governor was a Republican), 17 Democratic trifectas (plus the Democratic party controlled District of Columbia), and 10 divided governments where neither major political party had trifecta control. As a result of the 2023 elections, there are fewer divided governments across the United States than at any other point from 1992 to 2022.
In all of those ten states, except Pennsylvania and Alaska, both houses of the state legislature is controlled by the same political party. In these eight states, one major political party controls the legislature and the other major political party holds the Governorship (with a Governor who is almost invariably a moderate within his or her own political party and who usually holds a line item veto that brings more give and take to partisan budget negotiations).
Alaska's state legislative houses both have split party control after adopting ranked choice voting, with the state house also having a significant number of members who aren't members of the two major parties. This has produced a political culture which is "moderate and consensus based." A majority of the legislators in both houses of Alaska's state legislature are Republicans (as is Alaska's Governor), but each house has chosen instead to organize itself on a bipartisan basis.
Pennsylvania is the only U.S. state where the legislative process is even close to being as vulnerable to being gridlocked as the federal legislative process. It has a Governor who is a Democrat, Democrats control the state house by one seat out of more than two hundred, and Republicans control the state senate.
Footnote Re Non-Constitutional Presidential Election Reform
Congress has less authority to enact statutes governing how Presidential electors are chosen than it does to do so in Congressional elections under the U.S. Constitution (which is not to say that it has no authority at all to regulate Presidential elections, particularly in light of the enforcement clauses of various U.S. Constitutional amendments pertinent to elections).
The focus of current reforms short of a constitutional amendment in Presidential election is to have states with a majority of the electoral vote enter into an interstate compact to apply their electoral votes to the popular vote plurality winner in the general election for President. This requires the approval of every state joining the compact and also a majority vote in both the U.S. House and the U.S. Senate, although the need for Congressional approval in this case is disputed.
Currently, this is supported by states with 38% of the electoral vote and is being considered by enough states to bring the total to a majority of the electoral vote (states with 90 electoral votes have considered it, and it needs states with 65 more electoral votes to take effect).
Polling shows widespread popular support for this reform, even in states whose state preferred candidates have won in recent years despite not receiving the popular vote.
If this became a fait accompli, a constitutional amendment formally abolishing the electoral college would probably follow uncontroversially, and might institute a requirement that a majority of the popular vote needs to be secured to win with a runoff held in other cases, a system widely adopted in many countries with multi-party election systems for singular offices like their Presidencies.
Footnote Regarding Other Irregular Presidential Elections
@Dan04 mentions in the comments the situation in the somewhat irregular election of 1800, arising from a now superseded part of the U.S. Presidential election process.
Back then, the Vice-Presidency was given to the runner-up in the
strategic election. But the parties strategically exploited the rule
that each Elector got two votes by nominating two candidates, so that
if they got a majority of the Electors, they would win both the
Presidency and the Vice-Presidency. But this worked a bit too well,
and the winning party's candidates tied each other necessitating a
tiebreaker vote in the House (which Thomas Jefferson ultimately won).
Not wanting this situation to occur again, Congress passed a hasty
rule patch separating the elections for President and
Vice-President.
The "hasty rule patch" is the 12th Amendment to the U.S. Constitution.
The Presidential election of 1876 was more hotly contested and disputed, but that was a two way race with allegations of election maladministration, not due to a three or four way split of the electoral vote.
