This post restates an answer I made at Politics.SE where I am a moderator and participant, with only one minor modification to remove a reference to another answer at the site, adding a link, adding some discussion of the situation in Alaska, making minimal formatting modifications, and quoting a comment to the answer. I quote the question I am answering piecemeal during the answer.
In the course of answering this question, I was surprised to learn just how undivided and not gridlocked the state political process in the United States has become, in stark contrast to the federal political process in the United States.
A false premise
What kind of amendment clause can encourage many parties to represent the voters in the way originally intended by the founding fathers?
The Founding Fathers intended the constitution to result in a no party system within many disorganized majority and minority factions (see, e.g. The Federalist Papers, especially Federalist No. 10 written by James Madison), not a multi-party democracy. They predicted wrong, in part, because the world known to them had very little experience with national level democracies in early 1789 when the U.S. Constitution was drafted.
In particular, they were unaware that political parties arise spontaneously, more or less automatically, whether formally recognized or not by the electoral system, in any governmental system with a group of multiple legislators, even when legislators are appointed, rather than elected. But political parties profoundly change the dynamics of the legislative and electoral process in ways that they didn't anticipate.
Also, to slightly nitpick the title question:
What kind of amendment can oblige multiple political parties, to fix the unintended two-party malfunction of the constitution?
You can't oblige people to form multiple political parties. Some electoral systems favor the creation of multiple political parties, but this only happens if someone decides that it a worthwhile thing to do and creates and runs them. Often at the outset of a new political system, the people who caused the system to come into being are so united from that struggle that multiple political parties aren't established right away.
Securing a multi-party system through electoral reforms
But securing a multi-party political system, which is the international norm for democratic countries, rather than a two party system, in the United States wouldn't be that hard to achieve in terms of the formal constitutional process to do so. It wouldn't even require a constitutional amendment. Politically, however, there would be big barriers to achieving this goal.
Duverger's Law, a law in the social sciences sense, says that first-past-the-post election systems tend to cause dual party systems (there is an exception to this law for geographically segregated political movements, such as nationalist parties for a region like the nationalist parties in Quebec and Scotland). So, all one needs to do in order to end a two party system is to change the election law system. This doesn't require a constitutional amendment.
Reforms possible with a change to federal law without a constitutional amendment
The U.S. Constitution does not direct that members of Congress be elected from single member district plurality election system. This system exists in the U.S. because it is mandated by 2 U.S. Code § 2c, which currently mandates single member districts for U.S. Congressional elections in states with more than one representative in the House.
Historically, before 2 U.S.C. § § 2c was adopted in 1967, multi-member Congressional districts were common in U.S. states, although not by a proportionate representation system. The reason for this reform in 1967 is that the majority in a multi-member district would elect all members of Congress from that multi-member district from the party with a majority in that multi-member district and this approach was used to suppress the black vote in the South, and this legislation reinforced the mandate of the Voting Rights Act of 1964 to prevent the suppression of the black vote in the South.
This statute states, in its entirety, that:
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).
Even with this statutory limitation, some U.S. states (e.g., Maine and Alaska) already elected members of Congress by ranked choice voting. Several other states require a majority vote to elect a member of Congress with a runoff election held if no candidate receives a majority of the vote in the first round (e.g. Louisiana), which like an instant runoff voting system eliminates the spoiler effects associated with third-party candidacies.
There is no reason that you can't have proportional representation in a country with a strong Presidential government like the U.S. with its current constitution. This is what is done in almost every other country with a strong President system countries (e.g. Turkey and Russia).
A conversion to a proportionate representation method of selecting members of Congress in states with more than one member of Congress could be accomplished without a constitutional amendment simply by repealing 2 U.S.C. § 2c and replacing it would a statute that mandated either rank choice voting or majority required to win with a runoff voting in states with a single member of Congress, and mandating proportional representation with a party list system of some kind in states with more than one member of Congress. This would also, simultaneously, end the problem of gerrymandering.
A statute, needless to say, is much easier to enact than a constitutional amendment which requires a two-thirds majority of both houses of Congress (or identical proposals from two-thirds of the U.S. state legislatures, or by constitutional conventions in two-thirds of U.S. states) to propose, and ratification by three-quarters of U.S. states to approve.
The relevant statute would require a majority of the U.S. House, a majority of the U.S. Senate (after overcoming a 60% of the U.S. Senate filibuster or using the nuclear option to abolish the filibuster in this situation with a majority of the U.S. Senate) and the signature of the President (or an override of a Presidential veto by two-thirds of the U.S. House and the U.S. Senate), with no state legislative action before the law in enacted.
The main barrier to this kind of change (which would be even greater to enact a U.S. Constitutional Amendment) is that at least naively, it is not in the interest of either of the two major political parties that control all but a handful of seats in Congress to create a multi-party system that would reduce their control of the process. But reforms of the electoral process contrary to the seeming narrow interests of those currently in office aren't unprecedented, usually because the political party backing the changes sees partisan gain from doing so, even though it technically makes their current voters less powerful.
For example, if the Democrats had a thin majority in both houses of Congress and held the Presidency, and abolished the filibuster in the U.S. Senate with the nuclear option, they might decide that proportional representation was the lesser of two evils to end the disadvantages that they face due to gerrymandering at the state level, and this might cause them to enact a statutory reform like this one.
On the other hand, if Congress simply repealed 2 U.S.C. § 2c, the laboratory of democracy in the states could reopen and some U.S. states with more than one member of Congress, perhaps by citizen's initiative following the model of Maine and Alaska adopting ranked choice voting, could adopt proportional representation, and if this system was popular, other states might follow suit and this could become the national norm, or provoke a national level re-enactment of 2 U.S.C. § 2c that mandated proportional representation.
Proportional representation at a national level, rather than state by state, would require a constitutional amendment. But since the practical difference between a state by state proportional representation system and a national one would be slight (basically just a rounding error scale effect), and because this would also require amendment to the Presidential election contingent election system at the same time, it probably wouldn't be worth the additional effort to attempt to achieve one.
Furthermore, you don't want to have too many seats at state in any proportional representation system because then it becomes possible to elect fringe candidates backed by just a tiny percentage of the vote (less than 0.25% in a single national proportional representation system) which if the majority coalition is thin, gives outsized power to fringe groups. This has historically been a problem in Weimar Germany which dealt with it by adopting a 5% threshold to get any seats post-WWII, in Italy where unstable coalitions of centrists designed to keep the extreme left and the extreme right out of power led to a very fragile democracy after WWII until recently, and in Israel. In contrast, only a handful of states have enough seats to allow a party with less than 5% support in the voting public to gain a legislative seat because they have 20 or fewer members of Congress.
Reforms possible without federal statutory reform or constitutional amendments
Short of this kind of statutory amendment, it would be possible to enact more limited reforms that don't so strongly lead to a two party system without amending 2 U.S.C. § 2c, either a state by state level (possibly with reforms enacted via citizen's initiative to overcome the biases of legislators elected in a two party system in many states where this is possible), or by enacting an additional law mandating certain reforms for the conduct of U.S. House elections from single member districts in addition to 2 U.S.C. § 2c.
Any single member district system inherently distorts the results in a state with more than one member of Congress relative to proportional representation except in the most idealized distribution of voters. But one can (and a number of states, such as Colorado and Ohio have) imposed standards implemented on a non-partisan basis for how Congressional districts are drawn that reduce the impact of partisan gerrymandering relative to the worst case scenario. This doesn't weaken the two party system, however.
But if you mandate, either nationally or in a single state at a time, that states used ranked choice voting, or require the winner to have a majority of the vote to win (with runoff elections if necessary) or have a California style "jungle primary" with the top two finishers in the primary facing off in the final round vote, you can eliminate the spoiler effect of first past the post voting systems.
In a first past the post voting system, a vote for a third-party or independent candidate always helps the candidate from the political party least similar to the third-party or independent candidate that you vote for.
This inherent bias against third-party candidates in first-past-the-post voting systems prevents viable third-party candidates from emerging. But if you have a system that eliminates the spoiler effect, voters are free to support a third-party or independent candidate in a first choice or first round vote, without worrying about helping their least favorite candidate. And, free to do so, third-party candidates would receive more support and stronger candidates would be more comfortable running on third-party tickets, and gradually, a multi-party system would emerge, although probably not one with as many viable political parties as a pure proportional representation system, because any candidate elected would have to receive at least second choice support from a majority of voters in a single Congressional district. Still, it might make three or four political parties, rather than just two, viable and would allow more unaffiliated candidates to be elected.
Any of these systems (but especially "jungle primary" systems) also inherently favor more moderate candidates relative to a system in which each of two major political parties holds a primary election and those two candidates then compete in a general election (which is the status quo in most, but not all, U.S. states). Partisan primaries favor farther left of center candidates in Democratic primaries and farther right of center candidates in Republican primaries, and in the process make it harder for moderate or centerist candidates to make it to the general election.
In 2024, the most moderate U.S. Senator who caucuses with the Democrats will probably be the independent U.S. Senator from Maine Angus King, and the most moderate U.S. Senator on the Republican side will probably be U.S. Senator from Maine Susan Collins, since there are no strong candidates campaigning for U.S. Senate seats in the 2024 election right now who are more politically moderate than either of Maine's Senators, and they are quite far apart. In contrast, for much of recent U.S. history, there has been some overlap in political ideology at the moderate end between the Democratic party and the Republican party in the U.S. Senate and in the U.S. House.
On the other hand, these election laws clearly aren't the only reason for the currently highly divided partisan breakdown in Congress. More states have reformed their election laws incrementally to reduce the tendency of those laws to elect less moderate candidates than had done so a couple of decades ago, but Congress has nonetheless grown more divided on partisan grounds. These institutions have only led to the current status quo with the help of additional factors not so directly related to U.S. election laws (most notably the fact that "realignment" of the two main U.S. political parties has run its course as described below).
Reducing partisan voting with legislative rule reforms
It would also be possible to reform legislative rules in the U.S. House and U.S. Senate respectively, in ways that would reduce the pressure on federal legislators to vote with their political party, weakening party discipline and the hold of the majority party on each house of Congress.
Unlike a parliamentary system, in the strong President system of the United States, you don't structurally need stable partisan majorities in either house of Congress to have a stable, functioning government. As long as there are majorities to pass the necessary appropriations bills every year to keep the government running, and to approve enough Presidential nominees to executive branch and judicial positions to keep the government running, you don't need bills that are passed to have the same partisan majority backing them for every bill.
The U.S. already has relatively weak party discipline compared to parliamentary systems, but it could be weakened further.
We know this from experience.
In the 1970s and 1980s, the United States political party system was in the middle of a transition of the policy positions of the two major political parties (called "party realignment"), which basically traded ideological positions on most issues in a process that began with Presidential candidate Goldwater's "Southern Strategy" for the Republican Party in the 1960s.
This produced a de facto three party system of Northern Democrats (who are similar to today's Democratic party), Republicans (who are similar to today's Republican party), and Southern Democrats, who were conservative on issues of national defense, foreign policy, and social issues, but liberal on economic issues. So, the working majority in Congress on economic issues was made up of Democrats, and the working majority in Congress on national defense, foreign policy, and social issues was made up of Southern Democrats and Republicans. But this lack of a consistent one party majority of every policy subject matter didn't seriously interfere with the operations of the government.
This de facto three party system eventually ended as the two major political parties completed their realignment into one fully liberal Democratic party and one fully conservative Republican party. But if electoral reforms produced a new groundswell of mode moderate legislators in Congress, this could resurface.
To make this work, however, partisanship in the procedural rules of each house of Congress would have to change.
In the U.S. House, the main reforms that would be necessary would be (1) to remove the control of the partisan leadership over the committee assignment system (e.g. by seating members on the committees of their choice by seniority with a proportional partisan balance in each house), and (2) to remove the authority of the House Rules committee to decide on a partisan basis what legislation is taken up on the floor once bills clear committees, for example, by granting every bill that clears a committee a right to a floor vote with significant right to make amendments, in the order adopted, without a supermajority vote to consider urgent legislation out of order. The allocation of U.S. House resources, like office space, would also have to be vested in some non-partisan decision-maker.
In the U.S. Senate, partisan control is already weaker, but rules that strongly empower the minority acting in a partisan fashion, like Senatorial holds and the filibuster would have to be repealed.
Is the system actually not working as intended?
The founding fathers did not foresee that the constitution would foster a two-party political system that is radical, inflexible and deadlocked. There is probably little political will to reform it for many reasons, at the cost of prosperity, security, efficiency and peace.
The U.S. federal government is undoubtedly very prone to deadlock. A majority of representatives in the U.S. House, a large minority of U.S. Senators, the President, or the courts applying constitutional rules that invalidate federal laws, each have de facto veto power over new legislation. And, the power of the two major political parties in the U.S. is equally balanced.
One of the other well known political science laws is that in a two party system (or generalizing it, to a two coalition of parties system), where the parties (or coalitions) are ideologically coherent are prone to continually attempt to tweak the composition of their pre-election coalitions by changing their policies or political tactics, in a way that tends to bring them close to a 50-50 balance of power in the governmental institutions that they most strongly wish to control (the federal government in the U.S. case).
The U.S. federal level political system has been quite evenly balanced between the two major political parties for most of the period since the 1980s (more than four decades) with only brief periods when a single party had "trifecta" control of both houses of Congress and the Presidency, and courts that have been disinclined to thwart their agenda.
In contrast, during the Great Depression and into World War II, the federal government was a dominant party system united under FDR's Democratic Party, and the initially combative Lochner era U.S. Supreme Court eventually backed down when faced with court packing legislation that was likely to pass.
Also, the most recent Congressional elections in 2022 produced outcomes in terms of legislative seats held in the U.S. House that quite closely tracked the overall popular vote for each political party nationwide, with factors that favored Republicans in some places balanced by factors that favored Democrats in other, ultimately balancing out for the nation as a whole. And, the increased partisanship and ideological distance between the political parties seen in Congress mirrors increased partisanship and ideological distance between the political parties in the electorate itself.
Legislation that has bipartisan support (e.g. aid to Israel in the wake of recent events there) can still get passed. But it has been the exception rather than the norm pretty much since the 1980s (before which there was a short period when the Democratic party was dominant at the federal level) that a single party without bipartisan support can pass federal legislation leading to major policy changes. These windows of opportunity have appeared now and then and been utilized by the parties having them. But these windows of opportunity have generally been short-lived and resulted in only moderate and somewhat incremental, rather than decisive and bold reforms.
Arguably, a system that produces gridlock and little federal legislative activity in time periods when the nation is deeply and fairly evenly divided on most political issues, is exactly what the Founders intended when they created a federal political system. When the nation is united, major new national political policies can be enacted, but when the nation is divided, real major policy innovations become much easier to achieve at the state and local level than they are to achieve at the federal level.
The two party system doesn't necessarily have a lot to do with that. Ultimately, exercising political power to change the status quo is about securing legislative majorities to take action, which requires majority support from legislators as measured by the standards of the political system to pass legislation.
In a two party political system, one assembles coalitions that the organizers of the respective political parties hope will be sufficient to secure the majorities necessary to pass legislation before the election into two pre-negotiated coalitions.
In a multi-party political system, coalitions that their member political parties hope will be sufficient to secure the majorities necessary to pass legislation are negotiated after the election.
Lots of countries, especially non-federal "unitary" political systems, make it easier to secure a legislative majority than the U.S. does. But, it isn't manifestly obvious that the task of organizing a multi-party coalition (probably balanced close to 50-50 anyway) with sufficient backing to pass legislation after Congressional elections are held would have an easier time passing legislation than the task of building one of the two major party coalitions before the election to achieve this goal in the status quo.
Also, countries with these unitary systems where the majority threshold needed to pass legislation is lower are often more politically homogeneous than the United States is politically. This lack of political consensus at a national level was a fact that was apparent even back in the time when the Founders set up the current U.S. Constitution, and it shaped how the U.S. Constitution was written.
Federal level political gridlock is ugly and frustrating.
But political gridlock is not the norm in most U.S. states, despite the fact that they also have two party political systems, mostly because most U.S. states aren't so evenly politically divided and secondarily because most U.S. states have fewer barriers to legislating (like the minority veto powers created by U.S. Senate rules and unequal populations for U.S. Senate electoral districts, i.e. U.S. states).
Republicans secured a trifecta in Louisiana after the 2023 general election. Democrats gained control of both houses of the Virginia state legislature in the same election, although Virginia's Governor is still a Republican.
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 theses 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.
Also, legislative process gridlock on particular key issues can be overcome with citizen's initiatives in many U.S. states, an option that is not available at the federal level in the United States.
Federal government political gridlock has not been accompanied by corresponding state level political gridlock in the U.S.
Divided control and gridlock is the exception rather than the norm at the state level in the United States, and there are no states with legislatures elected from districts with unequal populations nor are there any states that give legislative minorities the privileges the receive in the U.S. Senate. So, getting clear majorities to pass legislation is easier at the state level than at the federal level in all but a modest minority of U.S. states.
Given the currently deeply divided state of political preferences in the U.S. at the national level, that has a strong regional geographic character, a system where state level policy reforms are much easier to achieve than federal level policy reforms where gridlock prevails, is arguably a feature and not a bug, of just the kind that the Founders intended.
One Comment
There were a number of comments to this answer, but one in particular deserves to be mentioned as it adds an important factual observation:
"not in the interest of either of the two major political parties" In the simplest case where no new parties get founded and actual voters' votes remain the same, PR would have denied the Republicans a majority in the House in 1996, 1998, 2000, 2004, 2012, and 2016; but there has been no case since the present system was introduced when the Dems won a majority under the present system but would have been denied it under PR. Hence, PR could be argued to be in the Dems' interest. – Daniel Hatton
