To belabor my point about Duverger's law and why it doesn't mean third parties shouldn't run at all.

In 168 House districts Trump got only 40% of the vote or less in 2016 -- according to The Cook Political Report . If you want a more cushy threshold we can say in 92 House districts Trump got only 30% of the vote in 2016 or less. If we include all of California's House districts because they have a jungle primary where the top two candidates move on to the general election regardless of party status, that means the People's Party (or any other left-wing third party) can run in somewhere between 100 to 200 House districts (again depending on which threshold you prefer) without jeopardizing the district to far-right Republicans and either the PP or Dems would win an overwhelming majority of those seats. 

The result would be that it would be a competition between Democrats and PP candidates in these districts, and since the PP candidates would be challenging Democrats to the left they'd pull their Democratic competitors to the left. Republicans voters in those districts would have to decide whether they'd want to vote Republican or not because chances are that the GOP would be a third party in this situation. So they might cross over to vote Dem instead of Rep so that the PP doesn't win, if they prefer Dems to PP. 

Assuming the People's Party only gets a third of the seats, Democrats get 65% of them, and moderate Republicans get 2%, that'd give PP somewhere between 33-66 seats (depending on threshold), Dems somewhere between 65 - 130 seats (depending on threshold), and moderate Republicans somewhere between 2-4 seats (depending on threshold.) This might sound bad to give Republicans 2-4 seats they'd otherwise not have, but the ideological median likely would be further left than it would've been otherwise because the PP would pull Democrats leftward, and Democrats would pull moderate Republicans leftward in these districts. 

It makes the chances of progressive legislation passing much higher as the whole Overton Window has shifted leftward when you have a House of Representatives with say 66 Populists (synonym for People's Party members), 162 Democrats, 1 Libertarian, and 202 Republicans with the Populists and Democrats forming voting coalitions for a majority and to elect the Speaker of the House, but otherwise having separate infrastructures. 

Like @vivster said, we need major electoral reform if American democracy can ever hope to support more than two major parties. Our electoral system is based on first-past-the-post, winner-take-all rules. Whoever wins the most votes wins the election, even if they only have, say, 35% of the vote. Because of this in nations with only two viable major parties, third parties serve only as a spoiler. In nations with three or more viable parties, this can result in incredibly unrepresentative outcomes in elections. The formation of a large left-leaning party would only serve to siphon votes away from the Democrats, and would only benefit the Republicans. Of course, conservatives would absolutely love this outcome, as if at least 10% of the Democratic base were to permanently shift their support to a new party separate from the Democrats, it would essentially guarantee Republican hegemony in American politics. Personally, I doubt this new "alternative" will ever amount to anything. Disaffected progressives have had the Green Party for decades as that alternative, and Nader managed to get close to 3 million votes running as a Green in 2000 (more on this in a bit).

Before we even consider forming a major left-wing alternative, we need to change the rules of our electoral system. First and most important of all, FPTP rules need to be eliminated and replaced with ranked-choice voting. That by itself would result in third-party candidates being far, far less likely to serve as spoilers in any election. Additional reforms may be needed as well, including replacing single-member districts for House elections with multi-member districts (which in addition to making the House more representative would make gerrymandering difficult if not nearly impossible) and replacing the Electoral College with a national popular vote for president. But until we get those much-needed reforms, voting third-party does nothing but help the other side. You play the game by the rules as they are, not as you wish they would be. If you don't, the other side wins.

As a progressive, one thing that bugs me most about my side is the willingness of so many of us to vote third-party. While the vast majority of us always vote Democratic, there is a non-trivial minority that has a tendency to vote third-party. Based on exit poll data, for at least the past 20 years, we have done so at an average rate that far exceeds that of conservatives:

The 2000 election saw Ralph Nader siphon votes away from Al Gore. It was sufficient to cost Gore both Florida and New Hampshire. Had only 1% of Nader voters in Florida decided instead to vote for Gore on Election Day, we wouldn't have had Bush as president. After facing the actual reality that was the Bush presidency, progressives became far less likely to vote third-party over the next two presidential election cycles. It didn't help in 2004, as Bush was still sufficiently popular and was successfully able to paint Kerry as a flip-flopper and himself as stronger on the issue of terrorism (plus moral/"culture war" issues helped get out the conservative vote), but the election was still closer than it would have been had Nader done as well among progressives as he did in 2000. By 2008, not just progressives but even most independents and moderates had gotten tired of Bush & the GOP, and Obama won by a considerable margin.

But by 2012, old habits started to re-emerge. The third-party vote expanded somewhat (about 19.8% higher than in 2008), and exit polls showed self-identified liberals voting third-party at a three-to-one rate versus conservatives. It wasn't enough to affect the whole election as Obama was still sufficiently popular with independents, and the progressive third-party vote wasn't distributed evenly, with key swing states showing low rates of voting third-party overall.

And in 2016, we saw a repeat of 2000. If we were to judge electoral performance in terms of improvements from the previous election, third-party candidates were the real winners in 2016, with a 3.5 times increase in their combined vote total from 2012. While there was an across the board increase among all ideological groups and parties in the frequency of third-party voting, the vast majority of that increase was felt among the left and Democratic-leaning moderates. I've said on multiple occasions in various places since the 2016 election that Trump only just barely won that election, with razor-thin victories in Michigan, Wisconsin, and Pennsylvania being the decisive factor. Had Hillary held on to those states, she would have won. Exit poll data suggests that progressive voters voting third-party account for the entire deficit Hillary had against Trump in those states (there was also an increase in self-identified liberals voting Republican, presumably as a protest vote against Hillary). Had more progressives been more willing to vote Democrat, we probably wouldn't be having this discussion right now.

To be fair, disaffected liberals/progressives refusing to vote Democratic are not the only issue at hand. Gore and especially Hillary could have campaigned better than they did. Hillary herself was the target of constant attacks by the right (and even some elements on the left) since the early 90s, which obviously contributed to her relatively poor favorability among the general population. There was the Bush v. Gore case in 2000. And of course there's the distorting effects of the Electoral College, which resulted in both Gore and Hillary losing the election despite winning the national popular vote. But the effects of the voting habits of progressives cannot be denied. They are more likely to refuse to support a Democrat than a conservative is to refuse to support a Republican over a candidate's inability to pass some litmus test for ideological purity. Whether it was Nader voters in 2000 or angry "Bernie or Bust"-ers in 2016, progressives refusing to vote Democratic has been perhaps the deciding factor determining the outcome of several key elections in critical swing states. If progressives consistently voted third-party at a rate of only 1% instead of 3-7% like in three of the past five elections, Democrats likely would have won every election this century.

Now, I fully understand the disappointment many progressives feel with the Democratic Party. I wasn't a huge fan of Hillary even though I voted for her. I'm not even a huge fan of Biden even though I will be voting for him. I voted for Bernie in the primaries both this year and in 2016. But we have to realize that we share the Democratic base with a large portion of non-progressives. Not just the U.S. as a whole, but even the Democratic base in specific is not as left-leaning as a lot of progressives would prefer. According to Gallup, while the Democratic base has been gradually moving leftward since the 90s, moderates were a plurality as recently as the mid 00s, and it wasn't until very recently that self-identified "liberals" accounted for a majority. Meanwhile, the GOP had already been majority conservative for a very long time, and has been moving further to the right over time, with nearly three-quarters of Republicans self-identifying as "conservative." Interestingly, the ideological makeup of independents hasn't budged much, showing that the net decline in Americans identifying as "moderate" has been within people who identify as belonging to one party or the other. Polarization has been asymmetrical in America since at least the 90s, and we've had an obvious right-wing GOP up against a relatively centrist Democratic party. But that is changing, slowly but surely.

If I were to offer advice to progressives who are still thinking of voting third-party (most of them still quite young; the under-30 demo has long been statistically far more likely to vote third-party than older voters), it would be this: Wait. Be patient, young padawan. Work with what you have now. The Democratic Party is moving in an increasingly leftward direction, and eventually that ideal progressive you want will win the nomination (maybe AOC in 2028?). If you didn't get your ideal candidate this time, vote Democratic anyway. Don't even think of it as "voting for the lesser of two evils." Just remove that thought from your mind. Rather, think about what the GOP stands for, and how much you want to see them lose to keep them from getting their way. Anything that could contribute to Republican victories will only hurt what you care about if it does result in a GOP win. And if the GOP continues to win, they will continue to get more nominations to the Supreme Court, they will continue to work to undermine everything you support, and they continue to move themselves and our government in a rightward direction. At worst, a Biden presidency will keep things from getting worse than they already are. At best, we might actually make strides in undoing some of the damage and getting at least some meaningful reforms passed.

Trump and Pence and McConnell are only symptoms of the rightward shift in the GOP, not the cause. The Republican Party has for the past 40 years been defined by a fusion of the social policies of the Christian right with Reaganomics and other quasi-libertarian economic policies. They've been long primed for authoritarian tendencies and conspiratorial beliefs. They long ago convinced themselves that scientists are lying about climate change or evolution. Now we're seeing GOP candidates who believe in QAnon conspiracies get onto the ballot. The John Birch Society types are now the mainstream in the GOP. Do not underestimate the threat the GOP poses to everything you hold dear. They believe you are the enemy. They do not believe you are a "real" American. Their political pundits and more strident politicians make that abundantly clear. When they call the Democrats and everyone else to their left a "communist" or a "Marxist," they aren't just joking or being hyperbolic. They mean it. Or at least their base means it (it's hard to tell if propagandists ever really believe their own propaganda). You're not going up against a party that can be reasoned, bargained, or negotiated with anymore. Compromise is dead, and they killed it. As long as a Repubilcan is in the White House, we will accomplish nothing. As long as the GOP has a majority in the Senate, we will accomplish nothing. It's that asymmetrical polarization in effect. The only way to stop the Republican agenda from making any gains is by winning elections. Progressives really need to fully understand what they are up against with the modern GOP. I had hoped Trump's incompetence, disregard for norms, and authoritarian tendencies would make that abundantly clear, but for some it hasn't. While polls suggest that most progressives that didn't vote Hillary in 2016 will vote Biden this year, there are still plenty of vocal progressives who think it makes perfect sense to not vote Biden because he's not their ideal progressive candidate.

I understand the temptation to cast a protest vote over a moderate candidate winning the Democratic nomination. Perhaps some progressives think it might provide some incentive for the Dems to put forward a more progressive candidate, but it doesn't, because it's not the DNC picking who wins. It's your fellow Democratic primary voters. They chose Hillary. They chose Biden. The party base is still sufficiently centrist to where moderate establishment candidates are favored (and let's not forget that Bernie is not a Democrat). Older voters (especially over-30 African-American voters) in Democratic primaries in particular heavily favor moderate establishment candidates. Their voice matters, too. Potentially costing the Democrats elections by voting third-party to protest how most Democratic primary voters voted will not help you, nor will it compel the party base or leadership to change to better suit your desires. If we want to reform the Democratic Party to become less like the centrist DNC and more like the Congressional Progressive Caucus, the most constructive means of doing so is through the primary process. Also, do more to convince more moderate Democrats you know to vote progressive. It's possible that they may be more progressive-minded than your or they think, and they keep voting for moderate candidates in primaries because they think it makes more sense tactically, or because they think identifying as as a moderate is somehow more "respectable" than identifying as a "liberal," which is seen as a dirty word in American politics by many. Work to transform the party from within, not destroy it by fragmenting it.

Again, the Democratic base keeps moving in a more progressive and less centrist direction. Help keep that momentum going. In the meantime, make sure you do what you can to ensure the Democrats win. Even a moderate Dem will be far better than any Republican. A moderate Democrat is more likely to enact policies that you approve of. If you're a progressive, Biden and the Democrats may give you only 80% of what your want, but the Republicans will give you zero percent of what you want and actively work to undo existing progressive reforms, because the GOP hates everything you support. Our only choices on November 3 are either A) four more years of Trump, or B) a Biden presidency. There will be no other possible outcome. Make the right choice, even if it's not the ideal choice.

Here is a map of Canada's 2015 election. Canada has a FPTP system, just like the United States. You'll notice that four parties had representation 

Here is a 2019 electoral map. 

Notice that five parties have representation. 

Here is a map of the 2015 U.K elections, like Canada and the U.S they have a FPTP system. 

Here is a map of the 2019 U.K elections. 

Duverger's law tells us that there will be two major parties in any system based on FPTP, but it doesn't say that third parties will have absolutely no influence or ability to influence elections. 

Like I noted in my previous post, roughly 90 House seats are solidly Democratic to the point that only 30% (or less) of their constituents vote Republican. This means that the vote could split down the middle Democratic/left-wing third party 35% for each, and one of them would still win because the Republican only gets 30% (at max) of the vote normally. 

Duverger's law doesn't apply in the situation where one of the national parties are so weak in a certain region to the extent that it becomes essentially a third party in that region. 

This is why you find Lib Dem/Conservative constituencies in Britain, or NDP/Conservative ridings in Canada. There is no reason why there can't be Populist Party/Democratic districts or Populist Party/Republican Party districts in the U.S where those are the two major parties of that district. 

And there lies the hen-and-egg problem.

Neither Democrats or Republicans would ever change the system unless forced to, as it would mean they'd loose power to other parties. In other words, you can kiss goodbye the dream of winner-takes-all go away anytime soon - or ever, really.

Since the states choose themselves what system they use to vote in the presidential election, they need to win states (I think governor, or does it need a different post to be able to change state voting laws?) to be able to slowly change the voting laws in the states one by one until the number of states with winner-takes-all is relatively small and don't singlehandedly decide over the outcome in elections. Only then can third parties really attack the presidency.

The problem: They need to run in the next presidency to make themselves both visible to people who don't follow politics closely and for their own credibility. But that doesn't mean they'd have to run in swing states yet to not hand the election to republicans on a silver platter. Or that they even get widespread ballot access in the first place for that matter.

Fortunately for many states all that is needed to change the voting system (likely to ranked choice, but maybe proportional or a mixed system in a few states as well) is a ballot initiative. This is how Maine got ranked-choice voting a few years ago. 

Here are the states that allow ballot initiatives from their populations. If the population votes yes, then the legislature and governor have no choice but to enact their vote.  

Then the remaining states that don't have initiatives are going to have to get a coalition of third parties to push for either the major parties to change the system, or otherwise they'll run a legislative reform campaign designed to oust the major parties and get that sole reform done. 

Also See: 

Well if people don't think they are represented by any of the 2 parties then it is good that they try to make a new one. But they should have to look at Brazil and the several dozen parties here. It isn't much better to have plenty of parties versus having 2 parties with several sub parties inside.

There is one major difference between the FPTP in Canada and the UK compared to the US: They're local elections while in the US, it's almost always entire states. I would agree with your assessment if the US had all their states divided up into voting districts like in Maine for instance, but the way it is, entire states are just too big in weight for most voters to go off the GOP/Dem rails.

But like you said in the other post, if voters can make the choices themselves on how they would like to vote, then getting more equitable voting systems in place should be a real possibility, at least in those states that allow those.

House of Representative elections are not state-wide elections, nor are state-senators and state House of Representative/assembly elections, nor are local elections. 

Sure the Senate and Presidency are elected state-wide or through a system of fifty one (state + D.C) elections, but they are only two parts of the whole system.

Third parties and independents have won Senate seats in the past too, and two Senate seats are held by independents currently (Vermont - Bernie Sanders, and Maine - Angus King.) 

And what has the results been? Outcomes that are unrepresentative, sometimes incredibly so. The actual composition of their Houses of Commons is often way out of line with how people actually voted. Many MPs in recent elections won with less than 40% of the popular vote in their electoral district. As an example of these unrepresentative results, in the 2015 Canadian federal election, the Liberals won an absolute majority of seats with less than 40% of the national popular vote, while in 2019 they came in second and still won the most seats (though not a majority). The NDP had 16% of the vote but only 7% of the seats. In a good number of districts won by the Conservatives, the NDP appears to have served as little more than a spoiler. How many seats would the Liberals and Conservatives have won if it was just the two of them? The Conservatives don't have a rival right-wing party like the Liberals have three rival left-wing parties, and they were able to control the House of Commons for nearly a decade under Stephen Harper while never gaining more than 40% of the national vote.

Additionally, some of those smaller parties in Canada & the UK, like Bloc Quebecois, SNP, and Plaid Cymru, are limited to specific cultural regions that vote overwhelmingly for that party. In the UK, for example, England by itself is closer to a two-party system, with the Conservatives and Labour winning a combined 81.2% of the popular vote and nearly all the seats in Parliament in the last election, with the Lib Dems, Greens, and Brexit Party being incredibly underrepresented in proportion to their vote share, and probably also serving as spoilers in most elections. Aside from Labour, the Conservatives, and the Lib Dems, most of the other parties that hold seats in the British Parliament get the entirety of their representation in Parliament from Scotland, Wales, and Northern Ireland, and are, at present, generally over-represented.

Elections in the UK and Canada are a horrible mess because of the existence of more than two major parties. They make our elections look neat and tidy by comparison, and ours are already unrepresentative enough. FPTP rules are not the norm for lower house elections in most of the world, and it's easy to see why.

Also, those nations have a parliamentary system, while the United States has a full presidential system. When we talk about elections in the UK or Canada, we're talking purely about those lower house elections. The executive in parliamentary systems is an unelected but largely ceremonial office, while in the United States the president is elected by the people (albeit indirectly), exists separate from and co-equal to the Congress, and exercises actual power as, unlike in parliamentary systems, full separation of powers is unique to full presidential systems. The upper house is likewise unelected but with less power than the lower house in parliamentary systems, whereas our Senate exists co-equal to the House and its members have been directly elected since 1913. Their legislative process and general rules are different. There is no such thing as a minority government, hung parliament, or snap elections in the U.S. Either a majority of the members of Congress vote in favor of a bill or they do not. If they can't get stuff done at all, well, that may or may not get fixed next election, which will happen on a fixed date every even-numbered year and not a day before or after.

And when it comes to presidential elections, it's not a lot of smaller district-level elections. It's the whole country voting for one person. Whoever wins the most votes in a state wins that state's electoral votes. If the Democratic base was heavily split between two parties, most swing states would effectively become solid blue states. Republicans could win Florida, Ohio, Wisconsin, Pennsylvania, Michigan, and so on. Some states that are more firmly blue could reverse course and end up flipping to the red column as Republican candidates still manage to get 40-45% of the vote. All they would need to win is for that remaining 55-60% to be divided heavily enough. Even if we abolished the Electoral College and replaced it with a direct popular vote, the GOP candidate could still win the election with only 40-45% of the vote if the progressive vote is sufficiently split, and if they get above 45% but not quite 50%, they're almost guaranteed election if a major left-wing third-party consistently manages to nab at least 5-10% of the vote.

Realistically, though this proposed new party would itself never stand a chance of winning the presidency itself, given the ideological makeup of America. While self-identified "liberals" have been growing as a percentage of the population, they are still a minority, with self-identified moderates being a plurality. Not all of them are going to abandon the Democrats, either. Given the typical third-party vote on the left, I would imagine that the Democrats might lose at most about 10-15% of the progressive vote, or approximately 5-7% of their total base. That would never give this new party a chance at capturing the White House for a very long time, though it would be sufficient to cost the Democrats close races. In other words, they'd simply do what third parties have always done in America: serve as a spoiler.

The United States is not Canada. It is not the United Kingdom. We do not operate on the Westminster System. And in our system, third parties have only ever served as a spoiler. But in all of these countries, we need ranked-choice voting and, for lower house elections, proportional representation.

See Also:

https://www.youtube.com/watch?v=r9rGX91rq5I

https://www.fairvote.org/anything-but-fair-the-sad-tale-of-the-canadian-election-system

The most successful third party in history, by far, was the American Independent Party. The entire basis of the AIP's existence was white Southern rage over the Civil Rights Act of 1964, which was passed entirely along geographic lines. The opposition was almost every Southern legislator, regardless of political party, with Southern Democrats and Southern Republicans alike voting against it, plus a handful of non-southern Republicans. All but two or three Democratic legislators outside of the south voted to pass the Civil Rights Act. The only non-southern Democrat in the Senate to vote "nay" was Robert Byrd from the border state of West Virginia, who filibustered the Act for 14 hours. President Lyndon Baines Johnson, a Texan and a Democrat, worked at getting as many Southern Democrats as he could to cross the aisle and support the Civil Rights Act, with some success, and he signed the bill into law despite Southern opposition and anger. 

One of the "nay" votes came from Senator Barry Goldwater of Arizona. Goldwater was the Republican candidate for president in 1964. Johnson won the 1964 Presidential election in one of the largest electoral landslides in American history, and with the largest popular vote margin in American history. Goldwater won only six states, but the pattern of states he won attracted a lot of interest from GOP leadership. All of the five states that Goldwater won, other than his home state of Arizona, were Deep South states that up until then had been part of the Democratic "Solid South" - Louisiana, Mississippi, Alabama, Georgia, and South Carolina, angered over the passage of the Civil Rights Act. They voted for an Arizona Republican over a Southern Democrat. Goldwater's reason for voting against the Civil Rights Act was that he felt it was a violation of states' rights, which was the same argument that was used to oppose abolition and desegregation. The other Senator from Arizona, Democrat Carl Hayden, voted to pass the Civil Rights Act.

The Republican Party capitalized on Goldwater's vote to appeal to Southern voters, but they ended up losing the rest of the country in the process that year because most of the country outside of the South was alienated by the idea of open segregation, even though there was plenty of de facto segregation outside of the South thanks to redlining, which was the practice of keeping blacks out of white suburbs by refusing to sell to them and denying them mortgages to buy homes in the suburbs. Segregation was apparently okay as long as it wasn't called segregation. 

The American Independent Party was an extreme right-wing party founded on open support of segregation and "law and order," which was coded political language for keeping minorities out of the white suburbs that sprung up as a result of white flight. In 1968, they nominated George Wallace, the Democratic governor of Alabama famous for trying to block black students from entering an all white school with his own body and his inauguration speech as governor, "Segregation now, segregation tomorrow, segregation forever".  Wallace didn't run as a Democrat because the mainstream Democratic Party by that point had completely rejected overt segregation (meanwhile, blacks in non-southern states continued to be redlined). He said that "there isn't a dime's worth of difference between the two parties." Wallace's supporters included segregationists, radical right-wing supporters in California, and the John Birch Society. 

Almost as controversial as Wallace himself was his running mate, Curtis LeMay, the former Chief of Staff of the USAF.  LeMay advocated using nuclear weapons in Vietnam and said that the public had a "phobia" of nuclear weapons. 

Wallace ran on segregation and "law and order," which was coded language (dog-whistling) for keeping minorities out of white suburbs and confined to the inner cities. Nixon adopted a "law and order" campaign in response, wanting to appeal to Southern voters over racial angst while also not wanting to alienate Northern and Midwestern conservatives by openly advocating for segregation. The Democratic candidate, Hubert Humphrey of Minnesota, also felt forced to run on a "law and order" campaign so as to not appear soft on crime and violence. The violent "long, hot summer" of 1967 and the continued unrest in 1968 forced his hand on the issue.

The Democratic Party was in disarray. Johnson was initially running for reelection, but by that time, the public strongly disapproved of his handling of the Vietnam War, and the Tet Offensive was the last nail in Johnson's presidential coffin. Johnson was also in poor health and ultimately dropped out. Robert F. Kennedy had the support of a broad coalition of people who opposed the Vietnam War, Blacks, Catholics, and poor whites, and was heavily favored to win the election in 1968, but he was assassinated in June. Hubert Humphrey was the eventual nominee, but was unpopular because he wouldn't commit to ending the war, which aroused the ire of antiwar activists and led to the 1968 DNC Riots in Chicago. The Democrats were splintered while the Republicans were united, and that put Nixon in office. 

Wallace won 10 million votes and five Southern states, plus one faithless elector in North Carolina, which otherwise voted for Nixon. Nixon only got a half-million more votes than Humphrey but still won with a huge electoral majority. Wallace was by far the most successful third party candidate in the history of the United States, all on a platform of racial hatred. The American Independent Party faded out after the 1968 election. 

In 1972, Wallace ran as a Democrat. Segregation had turned into a third rail, so he renounced his former segregationist stance. He was shot during a political campaign in Maryland. He survived, but it put an end to his presidential campaign. He was a paraplegic for the rest of his life. Nixon won 49 states in 1972 and swept the entire South for the first time in the country's history. George McGovern, the Democratic candidate, only won Massachusetts, the liberal home state of John and Robert Kennedy.  

But the Republicans had seen the pattern of states that Goldwater and Wallace had won, they saw an opportunity to bring new blood into the party, and they took it. Some Southern Democrats, including Wallace, repented of their former segregationist stance. Wallace said in 1979, "I was wrong. Those days are over, and they ought to be over." Byrd, the WV senator who had filibustered the Civil Rights Act, also renounced his former views and expressed shame over his own history in Congress. But Strom Thurmond of South Carolina became a Republican and helped bring more Southern Dems into the Republican tent, as did Jesse Helms of North Carolina, who was a Republican for his entire Senate career.  Since segregation was now a third rail, they instead made those same promises of "law and order" to white flight suburban voters. The GOP also began infusing evangelical Christianity into the party's DNA. 

But Wallace had dragged the entire Republican Party to the right, and since the Democrats didn't want to appear to be soft on crime, they too had to advocate for "law and order."  So the Democrats also got dragged to the right. 

I hope all of this illustrates some of the problems with third party voting in the United States. This was by far the most successful third party in American history, and it ran on a platform of racial hatred, with a lunatic who though the casual use of nuclear weapons was okay thrown in for good measure. Republicans today are smart enough not to be distracted by third parties. They're keeping their eyes on the prize.