There was an interesting new post on the subject at Ballot Access News written by the widely-respected election expert and advocate for third party/independent ballot access Richard Winger. Take a look at this excerpt:

On February 10, the Second Circuit refused to enjoin the new New York definition of a qualified political party. SAM Party of New York v Kosinski, 20-3047. Here is the twenty-page opinion, which was written by Judge Michael H. Park, a Trump appointee. It is also signed by Judge Robert D. Sack, a Clinton appointee, and Steven J. Menashi, a Trump appointee.

The new definition requires a party to poll 2% of the presidential vote to retain its qualified status. The decision says there are two state interests in the new, more difficult requirement: (1) to improve the chances that the winner will get a majority of the popular vote; (2) to save money, because the state now has public funding for candidates for state office, although it doesn’t start until 2024.

Both justifications are utterly without merit. Point one could be solved if the state used ranked choice voting. Point two is easily rebutted by pointing out that the Second Circuit already ruled in a Connecticut case that states need not provide public funding to minor parties or independent candidates.

Larry Neumeister of the Associated Press wrote a related piece with more information. Here is an excerpt:

New York state is within its rights to keep its election ballots decluttered and prevent voter confusion with rules limiting how a political party gets on ballots, an appeals court said Wednesday.

The 2nd U.S. Circuit Court of Appeals rejected a challenge to the state’s new election ballot rules by the SAM Party of New York. It said the party, whose full name is Serve America Movement, was unlikely to succeed with claims that ballot rules violate the First and 14th amendments.

SAM became a political party in 2018 when it ran a gubernatorial ticket that drew over 55,000 votes.

Ballot access laws are the main barrier to many potential candidates. Ballotpedia is an amazing website for information on ballot access for third parties. Check out this key information for New York State:

In order to get on the ballot in New York, a candidate for state or federal office must meet a variety of complex, state-specific filing requirements and deadlines. These regulations, known as ballot access laws, determine whether a candidate or party will appear on an election ballot. These laws are set at the state level. A candidate must prepare to meet ballot access requirements well in advance of primaries, caucuses, and the general election.

According to the NYC government website:

Primary Elections are held so that voters registered with a qualified political party may select their party’s nominees to the general election for partisan offices. Because a primary is a party election, only voters registered with one of the parties qualified to conduct a primary in New York City may vote in their party’s primary.

General Elections are held to elect candidates to public offices. For partisan offices, nominees from the party primary elections appear on the ballot, along with independent candidates.

Also, see this video from Democracy Now:

Democracy Chronicles has put together an in-depth review of the majority of America’s third parties in a handy overview where all the country’s political parties, other than the two big parties, are separated into categories and contextualized. Links to their websites and party platforms are included too. See the overview of all American political parties at Democracy Chronicles Third Party Central.