Since 1947, New York state has restricted the ability of outsider candidates to run in party primaries. Outsiders can run in a party primary, but only if party leaders approve letting any particular non-member candidate run in that party’s primary. This restriction is called the Wilson-Pakula law.
Virtually all public offices in New York are partisan, so there are thousands of local partisan elections in very small-population jurisdictions. Governor Andrew Cuomo has proposed to the legislature that the Wilson-Pakula law be repealed. But leaders of the Conservative Party and the Working Families Party are afraid that if the restriction is repealed, they will be raided, especially in small jurisdictions where those parties may have very small numbers of registrants. The Green Party of New York, which is also ballot-qualified, probably shares their sentiments, because its enrollment is smaller than the enrollment of the Conservative Party and the Working Families Party. Parties feel that activists of the Democratic and Republican Party will enroll in those parties, in certain areas, just to control the nomination process of those parties.
One solution would be to let small qualified parties nominate by convention instead of by primary. States that let any ballot-qualified party choose whether to nominate by convention or primary are Alabama, South Carolina, and Virginia. States that provide that small ballot-qualified parties nominate by convention in all cases, or virtually all cases, are Colorado, Connecticut, Delaware, Georgia, Indiana, Kansas, Kentucky, Maryland, Michigan, Nevada, New Mexico, Oregon, Texas, Vermont, West Virginia, and Wyoming.