N.Y. Elec. Law § 6-124
A judicial district convention shall be constituted by the election at the preceding primary of delegates and alternate delegates, if any, from each assembly district or, if an assembly district shall contain all or part of two or more counties and if the rules of the party shall so provide, separately from the part of such assembly district contained within each such county. The number of delegates and alternates, if any, shall be determined by party rules, but the number of delegates shall be substantially in accordance with the ratio, which the number of votes cast for the party candidate for the office of governor, on the line or column of the party at the last preceding election for such office, in any unit of representation, bears to the total vote cast at such election for such candidate on such line or column in the entire state. The number of alternates from any district shall not exceed the number of delegates therefrom. The delegates certified to have been elected as such, in the manner provided in this chapter, shall be conclusively entitled to their seats, rights and votes as delegates to such convention. When a duly elected delegate does not attend the convention, his place shall be taken by one of the alternates, if any, to be substituted in his place, in the order of the vote received by each such alternate as such vote appears upon the certified list and if an equal number of votes were cast for two or more such alternates; the order in which such alternates shall be substituted shall be determined by lot forthwith upon the convening of the convention. If there shall have been no contested election for alternate, substitution shall be in the order in which the name of such alternate appears upon the certified list, and if no alternates shall have been elected or if no alternates appear at such convention, then the delegates present from the same district shall elect a person to fill the vacancy.
N.Y. Elec.Law § 6-124