New York is one of nine states that constitutionally specifies a method for election administration. The others are Arkansas, California, Louisiana, Mississippi, Texas, Vermont, West Virginia and Virginia. Of these, Arkansas, California, Louisiana, Mississippi, Vermont and West Virginia give this duty to an elected Secretary of State; in Texas a Secretary of State appointed by the Governor (with no legislative advice and consent) is responsible.
Whether elected or appointed, the Secretary of State position is highly political, and therefore not a good model for fair elections. (As an example, see the role of Katherine Harris in the Bush/Gore recount, where she served as both Secretary of State and Co-Chair of the Bush Campaign.
Virginia’s constitution makes no provision for a state election board: it calls for three-member city and county election boards, with representation assured for the two major parties. Only New York has a constitutional provision that specifies the use of a board at both the state and local levels to oversee election administration.
For the administration of elections, about three-quarters of American states use a single headed agency. 18 states have ethics commissions.
Only one state, however, has experience with a nonpartisan board of elections.
In 2008, “in a moment of rare enlightenment,” the state legislature created the Government Accountability Board, which combined nonpartisan election administration with an ethics board. From The American Prospect:
To ensure the board would be nonpartisan, the structure for appointing its six members is complicated. A panel of four state appeals court judges nominates several former judges, and the governor then makes his or her appointments. From there, the selection must be confirmed by the state senate. There’s also a good deal of turnover; the six ex-judges all serve staggered terms, meaning one member’s term expires each year. Judges in Wisconsin cannot be affiliated with a political party, and a judge must have served at least six years to be nominated for the GAB. That means anyone on the board has spent years away from partisan politics.
The board was not enshrined in the state constitution but was created by statute, and it died by statute. When the Republican Party took control of both houses of the state legislature and the governorship, it dissolved the board in 2016 and replaced them with a partisan election commission and a partisan ethics commission.