It's been a long since my intellectual property final, but let me try to help. I am not familiar with New York law as I practice in California.
Additionally, as I am not licensed to practice in New York, consider this to be merely my informal opinion and conjecture, and NOT professional advice.
You have two separate problems here:
1)Copyright:
Basically, in today's day and age, unless an item has been affirmatively "abandoned" or declared open for use it would be extremely imprudent to assume it is not copyrighted. Any analysis of your use of these photos should begin with that assumption.
As discussed above, I think your use of the photos will fall within the "fair use" proviso, with a few large caveats. Be careful that the use is truly non-profit, or the analysis changes.
Also, simply because a use is non-profit does not mean you have carte blanche. The photos you use should be drawn from individuals somehow involved in the voting process, or tangentially linked to voting, or individuals who have otherwise injected themselves into the public debate/forum on voting. As will also be discussed below, I think if you simply grab photos randomly you are asking for trouble, as I believe a very good argument can be made that using random photos is not truly fair use: you should use photos that have some relationship to the article you're writing. If you linked your photos intelligently to the article (i.e., this is the type of individual who did not vote in the 1950's, but votes now), you would be bolstering your fair use argument. Be careful, as I am sensing that you are not choosing photos due to their relevancy to your article, but merely because of the appearance of the individuals.
2)Invasion of Privacy (which has two prongs, discussed below)
Depending on the source of the photo, i.e., if the individual did not willingly inject a photo of their face into the public domain, your use of the photos might be construed as violating their privacy. Generally people cannot use private images for public use without violating someone's privacy unless the story or image is newsworthy or logically linked to the news story. Be careful in the photos you choose. I don't see how you're going to get around this problem without permission, unless these photos in and of themselves are directly linked to the article you're writing. I.e., the photos of these individuals should be drawn from news articles or sites that deal with voting, thereby creating a plausible link between your use of the photo and the content of your article (rather than you just randomly choosing a bunch of faces that have no connection with voting). I see this as being the biggest problem with your idea. However, if you grab photos of people that are themselves used in articles about voting, you'll be in the clear.
Depending on the content of your article, your use of individual portraits might be placing these individuals in a "false light", which could also cause trouble. For example, if someone wrote a site about gays in Hollywood, and included a photo of Tom Cruise WITHOUT expressing that he is gay, they would likely be liable for the "false light" prong of invasion of privacy. However, unless you are writing something truly inflammatory, this shouldn't be a problem.
**regardless of what you decide, withdraw a photo if you receive an objection. I have no knowledge thumbnails or otherwise, these are just general legal principles.
***if the photo is of a dead person, generally their right to privacy is considered extinguished, but not their copyright protection.
****that took about fifteen minutes, typically I would bill $75.00 for that. Man, my firm is making a killing....
