The county web site explains that each precinct has a different ballot and there are more than 500 different ballot in Bernalillo County alone. It doesn't say why. There are obvious reason why ballots would differ from, say, one congressional district to another, but as to why they differ by precinct I can only guess that it's because each precinct has a different combination of ballot measures and of boards and bodies people are being elected to.
It's been pointed out that there's no way to write in someone's name for president this year. I'm not sure this is legal and I'm not sure it matters in New Mexico. There seems to me to be law, and New Mexico law. Rather, different localities here have their own ways of doing things and it's accepted that that's OK. I'm sure a native could give you quite a few examples of this. I'd think it's owing to our unique historical background and values and the fact that the federal government is looked upon differently here. A guess.
The first time I encountered this was the first time after moving here that I renewed the physical that's required for my commercial driver's license. Most of the physical -- eye test, urine test, blood pressure, etc. -- is conducted by nurses and then a doctor or nurse practitioner comes in and looks you over and pokes you, looks over the other results and then signs off on it, except that this particular nurse practitioner wrote on my physical card that I needed to wear eyeglasses even though I had passed the eye test, just not by enough for her satisfaction. These physicals are federally mandated and have federally mandated standards, but in New Mexico there are New Mexico standards.
For president, incidentally, I'll vote for the ticket of Gloria LaRiva and Dennis Banks running on the Party for Socialism and Liberation ticket. I'll have more to say about this later. It will be a disappointment to people like me that Hillary Clinton's victory will be so lopsided that not voting for her won't matter and that we can't spend the next eight years defending ourselves against accusations that we put Donald Trump in office. People still blame Ralph Nader for George W Bush getting into office, despite the fact that this has been disproven. Nader took votes equally from Bush and Gore, and more Democrats voted for Bush than for Nader, the Democrats being unable to come up with candidates people like, Hilary Clinton being a prime example of this. She's very disliked and will only be elected because people dislike Trump more. Most Americans and especially young people won't even vote, they are so disillusioned by the candidates that get put up and by the way politics has come to serve only the ruling class. And people don't like candidates Democrats nominate because they're Republicans who are only liberal on gay rights and abortion, as Jim Hightower pointed out at the time.
There's also a ballot measure that would convert Bernalillo County to a "home rule" county. This would give the county board more independence from the sate legislature in various ways and is fairly common around the country, but the way it's done here is unique, too, owing to the right of local governments to rule themselves via home rule being enshrined in the state constitution, and then a vote of the people in 1970 that broadened that right. This ballot measure has been put before Bernalillo County voters twice before and has been defeated twice, so why it's being brought up again I don't know.
I've seen nothing about this ballot measure in the media save for a recent article in the Albuquerque Journal from the point of view of an attorney who helped draft the measure and is in favor of it passing. I have no particular reason to oppose the measure except for the fact that when something like this hasn't been publicized it raises concerns about why not. It's possible, for example, that the county board wants to do something it can't do unless this gets passed. Law and New Mexico law.
It's suggested in the Journal article that it's supporters might use home rule to change the size of the county board, or to change some county offices, like treasurer, from being elected to being appointed by a county executive. People might see these kinds of actions as "power grabs" and if so that's probably why it failed before.
But there might be more to it than appointing a treasurer who knows what they are doing instead of letting the people elect someone who doesn't. Think of the controversial Santolina development, which was approved by the county board but may have not been done so legally if they didn't have home rule. Or, without home rule, it's possible the state legislature could overrule the county board's decision. I don't know if anything like this is the case but it doesn't hurt to ask or to wonder why we haven't heard very much about this ballot measure.