Casting a ranked-choice ballot should be a straightforward process. In half the city, voters who are faced with Santa Fe's new ballot system will only have to worry about ranking the mayoral candidates. In the other half, they'll rank three candidates for City Council, too.

At the most, then, that's two total ranked-choice races for any one voter. But there are enough permutations of how to rank the candidates that the math involves letters. There are 325 ways to rank just the mayoral candidates, a number that doesn't count the ways you can do it incorrectly. And the city hopes to have considered how to count all of them.

"We want to make sure we're counting the highest-ranked continuing candidate," says city spokesman and ranked-choice public education guy Matt Ross.

That's the simple philosophy behind the complex algorithm designed by Dominion Voting Systems: If your top choice is eliminated, who's next? While it sounds simple, voters who are either confused or trying to out-think the computer (as in the 1983 Cold War classic WarGames) can come up with some pretty interesting voting theories.

In most situations where there's an unorthodox ranking—like one candidate in all five positions or only a single candidate in a single position—the voting machines will signal a ballot error and tell the voter there's an issue. If the ballot can still be counted, the machine will let the voter verify that the "errors" are on purpose. It also gives them the option to try again. In that case, a poll worker will "spoil" the ballot and then give the voter a new one. If the offending ballot can't be counted, such as when two candidates are ranked in the same position, the voter is forced to try again.

While it may seem like all kinds of things can go wrong, you'd be surprised what the software counts as correct. Ross says one of the biggies is a voter trying to force the system to rank a candidate dead last. In this election, that would happen when a voter puts a preferred candidate as first choice in the mayor's race, then leaves three empty places and ranks the unfavored candidate fifth. But the software doesn't see the empty places. It just zips down to the highest-ranked continuing candidate. The person a voter wanted to rank fifth is actually ranked second.

Ranking the same candidate in all five places is the same as ranking that candidate in only the first spot. Again, the software is just looking for the highest-ranked continuing candidate.

That either makes intuitive sense or it's mystifying. But either way, keeping your ballot simple will make life easier for you. The computer really doesn't care.

Ideally, Dominion's software will be able to determine the winner in a matter of seconds, or maybe minutes. And instead of announcing the winner of each round in dramatic fashion, the City Council, where there are three district representatives running in the five-candidate field for mayor, told city staff it wants a winner first. The electoral archaeology can wait.

"The system is described as instant runoff, so I suppose from my perspective, I think it makes sense … that one would announce the winner and then go back and analyze results as you care to," Councilor Peter Ives told the city attorney last month.

District 4 representative Mike Harris, whose seat is not up for re-election for another two years, was the lone voice on the council to entertain the idea of slowing things down after a hard-fought election that will decide at least three new city councilors and the city's first full-time mayor.

"Actually, I've thought about this and how it was going to be reported," Harris told his colleagues at the January meeting. Given the novelty of ranked-choice voting, he wondered, as well as the work that's been put in to explain both how to vote and how the results will be counted, and given the interest in the election itself, might it be wise to show the public how it was all playing out first?

While his gut reaction was to slow it down, Harris ultimately told the council he wasn't attached to the idea and understood the desire for an immediate result.

Election night won't be devoid of early drama, however. In a change from years past, City Clerk Yolanda Vigil said final vote totals won't be posted at each of the polling places. Only the results of the first round will be printed and taped to the window. The more advanced tabulation will take place at City Hall.

That means campaigns with poll-watchers at each of the 12 locations will know within minutes if anyone has won the election outright or, in the alternative, who the first candidate to be eliminated is in the brave new world of ranked-choice voting.