Why does New Mexico resolve election ties with a game of Poker?

Question

I just learned today that, according to the New Mexico Constitution, if an election ends in a tie, the race will be decided by a game of chance, either a coin-flip, high-card draw, or a single hand of poker. According to the New York Post, this was discussed during the 2000 election, where Gore eventually won the state by only 4 votes:

A little-known, rarely exercised provision of New Mexico’s state constitution calls for ties to be settled by a game of chance.

That one-in-a-million statute looms over a race that’s separated by a handful of votes.

While there have been no statewide elections ever settled this way, election officials said yesterday, some local ballots have actually come down to a coin flip, high-card draw or a single game of poker.

“It’s hardly likely we’ll get Al Gore and George W. Bush back here for one hand of five-card stud,” said Denise Lamb, director of the state Bureau of Elections. “But if there is a tie, it’s supposed to be settled ‘by lot,’ a game of chance, agreed to by the two candidates.”

Where did this provision come from? While a coin-flip is common a game of poker seems pretty outlandish (and extremely "Wild-West").

Answer 1

By "single game of poker" the Journalist (who may not be a poker player) should have said "single poker hand". In other words, the cards are shuffled, five are dealt to each candidate (or their agent) and the better hand wins. There is no drawing of cards, and no betting so no skill.

It is "wild west" and intentionally so. It shows off the state, and adds a "wild west" twist. A single hand of poker is as good as any other ways of generating a random outome. But it is more "Nevada".

Answer 2

Why is that in the constitution?

As it turns out, it isn't. The constitution is silent on the treatment of tied votes for local elections, which may account for the mechanism used to resolve the 1988 mayoral race in Estancia, but it is explicit about statewide offices. Article V, Section 2:

The returns of every election for state officers shall be sealed up and transmitted to the secretary of state, who, with the governor and chief justice, shall constitute the state canvassing board which shall canvass and declare the result of the election. The joint candidates having the highest number of votes cast for governor and lieutenant governor and the person having the highest number of votes for any other office, as shown by said returns, shall be declared duly elected. If two or more have an equal, and the highest, number of votes for the same office or offices, one of them, or any two for whom joint votes were cast for governor and lieutenant governor respectively, shall be chosen therefor by the legislature on joint ballot. (As amended November 6, 1962.)

Because of the 1962 amendment, I sought out an earlier version; here's the version as of 1912:

The returns of every election for state officers shall be sealed up and transmitted to the secretary of state who with the governor and chief justice shall constitute the state canvassing board which shall canvass and declare the result of the election The person having the highest number of votes for any office as shown by said returns shall be declared duly elected If two or more have an equal and the highest number of votes for the same office one of them shall be chosen therefor by the legislature on joint ballot

In a comment, divibisan points to NM Stat § 1-13-11, which does call for deciding ties by lot. However, since it mentions "county canvassing board," singular, it reinforces the suspicion that it does not purport to supersede the mechanism specified in the constitution for statewide offices:

In the event of a tie vote between any candidates in the election for the same office, the determination as to which of the candidates shall be declared to have been nominated or elected shall be decided by lot. The method of determining by lot shall be agreed upon by a majority of a committee consisting of the tied candidates, the county chairmen of the political parties that participated in the election and the district judge. The county canvassing board shall issue the certificate of nomination or election to the candidate chosen by lot.

This perception is also reinforced by the fact that it is situated among several sections that concern "county canvass," with "state canvass" appearing only a few sections later.