On Tuesday, North Carolina will vote on a state constitutional amendment that declares, “Marriage between one man and one woman is the only domestic legal union that shall be valid or recognized,” thereby banning recognition of same-sex marriage, civil unions and domestic partnerships of any kind.

Both recent polls of the state and an analysis of past ballot initiatives in other states suggest that the measure, Amendment 1, is likely to pass, although there is ambiguity over the outcome because of voter confusion about what the amendment seeks to achieve.

North Carolina already has a statutory ban on same-sex marriage, but it is one the few Southern states that have not yet changed their constitutions to ban it. Although all three are sometimes considered Southern states, there is also no constitutional ban on same-sex marriage in West Virginia and Delaware, and same-sex marriage is legal in Maryland. However, the other 10 states in the former Confederacy all have constitutional bans on same-sex marriage and sometimes also civil unions.

Public opinion on same-sex marriage is shifting rapidly in the United States — with supporters of extending marriage rights to same-sex couples often finding themselves in the plurality and sometimes an outright majority in some polls.

The vote on Tuesday will be held in conjunction with the state’s Democratic and Republican primaries, which is headlined by a competitive gubernatorial race on the Democratic side in which a number of candidates are seeking to replace Bev Purdue, a Democrat who is retiring amid low approval ratings. Republicans are almost certain to anoint Pat McCrory, the 2008 gubernatorial nominee and a former mayor of Charlotte, as their nominee, but their voters have a number of competitive down-ballot races as well as the presidential nomination to vote upon.

Most recent polls show that voters are likely to approve the ban on same-sex marriages and civil unions, although results differ substantially from survey to survey because of the wording of their questions.

The most recent poll was conducted by Civitas Institute, a conservative think tank whose poll results have generally shown little partisan bias in the past. That survey polled Democratic and Republican primary voters separately, but projected that the measure would win by 16 percentage points when it combined the results.

An April poll by Public Policy Polling, which conducts polling for Democratic clients but whose surveys also have a track record of nonpartisanship, had the measure prevailing by 14 points.

Both the Civitas and Public Policy Polling surveys directly read the text of the amendment to the voters they were polling. Conversely, some polls that described what the amendment would do but did not read the ballot language have sometimes showed it failing, often by clear margins.

The ambiguity can be explained by the possibility that voters are not aware that the amendment would ban civil unions and domestic partnerships in addition to same-sex marriage. Groups that support the ban, like Vote for Marriage North Carolina, have generally emphasized only the marriage component of the bill. Meanwhile, groups that oppose it, like Coalition to Protect North Carolina Families, have emphasized the effects that the ban on domestic partnerships could have, like a reduction in protections against domestic violence.

Historically, ballot measures that seek to ban domestic partnerships or civil unions in addition to same-sex marriage have received more scrutiny from voters. In 2006, Arizona Proposition 107, which contained sweeping language against domestic partnerships in addition to same-sex marriage, lost in a 52 percent to 48 percent vote. However, a revised measure called Arizona Proposition 102, which banned same-sex marriage only, passed by a vote of 56 percent to 44 percent in 2008.

The Public Policy Polling survey found widespread voter confusion about what North Carolina’s Amendment 1 seeks to accomplish. Just 36 percent of voters answered correctly that it bans both same-sex marriage and domestic partnerships. An additional 26 percent thought it banned same-sex marriage alone. Meanwhile, 10 percent of voters thought a “yes” vote on the amendment would legalize rather than ban same-sex marriage, and 27 percent weren’t sure what it did.

Public Policy Polling, along with some nonpartisan polling organizations like Elon University, have found that a plurality of voters were opposed in theory to a measure that they were told would ban domestic partnerships and civil unions along with gay marriage.

It is also possible to test the amendment’s chance for success through statistical models that look at how such measures have fared in other states. This sidesteps the need to look at polls, which may be desirable both because of the ambiguity in the ballot language and because surveys in other states have sometimes understated the support for same-sex marriage bans.

A model I published last year, which uses the results of past ballot initiatives to project support for these measures based mainly on religious participation in each state and whether the initiative would ban civil unions in addition to same-sex marriage, implies that the amendment is likely to pass.

One version of the model, which recognizes the increasing support for same-sex marriage over time but treats the increase as slow and linear, projects that the North Carolina amendment will pass by 19 points.

However, another version of the model, which treats the support for same-sex marriage as increasing at a faster rate because of the particularly sharp increase in support for same-sex marriage in national polls in the past three years, sees the outcome as closer. That version of the model projects the amendment to pass by seven percentage points, which would make it a clear but not overwhelming favorite, since there is uncertainty inherent to statistical modelling given the idiosyncrasies of each state.

An amendment that banned same-sex marriage only would be almost certain to pass in North Carolina, according to the model.

Still, it seems clear that groups that oppose the amendment will need many voters to make a late decision about the ballot initiative. One advantage they have is that groups that oppose the amendment have raised $2.3 million, versus $1.2 million for groups that support the amendment.

A significant number of North Carolinians have already cast votes in the primaries through early balloting. According to the Civitas Institute, which tracks these statistics, about 160,000 Democratic ballots and 130,000 Republican ballots have been requested so far. One hopeful sign for opponents of the amendment is that an especially large number of ballots have been cast in Durham County and Wake County, which are home to colleges like Duke University and are socially liberal.

Minnesota and Maine will hold votes on same-sex marriage ballot initiatives in November.

Recent polls, as well as the statistical model, suggest that Maine is more likely than not to overturn its statutory ban on same-sex marriage, which voters narrowly approved in 2009, while the Minnesota result appears to be a tossup.