A group of 100 conservative lawyers and academics recently filed a Supreme Court brief arguing that gay marriage will cause 900,000 abortions over the next 30 years. Leading the charge is lawyer and former Antonin Scalia law clerk Gene Schaerr, who summarized the argument in a recent piece for the Heritage Foundation.

It goes something like this: same-sex marriage "undermines" traditional marriage, which leads to lower marriage rates. And lower marriage rates mean more abortions, because unmarried women get more abortions than married women do. This represents "a short and simple causal chain that the Supreme Court would be wise not to set in motion," according to Schaerr.

The problem, however, is that that chain of logic does not prove causality--and Schaerr freely admits this.  “It is still too new to do a rigorous causation analysis using statistical methods,” he told the Post's Dana Millbank. “The brief doesn’t even attempt to say conclusively that this reduction in marriage rates has been the result of adopting same-sex marriage.”

That acknowledgement aside, Schaerr and colleagues continue with that logic. For instance, they say that declining marriage rates in a handful of states that have legalized same-sex marriage -- Vermont, Massachusetts, Iowa -- are proof of the harmful effects of gay marriage. That evidence seems to ignore the fact that marriage rates have declined in places like Texas and Utah as well, or that the overall U.S. marriage rate has been on the wane for decades.

But rather than wondering if correlation is causation, we can look at published papers to figure out if there are real connections.

For instance, a 2013 paper by researchers at Portland State University examined the short- and long-term effects of same sex marriage using a sophisticated statistical model. They found that "rates of opposite sex marriages are not affected by legalization of same sex civil unions or same sex marriages." Claims about gay marriage harming straight marriage "do not appear credible in the face of the existing evidence," the authors conclude.

Or, you could look at the 2014 study by economist Marcus Dillender published in the journal Demography. Similar to the Portland State University researchers, Dillender found "no evidence that allowing same-sex couples to marry reduces the opposite-sex marriage rate."

We could head overseas to a study of marriage and divorce rates in Denmark, Sweden, the Netherlands, Norway and Iceland published in Sexuality Research and Social Policy. Rates of straight marriage and divorce "displayed no significant change in trends after implementation of rights for gay couples." Moreover, "because the United States gives many more incentives for heterosexual couples to marry than European countries, any effects of passage of gay marriage or partnership laws in this country would be even less likely to have an impact on the status of heterosexual marriage," the author concludes.

Now, here is one study conducted in the Netherlands which shows evidence of a small drop in straight marriage rates after the country adopted gay marriage, predominately in four urban areas. Schaerr emphasized this one, but arguably extends the study's conclusions beyond their scope.

Crucially, the Netherlands study also factored in the effect of domestic partnership laws in that country. These partnerships are essentially marriage in everything but name, and more importantly they're open to straight couples as well as gay ones, a relatively unique situation.

The study found that the overall "different-sex union rate" -- that is, the percentage of straight couples who either married or entered into a domestic partnership -- was unchanged by the introduction of same-sex marriage. Slightly fewer straight couples got married after gay marriage was passed, but this was offset by an increase in straight couples getting domestic partnerships.

It's difficult to generalize these results to the U.S., since we don't have a national domestic partnership program the same way the Netherlands does. But Schaerr does generalize, plucking the finding about the drop in marriage while ignoring the equally important fact about increased partnership.

More to the point, the Netherlands study is a very good study on its own -- but it's just one study, and you have to measure it against the weight of other research showing no impact on straight marriage rates.

Overall, Schaerr and his co-signers construct a 100-page legal brief on questionable statistical foundations. He has not proven terribly persuasive yet, at least in court: He left his legal practice last year to battle same-sex marriage in Utah full-time, a fight he ultimately lost.