Buddie, the mascot for the pro-marijuana legalization group ResponsibleOhio, holds a sign as he gives a thumbs-up to students at Ohio State University on Tuesday in Columbus. A majority of voters gave the marijuana initiative a thumbs down. (John Minchillo/AP)

On Tuesday, voters in Ohio rejected a constitutional amendment that would have legalized both medical and recreational marijuana use. Naturally, folks are wondering about the implications of Issue 3’s failure for similar measures in other states.

But there’s a larger question as well. Could the defeat of Ohio’s Issue 3 influence marijuana policy at the federal level — for instance, efforts to eliminate federal felony charges for non-medical marijuana, or to influence related questions like DEA funding and drug sentencing guidelines, and so on.

Yes, it probably it will.

Do your representatives in Congress care about statewide ballot votes?

In 2011, Dan SmithJosh Huder and I published an article in American Politics Research that explored whether the passage or failure of statewide ballot measures affects how members of Congress vote. In other words, do state ballot measures influence policy outcomes at the federal level?

[Ohio voters support and oppose marijuana legalization in Ohio. Wait, what?]

Our theory was that that when a statewide ballot measure either passes or fails, it tells lawmakers precisely what their constituents want, down to the district level. That helps reduce “policy shirking,” in which lawmakers vote contrary to the wishes of their constituents.

Lawmakers care about one thing above all else: winning reelection. Reelection-minded lawmakers try their best to behave as pure delegates — and to faithfully represent their constituents’ views.

But a number of studies have shown that lawmakers can be poor judges of their constituents’ preferences on specific issues. While they may know how liberal or conservative their district is, lawmakers have incomplete knowledge of voters’ beliefs on more nuanced issues, like marijuana legalization.

And so lawmakers search for reliable information about what their constituents want. Public opinion polls are an obvious resource. But polls are not always accurate. For example, a handful of polls — including one at my alma matter, Bowling Green State University — suggested that Ohio’s decriminalization measure would pass. In fact, a Kent State University poll suggested Issue 3 would pass with a whopping 58 percent support. What’s more, people who respond to polls are not always the same people who turn out to vote, which is one reason polls are inaccurate. But for obvious reasons, lawmakers are especially interested in voters.

And so we theorized that a ballot measure’s results offer the best possible information lawmakers can use to figure out what their constituents want. It offers information that’s specifically about a single issue, as opposed to a lawmaker’s more general intuition about how liberal or conservative constituents are. And it reveals what voters want, not just what poll respondents want.

Yes and no. 

Here’s how we tested our hypothesis. We took the results of statewide ballot measures on three issues — regulating campaign finance, raising the minimum wage and banning same­-sex marriage — and compared that to how lawmakers voted on those issues.

[How Democrats derailed marijuana legalization in California]

Our hypothesis appears to be partly correct. Members of the House do vote in ways that appear to be influenced by how their constituents voted on ballot measures.

But that’s not true for senators — which makes sense. Senators are more insulated from public opinion than representatives, since they generally have a larger constituency and only run for election every six years.

We also report in this paper that representatives are most likely to respond to what they learn about their median constituent — the constituent a lawmaker needs to win over in order to get at least half the vote.

In other words, the statistical results show that it matters little if the ballot measure passed with 70 percent of the vote or 51 percent of the vote. Both show a member of Congress where at least half of his or her constituency stands.

As Ohio goes, so goes the nation?

So how could the defeat of Ohio’s Issue 3 hurt federal efforts to decriminalize non-medical marijuana use and so forth? First, it could influence Ohio’s 16 representatives. Second, it could affect how lawmakers in similar Midwestern states vote — although that’s a theory we do not test that in the paper.

Ohio’s decision on marijuana, in other words, has national implications.

Jordan Ragusa is assistant professor of political science in the College of Charleston.