At the last two Republican debates, the looming center-stage presence wasn’t Donald Trump; it was the Islamic State. Many news articles have suggested that 2016 will be the rare election in which foreign policy will be central to the campaign.

Will those predictions come true? Not likely. But while foreign policy may only feature occasionally in the campaign, the voters’ chosen candidate will matter significantly for U.S.  foreign policy.

What do we mean by “foreign policy issues,” and how do voters think about it?

Many international issues get mentioned in campaigns, whether in general terms or by referring to a specific country or region. Most of these issues fall under the broad categories of foreign economic policy (such as free trade, currency policy, or foreign aid) or national security issues (such as military readiness, nuclear proliferation, crisis diplomacy, and what we now call “homeland security” issues like terrorism, though terrorism concerns long predate 9/11).

From decades of research, we know voters do not pay much attention to foreign policy. Some research shows that the public has stable, coherent attitudes on foreign policy, but few dispute that most voters have little concrete foreign policy information. Rather than follow debates closely, voters generally look to elites and the media for information, even for specific foreign policy issues.

As the Monkey Cage frequently reminds readers, the economy is “fundamental” in presidential elections. You might think, therefore, that voters would pay attention to an economic issue like free trade. But while trade policy has had its moments (think Japan in the 1980s or periodic attention to agreements like NAFTA or the TPP), voters rarely focus on it. Recent research suggests that people do not think about trade policy in purely self-interested terms, and may lack the economic knowledge to understand how trade policy would affect them.

What about national security? Public opinion research has shown that even in wartime, the public used elite cues as a shortcut for understanding conflicts ranging from Iraq and Vietnam to World War II. If elite opinion about a conflict is divided along partisan lines, then the partisan split will likely show up in public opinion.

Partisanship can even affect perceptions of facts: in a survey conducted by Adam Berinsky in 2004, Republican respondents were more likely to underestimate the number of casualties in Iraq, while Democratic respondents were somewhat more likely to overestimate. Political parties and the media can help inform the public, but that is not automatic, even in democracies.

So voters generally leave foreign policy to elites. This strategy may make sense for busy people focused on matters closer to home. But it brings us to our next question.

Does foreign policy affect how voters decide who to vote for and who gets elected?

The consensus is that foreign policy generally has little effect on elections, as Brendan Nyhan pointed out after the Paris attacks (see also Dan Drezner here and here). Of course, foreign policy can matter in elections. But it’s hard for a politician to sway large numbers of voters based on foreign affairs.

Why? Some issues are simply not salient enough: on trade, for example, research by Alexandra Guisinger found that voters did not hold their senators accountable for votes on the Central American Free Trade Agreement (CAFTA).

Another challenge is that a candidate must be able to draw a significant contrast with the other party. That may mean taking a popular position that the opposition cannot easily match (as Lynn Vavreck comments).

Consider Vietnam and the 1968 election. Benjamin Page and Richard Brody found that despite the apparently high salience of the war, most individuals’ votes were not based on Vietnam — because there was little difference between the public positions taken by Hubert Humphrey and Richard Nixon.

That’s potentially true in 2016 as well. The most likely Democratic nominee, Hillary Clinton, has taken more hawkish foreign policy positions than many recent Democratic candidates, presumably bringing her positions closer to the more traditionally hawkish Republican side.

Basing a vote on foreign policy can be difficult because candidates often have an incentive to be vague, as Humphrey and Nixon were in 1968. In 2015 and 2016, the Republican candidates have been long on talk of “toughness” but short on specifics. This can build broad primary support, but isn’t likely to produce sharply contrasting positions between the parties.

Foreign policy also cannot be completely separated from other views. If you value toughness on other issues like crime or immigration, you are more likely to also value aggressive foreign policy. Events like the Paris or San Bernadino attacks may provide a filter through which voters channel their views, rather than changing those views. Page and Brody found that voters tended to pick a favored candidate and then project their desired position on the war onto that candidate.

But wait — what about all those times foreign policy did matter?

Of course, foreign policy has mattered in some elections. The 2002 midterm election, coming so soon after 9/11, was influenced by worries about national security. In 2004, there is some evidence that George W. Bush lost vote share in states with higher per capita Iraq casualties.

But even as disenchantment with the war grew, Bush still won reelection. Not until the 2006 midterms did Iraq really become a decisive issue, showing how long it can take for even a war that is going badly to rise to the top of the agenda.

Even then, how it affects the election isn’t clear. In the 1968 New Hampshire primary, where Eugene McCarthy’s strong showing is credited with helping to push Johnson out of the race, McCarthy voters were just as likely to be dissatisfied with Johnson for doing too little in Vietnam as too much.

At the same time, foreign policy can shift votes enough to matter in close elections. Wartime casualties are especially relevant here. In 1973, John Mueller put forward the hypothesis that public support for war declined as the (logarithm of) casualties increased, although war support does not automatically translate into effects at the polls.

Since then, the effect of casualties has been hotly debated, but some evidence suggests that casualties cost incumbents at least some vote share. In the so-called “bread and peace” model of elections, the other “fundamental” besides recent economic performance is war casualties, which dragged down the incumbent party candidate’s vote share in 1952 (Korea) and 1968 (Vietnam), and to a much lesser extent, 2008 (Iraq).

There is also the state-level evidence that casualties mattered in 2004 (and in Senate elections during Vietnam). Another recent study also found that casualties can lead otherwise politically uninterested voters to turn out on election day, although both supporters and opponents of the war appear to be equally mobilized.

So how could foreign policy matter in 2016?

First, a significant terrorist attack on the scale of 9/11 could make foreign policy central. So could a smaller event that happens after Labor Day, when voters are particularly tuned in. But that requires a rare or precisely-timed event.

Even major events can recede quickly. Just ask George H.W. Bush, who said this about his reelection chances in March 1991, when his popularity after the Gulf War was at its height: “The common wisdom today is that I’ll win in a runaway, but I don’t believe that. I think it’s going to be the economy.”

Second, foreign policy might affect the primaries, as Drezner has suggested. The potential nominee may have to pass the foreign policy “sniff test” (a problem Scott Walker and Ben Carson have confronted).

That’s a relatively low bar, however. This year the Republicans have no contender with significant foreign policy experience. The Democrats have one, but that’s the exception for either party, not the rule. In general, we still know relatively little about how foreign policy matters in primary elections.

Third, foreign policy can affect a close election. But that is very different from suggesting that foreign policy will be key for most voters.

Is it pointless to talk about foreign policy and elections, then?

Not so fast. Although it is unlikely — — though not impossible — that foreign policy will be a central factor in the 2016 election, campaign debates about foreign policy can affect national debates and policymaking in other ways. For instance, Bethany Albertson and Shana Gadarian argue that anxiety can affect politics, a relevant issue given recent terrorist attacks.

And yet the election’s outcome may matter a great deal for U.S. foreign policy. Foreign affairs got little attention in the 2000 campaign, but George W. Bush’s presidency was defined by his response on national security and two wars. More generally, a wave of recent research (including my own) has shown that leaders matter significantly in foreign policy and international relations.

Even if foreign policy does not drive the campaign, the election will matter for foreign policy long after the voting ends.

Elizabeth N. Saunders is an assistant professor of political science and international affairs at George Washington University, and for 2015-2016, a Stanton Nuclear Security Fellow at the Council on Foreign Relations. She is the author of “Leaders at War: How Presidents Shape Military Interventions” (Cornell University Press, 2011).