There have now been well over 100 different studies on the effect of negative political campaigns on voters. The political scientist Richard Lau and his colleagues analyzed all of these studies and concluded that negative campaigns fail to achieve their desired goal.

This doesn’t mean negative advertising doesn’t affect voters. Negative ads are more memorable, and they stimulate knowledge about the campaign. They also appear to decrease trust in government and voters’ beliefs that they can influence government decision-making, or what political scientists call “political efficacy.”

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But taken together, these studies found no reliable evidence that negative campaigning does what candidates really want: win votes. Even when opponents go negative, the smarter move is to stay positive.

Our own research published in Research and Politics (open access) supports this. We studied negative and positive advertising (the latter of which includes ads that contrast the policy positions of candidates) in senate, gubernatorial and presidential general election races from 1996-2008. We found that positive advertising can win voters, although only when candidates air more positive ads than their opponent. Negative advertising, however, had at best no effect on vote totals and may even have hurt the candidate running negative ads.

The graph below shows the relationship between negative advertising and a candidate’s margin of victory. The horizontal axis goes from negative 1, when Republicans do all of the advertising, to 1, when Democrats do all of the advertising. In the middle, at 0, Democratic and Republican candidates advertise equally. The vertical axis shows the predicted Democratic margin of victory which is, of course, negative if the Republican candidate wins. If campaign advertising is effective, we would expect an upward sloping line.

No matter how many more attack ads a candidate airs against his opponent, there is no significant effect. What effect there is may actually be harmful: The downward sloping line suggests that when Republicans run more attack ads, it could possibly help the Democrats, and when Democrats run more attack ads, it could help Republicans.

Compare the impact of positive advertising:

When candidates run significantly more positive advertising than their opponent, their margin of victory increases. But when a candidate runs the same number of positive ads as their opponent, there is no effect. In that case, campaign advertisements appear to cancel each other out.

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Of course, Sanders is making a decision in the context of a primary election, not a general election. Campaigning can be more effective in primaries because voters cannot rely on partisan cues and have little information about how the candidates differ.

But even in primaries, there is no reason to expect that negative campaigning is more effective than positive advertising. On balance, the research suggests that Sanders should stick to airing positive ads that give voters a reason to vote for him, instead of a reason to vote against Clinton.

Shanna Pearson-Merkowitz is an associate professor of political scientist at the University of Rhode Island whose research focuses on political parties, elections and political polarization. Liam Malloy is an assistant professor of economics at the University of Rhode Island whose research focuses on inequality.