WHEREVER Donald Trump goes, protests follow. This week, anti-capitalists marched through Swiss cities to protest the president’s visit to the World Economic Forum in Davos. In America the previous week women protested against the president in a series of nationwide marches that marked the end of his first year in office. The women’s marches, in more than 250 cities, appear to be part of a new era of female political activism in America; a record number of women are running for office in mid-term elections in 2018.

Research suggests that protest movements can have a significant impact on elections. Stan Veuger of the American Enterprise Institute and colleagues made a striking discovery when they studied the effect of rallies held by the Tea Party movement on April 15th 2009 against high taxes and government spending. The researchers found that in places where it rained that day, rallies were half the size of places where it stayed dry. They used this randomly caused variation in attendance to estimate the impact of rally size. Districts with dry rallies saw larger contributions to political action committees associated with the Tea Party movement and a 4.6 percentage point larger share of respondents unfavourable to Barack Obama in subsequent months. They also saw a significantly bigger vote share for the Republican candidate in the 2010 House of Representatives elections.

Overall they estimated that a 0.1% increase in the share of the population protesting at a rally corresponded to a 1.9 percentage point increase in the share of Republican votes. From these results, they reckoned that the protests as a whole mobilised between 2.7m and 5.5m additional votes for the Republican Party in the 2010 House elections –or between 3% and 6% of all House votes cast that year.

The Tea Party rallies were an impressive mobilisation but they pale in comparison to the recent women’s marches. Erica Chenoweth at the University of Denver and her colleague Jeremy Pressman estimate that the 653 women’s marches across the country in January 2017 involved between 3.3m and 5.2m million people. The best guess is that 1.3% of Americans marched. The researchers also estimate that another 6,400 anti-Trump protests in America between the marches and the end of 2017 drew between 2.6m and 3.8m participants. While the women’s marches were officially non-partisan, survey evidence suggests otherwise. Michael Heaney of the University of Michigan estimates as many as 90% of the women attending the march in Washington, DC in 2017 had voted for Hillary Clinton.

Ms Chenoweth’s most conservative estimate of participants in the 2017 Women’s Marches (the biggest such rally that year) is five times Mr Veuger’s midpoint estimate of participants in the Tea Party rallies of 2009. If a similar relationship applied nationwide to Democratic Party vote share in the mid-terms after the women’s marches as to the Republican mid-term vote share after the Tea Party rally it would imply a Democratic landslide.

The impact is unlikely to be so dramatic, however. The Washington, DC metropolitan area and Los Angeles (home to the largest such march in 2018) are Democratic Party redoubts where improved margins might not translate into more seats. The Tea Party, moreover, promoted small government nativism that easily translated into support for particular primary and general election candidates. The Women’s March and #MeToo are less straightforwardly ideological.

But Ms Chenoweth and Mr Pressman also point that after California and New York, three important swing states—Florida, Pennsylvania and Texas—saw the highest number of protests in the year that followed Mr Trump’s inauguration. Many women, meanwhile, have turned out to be voted for: of the 15 seats Democrats took from Republicans in the Virginia House of Delegates election in 2017, 11 were won by women. The 115 federal Congresses in America's history have never had more than one woman for each five members. Perhaps the 116th Congress, seated in 2019, will do better.