Don't prosecute extremist parties. It only makes them stronger.

Last Friday, a member of Greece's neo-Nazi Golden Dawn party was expelled from parliament for mocking members of the leftist Syriza party as someone in the parliament chamber shouted "Heil Hitler." The Greek government's Golden Dawn problem continues to worsen as the U.S. State Department highlighted the group in its annual religious freedom report for causing an uptick in anti-Semitism. Criminal prosecutors recently launched a hate-speech investigation on the party after one of its members was filmed for a television documentary, saying, of immigrants: "We are ready to open the ovens. We will turn them into soap ... to wash cars and pavements. We will make lamps from their skin."

Odious as these statements are, the experience of other countries in Europe suggests that prosecuting extremist parties for hate speech may be counterproductive. In a study published in the journal Party Politics, Dutch political scientists Joost van Spanje and Claes de Vreese looked at the effect of the 2009 prosecution of controversial Dutch politician Geert Wilders on his Party of Freedom's political support. Wilders was charged with defaming Islam with various statements including describing the Quran as a "fascist" book and calling for it to be banned:

Our results suggest that the court decision caused an across-the-board increase in probabilities to vote for the PVV. In addition, we have found that this increase in vote probabilities translated into a 1 to 5-percentage points surge in PVV vote intentions among moderate assimilationists -those  who would like to see ethnic minorities adapt to Dutch culture and society. Both among those who are more radically assimilationist and among those who feel that minorities should be allowed to preserve their own customs and traditions, the court decision slightly increased PVV vote probabilities without resulting in more PVV vote intentions. This is because many radicals already supported the party, and because many multiculturalists have other parties that they still prefer to the PVV. More generally, the shift in vote probabilities largely occurred among those who would not normally vote for the PVV and would still not vote for it after the prosecution.

These findings imply that the decision to prosecute Wilders helped him in the electoral arena, both in the short run and in the long run.

This increase in support may have been critical in the 2010 parliamentary election, in which Wilders' PVV party earned enough votes to support a right-wing minority government. 

Admittedly, the statements that got Wilders prosecuted were mild compared to the sort of things that Golden Dawn members say on a regular basis. But the authors believe what's critical about these prosecutions is the way that far-right parties are typically structured:

Leadership, arguably key to electoral success of any party, is particularly important for anti-immigration parties. This is because these parties are generally strictly heirarchically structured. 

Prosecutions can help bolster an anti-immigrant leader's legitimacy. The parties can also benefit from the increased media exposure that a trial will bring for their issues of choice, a variation on the Internet's "Streisand Effect".

In any event, Wilders fared much worse in the 2012 elections, the year after he was acquitted.