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Definition:

The meanings of the words composing the term stochastic terrorism help to clarify its definition. "Stochastic" is an adjective which describes something that is random, or involves chance or probability (is probabilistic). While definitions of terrorism vary, this one contains the common and important elements: "the unlawful use of violence or threats to intimidate or coerce a civilian population or government, with the goal of furthering political, social, or ideological objectives . Stochastic terrorism, then, would be random or probabilistic terrorism.

However, as terrorism is a complex phenomenon there are many elements which could be random; the meaning of stochastic terrorism depends upon its accepted usage. The following definition reflects the term's current accepted usage: "Stochastic terrorism is the public demonization of a person or group resulting in the incitement of a violent act, which is statistically probable but whose specifics cannot be predicted." To reiterate and add some terms: an entity (an individual or group or organization) acts as a stochastic terrorist by demonizing a target entity which motivates a third group, the terrorist entity, to carry out a terrorist act against the target. This terrorist scenario is stochastic because with the public demonization of a target, a terrorist act against the target is not certain but is made more likely. It is also stochastic because the identity of the terrorist and the timing and means of the attack cannot be predicted.

Terminology
The term was initially used to suggest that a quantifiable relationship may exist between seemingly random acts of terror and their intended goal of "perpetuating a reign of fear" via a manipulation of mass media and its capacity for "instant global news communication". For example, careful timing and placement of just a few moderately explosive devices could have the same intended effect as numerous random attacks or the use of more powerful explosives if they were shrewdly devised to elicit the maximum response from media organizations. It was theorized by Gordon Woo in a 2002 paper that "the absolute number of attacks within a year, i.e. the rhythm of terror, might ultimately be determined as much by publicity goals and the political anniversary calendar as by the size of the terrorist ranks".

A variation of this stochastic terrorism model was later adapted by an anonymous blogger posting on Daily Kos in 2011 to describe public speech that can be expected to incite terrorism without a direct organizational link between the inciter and the perpetrator. The term "stochastic" is used in this instance to describe the random, probabilistic nature of its effect; whether or not an attack actually takes place. The stochastic terrorist in this context does not direct the actions of any particular individual or members of a group. Rather, the stochastic terrorist gives voice to a specific ideology via mass media with the aim of optimizing its dissemination.

It is in this manner that the stochastic terrorist is thought to randomly incite individuals predisposed to acts of violence. Because stochastic terrorists do not target and incite individual perpetrators of terror with their message, the perpetrator may be labelled a "lone wolf" by law enforcement, while the inciters avoid legal culpability and public scrutiny.

The anonymous blogger G2geek, on the Daily Kos platform, was the first to publish a version of the definition that is currently generally accepted: "Stochastic terrorism is the use of mass communications to stir up random lone wolves to carry out violent or terrorist acts that are statistically predictable but individually unpredictable" .  G2geek emphasized the importance of plausible deniability in the explanation of the concept.

G2geek presented stochastic terrorism as a novel type of terrorism where certain types of public speech that can be expected to incite terrorism without a direct organizational link between the inciter and the physical perpetrator. The only link between the inciter and the physical perpetrator are through mass communication. G2geek has labelled this type of terrorism as stochastic because the relationship between the cause (the incitation) and effect (the resulting violence) is indirect and can be described in terms of probabilities as to whether or not an attack actually takes place. This differs from Dr. Woo who suggested that a model of stochastic terrorism might be constructed to estimate the probability of an act of terrorism occurring. In Dr. Woo's stochastic terrorism model the mass communications link between the terrorism promoter and the resulting terrorism (G2geek's idea of stochastic terrorism) would be another element that would have to be assigned a probability in order to calculate the overall probability of a terrorist attack.

In general terms, using the concept as proposed by G2geek, the one in common current use, stochastic terrorism is a type of stochastic harm. With stochastic harms the cause (hazard) and its effect (harm) are indirectly linked by a probabilistic relationship. The idea of stochastic harm was first published in 1978, it originally applied to the unintended negative effects of medical procedures using ionizing radiation. For example radiation therapy for cancer causing another type of cancer. The term "stochastic harm" has since been generalized to include harm related to: climate change, some other types of environmental problems ,  some types of disinformation , etc.

Events that are not stochastic terrorism:

The 1994 Rwandan genocide. Radio Télévision Libre des Mille Collines (RTLM) was a radio station controlled by hard-line Hutus; it was important in the lead-up to and the subsequent massacre of Tutsis and their allies. A 1994 study by Harvard Kennedy School researcher David Yanagizawa-Drott reported that, based on areas of broadcast coverage, approximately 10% of the overall violence during the Rwandan genocide can be attributed to this (then) new radio station. Broadcasts were used to demonize Tutsis by labelling them as a dangerous enemy who wanted to seize the political power at the expense of Hutus and by labelling the Tutsi as inyenzi, meaning non-human pests or cockroaches which must be exterminated. Accompanying this there were, in total, 252 broadcasts that called for Hutus to kill the Tutsis. The presence of demonization of the target and the fact that the only link between the instigators and those carrying out the violence was mass communication is reminiscent of stochastic terrorism but because of the explicit calls for violence removing the element of plausible deniability, this instead, is an example of incitation.

The murder of Thomas Becket has been put forward as an example of stochastic terrorism. Thomas Becket was an Archbishop of Canterbury during the 12th century who had a long running conflict with Henry II, King of England, regarding the rights and privileges of the Catholic Church. In June 1170 an archbishop and two bishops, all without a connection to Canterbury, participated in a coronation of Henry II's son. This breached Canterbury's privilege of coronation and in November 1170 Becket excommunicated all three participating church officials. There are many versions as to Henry II's reaction to this, the historian Simon Schama accepts the account of the contemporary biographer Edward Grim, who gives, "What miserable drones and traitors have I nourished and brought up in my household, who let their lord be treated with such shameful contempt by a low-born cleric?" . Upon hearing his speech four knights travelled to Canterbury to confront and ultimately murder Thomas Becket on 29 December 1170.

There are several criteria of stochastic terrorism that this event does not meet. There is no demonization of his target, Thomas Becket, in this speech of Henry II. The instigator and the actors that carried out the attack are not linked solely (or at all) through mass communication but are linked by a household communication with the background of an ongoing, at least professional, relationship between the knights and the king. Lastly, there does not appear to be plausible deniability. According to Schama "To anyone present, the king’s outburst could mean only one thing: that he wanted the interminable, insufferable Becket problem to go away. Not necessarily as in six feet under. But if that’s what it took, so be it".

Stochastic terrorism is a process by which a public figure or group targets a perceived political enemy by using mass-media to denounce and demonize them, this may lead to a random terrorist attack committed by the perpetrator's audience. Whether the instigator's rhetoric leads to a terrorist attack is not predictable, however, it makes the statistical probability of an attack higher. The random, indirect nature of the violence provides the instigator with plausible deniability, as the public demonization of their target does not generally meet the legal definition of incitement .Sociologist Ramón Spaaij worries the increasing prevalence of this type of rhetoric in the discourse will lead to more political violence.

Stochastic terrorism is the public demonization of a person or group resulting in the incitement of a violent act, which is statistically probable but whose specifics cannot be predicted. Dehumanizing a targeted group or individual in a way that could incite violence may also provide plausible deniability for the instigator. Since 2018, it has been used to analyze possible inspirations of lone wolf attacks. Sociologist Ramón Spaaij worries the increasing prevalence of this type of rhetoric in the discourse will lead to more political violence.