Peace Economics, Peace Science and Public Policy

Transcription

1 Peace Economcs, Peace Scence and Publc Polcy Volume 17, Issue Artcle 1 Lone Wolf Terrorsm Peter J. Phllps Unversty of Southern Queensland, phllpsp@usq.edu.au Copyrght c 2011 Berkeley Electronc Press. All rghts reserved.

2 Lone Wolf Terrorsm Peter J. Phllps Abstract The purpose of ths paper s to nvestgate the nsghts that mght be generated nto the nature of lone wolf terrorsm through the applcaton of economc analyss. Orthodox approaches, partcularly (standard) expected utlty analyss and game theoretcal analyss, are dscussed. These tools prove useful n developng prelmnary or frst order nsghts. The lone wolf terrorst exhbts a number of dosyncrases that present challenges to both economc analyss and government securty polcy. An alternatve analytcal framework s constructed wheren a terrorstc agent makes choces on the bass of a preference orderng constructed over two moments of the dstrbuton (measured n terms of fataltes generated by terrorst attacks). Seven predctons are yelded from the mean-varance theoretcal framework and numercal estmates are computed as prelmnary steps towards the full exploraton of the mplcatons of the framework. Most mportantly, dependng on ther level of rsk averson (or rsk seekng behavour), lone wolves are expected to predomnantly choose assassnaton, armed attack, bombng, hostage takng or unconventonal attacks. Furthermore, wthn a range of between one and two standard devatons from the mean, t s possble that the quadratc utlty functon wll reach a maxmum. Followng attacks of a certan magntude (n terms of fataltes), t mght be expected that the lone wolf wll wthdraw from actvty for a perod of tme. Ths analytcal approach may assst governments and securty agences facng the threat of lone wolf terrorsm. KEYWORDS: lone wolf terrorsm, economc analyss, expected utlty, game theory, securty, mean-varance, assassnaton, armed attack, bombng, hostage takng I would lke to thank and acknowledge the three referees who provded valuable comments and helped to mprove the paper. Remanng errors are, of course, my own.

3 Phllps: Lone Wolf Terrorsm Introducton I am partcularly concerned about loosely afflated terrorsts and lone offenders, whch are nherently dffcult to nterdct gven the anonymty of ndvduals that mantan lmted or no lnks to establshed terrorst groups but act out of sympathy wth a larger cause. We should not forget the Oklahoma Cty bombng n 1995, for example, whch was carred out by ndvduals unafflated wth a larger group Robert S. Mueller III, Drector, FBI 1 Theodore Kaczynsk was the Unabomber. He was also a lone wolf terrorst who acted alone and outsde of a formal organsatonal or command structure. He klled three people and njured a further twenty-three. By contrast, the Weather Underground were responsble for one fatalty, the Grey Wolves were responsble for one fatalty and four njures, the Symbonese Lberaton Army were responsble for two fataltes and the Revolutonary Vanguard were responsble for eleven njures 2. True lone wolf terrorsts are ndvduals who, lke Theodore Kaczynsk, operate alone, wthout accomplces and outsde of a formal terrorst organsatonal or command structure. Ths s contrasted wth organsed terrorsm commtted by ndvduals operatng wth the assstance and cooperaton of others and wthn an organsatonal or command structure. The two types of terrorsm are dstnct. An analyss of lone wolf terrorsm s mportant because, as the examples show, a lone wolf terrorst may be more deadly than a terrorst organsaton. The soltary nature of lone wolf terrorsm s ts most perncous aspect and also the most mportant aspect to ncorporate nto a formal economc analyss of lone wolf terrorsm. Tradtonal approaches to the economc analyss of terrorst behavour have tended to concentrate on the terrorst organsaton as the unt of analyss. Ths makes sense. Although terrorsm may be perpetrated by formally or nformally afflated groups and ndvduals, the terrorst organsaton has been the typcal orgnator of terrorstc operatons. It s, for example, to terrorst organsatons and not afflated ndvduals that fataltes and njures are attrbuted wthn the GTD. The economc analyss of lone wolf terrorsm therefore nvolves a refocussng of the analytcal framework to encompass the terrorstc behavour of the lone ndvdual wth no formal tes to an organsaton and, for 1 Mueller (2003). 2 Data sourced from the Global Terrorsm Database (GTD). Publshed by Berkeley Electronc Press,

4 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 true lone wolves, no accomplces 3. The startng pont s that lone wolves respond to ncentves 4. Payoffs and rsks are weghed up and consdered carefully n the choce of attack type and target. Innovatons n the payoff-rsk structure generate nnovatons n the behavour of the lone wolf. The absence of an economc theoretcal framework wthn whch ths partcular aspect of lone wolf behavour can be analysed s an mportant defcency wthn modern defence economcs. When appled to terrorstc organsatons, the two man approaches of economc analyss of terrorsm expected utlty theoretcal and game theoretcal approaches have proven capable of generatng mportant results. It s to be expected that, wthn a certan degree of approxmaton, the applcaton of these orthodox models to lone wolf terrorsm wll generate some useful nsghts. There are, however, many challenges. Do game theoretcal negotaton models make sense n the context of lone wolf terrorsm? How s the lone wolf sucde terrorst to be encompassed wthn the analytcal framework? What scale of attack s lkely to characterse the lone wolf terrorst? Does the manner n whch the lone wolf allocates resources to dfferent attack types dffer from the terrorstc organsaton? Is publc support for the cause of the lone wolf an mportant consderaton? The lone wolf operates at the boundary of conventonal economc analyss of terrorsm. It s almost certanly the case that orthodox economc models of terrorsm must be augmented to ensnare the lone wolf terrorst wthn an economc-analytcal framework. In ths paper, the orthodox model s appled and some possble nnovatons to the orthodox approach are suggested and worked out. Ths paper s organsed as follows. In Secton II, a bref revew of the relevant lterature s presented. Ths sets the scene for the applcaton of economc models to the analyss of lone wolf terrorsm. In Secton III, the possblty of obtanng useful nsghts nto lone wolf terrorsm through the applcaton of expected utlty theory and game theoretcal analyss s explored. In Secton IV, an economc-analytcal framework that augments the orthodox or tradtonal approach to the economc analyss of terrorsm s developed and seven predctons for lone wolf terrorsm are derved. In Secton V, a prelmnary statstcal analyss of the payoff-rsk structure of ndvdual attack methods s undertaken and some numercal content s provded for the predctons yelded n the prevous secton. Secton VI concludes the paper. 3 See Insttuut voor Velgheds en Crssmanagement (2007) and Spaaj (2010). A lone wolf, by defnton, cannot be part of a group. 4 See Ehrlch (1973, p.522). DOI: /

5 Phllps: Lone Wolf Terrorsm The Economc Analyss of Terrorsm Terrorsm s, the premedtated threatened or actual use of force or volence to attan a poltcal goal through fear, coercon or ntmdaton (Russell, Banker and Mller 1979, p.4) 5. If the defnton s augmented by hghlghtng the fact that the targets of the volence are not drectly nvolved wth the polcy makng that the terrorsts seek to nfluence (Enders and Sandler 2002, pp ), the defnton may be sad to contan all of the elements that are normally present n a defnton of terrorsm: (1) non-combatants are the targets of terrorst aggresson; and (2) the terrorst acton s expected to affect polcy makng ndrectly by affectng the target audence of non-combatants (Vctoroff 2005, p.4). A lone wolf terrorst engages n operatons that are consstent wth the defnton of terrorsm but does so outsde of a formal command or organsng structure. The lone wolf may or may not sympathse wth a partcular terrorstc organsaton and may not be motvated by a completely unque deology or objectve 6. Ths s somethng qute dfferent to the phenomenon that s sometmes referred to as self-starter or autonomous cells, whch operate wthout afflaton wth an establshed terrorst network but may have an deologcal affnty wth the network (Krby 2007). These are, however, groups of ndvduals and not lone wolves. Ratonal actor models are appled by defence economsts to the analyss of terrorstc behavour. Once an ndvdual or group s terrorstc 7, ratonal actor models work from the assumpton that the ndvdual s or group s actons wll be charactersed by a ratonal pursut of the relevant objectve (subject to constrants). The applcaton of ratonal actor models to extreme behavour lke terrorsm may seem strange at frst. However, terrorstc behavour s structured and strategc (Wlson 2000; Pape 2003) wth poltcs apparently beng a motvatng factor for many terrorsts (see della Porta 1992). Psychologcal and psychatrc analyss has not found robust evdence of rratonalty or madness (Rasch 1979; Vctoroff 2005) and the hstorcal record of terrorstc ncdences s charactersed by structure rather than randomness (see Mckolus (1980; 1983); Im, Cauley and Sandler (1987); Wemann and Brosus (1988); Enders, Parse and Sandler (1992); Enders and Sandler (2002) and Lee, Enders and Sandler (2009)). Although ratonal actor models supply just one part of the complete pcture of terrorstc motvaton and behavour, the applcaton of such models to terrorsm has yelded several mportant results: (1) the deterrence effect; (2) the substtuton effect; (3) the endowment effect; and (4) the preference effect. 5 Cted n Sandler, Tschrhart and Cauley (1983, p.37). 6 See Insttuut voor Velgheds en Crssmanagement (2007). 7 The study of the causes of terrorstc behavour s mult-dscplnary. An example of an nvestgaton of the lnks between terrorsm and soco-economc varables s Berreb (2007). Publshed by Berkeley Electronc Press,

6 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 Frst, terrorstc agents or organsatons may be deterred from undertakng a partcular type of attack by the augmentaton of securty measures, for example, appled to partcular targets. Landes (1978) demonstrates, wthn a ratonal choce expected utlty framework, the mpact of ncreased securty (metal detectors) and harsher prson sentences on ncdences of U.S. hjackngs n the perod 1961 to Second, terrorstc agents or organsatons substtute other types of terrorstc operatons for those operatons that have dmnshed expected utlty because of enhanced securty. For example, ncreased securty at embasses decreases attacks on embasses but ncreases attacks outsde embassy compounds (Enders and Sandler 1993; Frey and Luechnger 2003). Thrd, the resource endowment of terrorstc organsatons s an mportant varable and one that governments and ther securty agences must target n order to reduce terrorsm. Because of the deterrence and substtuton effects, government securty polcy that focuses narrowly on partcular types of terrorsm may not reduce ncdences of terrorstc behavour. Polces that produce a dmnuton n the terrorsts resources are more lkely to have across-the-board effects (Sandler and Lapan 1988; Enders and Sandler 2002). Fourth, the rsk preferences of terrorstc agents and organsatons are of crtcal mportance. For example, f the government ncreases ts mean concesson to terrorstc organsatons durng negotatons, a rsk-averse terrorst organsaton wll ncrease demands (Sandler, Tschrhart and Cauley 1983). The rsk averson of agents and organsatons wll lkely have a sgnfcant mpact on the occurrences and outcomes of terrorstc ncdences (see Phllps 2009; Phllps 2010; Phllps 2011). All of these results are derved from the ratonal choce expected utlty model of terrorsm. Ratonal choce expected utlty underles game theoretcal analyss of terrorsm. Game theory 8 s especally useful for analysng the strategc nteractons of terrorstc organsatons and governments (Sandler and Arce M. 2003; Arce M. and Sandler 2005). Several mportant results relevant to the negotaton process have been generated: (1) the determnaton of the suboptmalty of the never negotate poston (Sandler, Tschrhart and Cauley (1983); Atknson, Sandler and Tschrhart (1987); Lapan and Sandler (1988)); (2) the dscovery of the role that barganng costs play n shapng the terrorst organsaton s demands, the concessons granted by the government and the duraton of an ncdent (Atknson, Sandler and Tschrhart (1987)); and (3) the dscovery that constrants on terrorst organsatons by host states have an mpact on the lkelhood that a terrorst organsaton wll negotate (Bapat 2006). In addton, game theory also generates mportant nsghts nto the nteractons between governments seekng to combat a terrorstc enemy. For example: (1) the 8 The game theoretcal analyss of terrorsm may be roughly dvded nto three compartments: (1) models of government-terrorst negotaton; (2) models of government-terrorst-government nteracton; (3) models ncorporatng another party, such as the populace. DOI: /

7 Phllps: Lone Wolf Terrorsm choces by governments about the level of deterrence that wll be appled to terrorsm mght result n too much or too lttle deterrence (Sandler and Lapan 1988); and (2) the strength of support for terrorsts causes s crtcal n shapng the nature of conflct (Squera and Sandler 2006; Bueno de Mesquta and Dckson 2007). The rgorous dervaton of results that often hghlght weaknesses n conventonal wsdom or ntuton s a man advantage of game theoretcal analyss 9. Wthn all of ths economc analyss, the focus s predomnantly upon the terrorstc organsaton and almost never drectly upon the ndvdual terrorstc agent. Ths s not because the models cannot be appled to ndvdual behavour. Indeed, they have been constructed to be appled to the analyss of ndvdual behavour. It s just that certan aspects of terrorstc behavour (for example, negotaton processes) are more easly analysed when the terrorstc organsaton s the unt of analyss and other aspects of terrorstc behavour (for example, the sucde operatons of ndvduals) are not easly captured wthn the orthodox analytcal approach. The lone wolf terrorstc agent nhabts the boundary of orthodox economc analyss of terrorsm and t s the ndvdualstc nature of the lone wolf that s the most pertnent characterstc. Lone wolf terrorsts operate n a manner that s consstent wth the defnton of terrorsm but engage n such behavour wthout any drect lnks to a group or organsaton. A lone wolf operates alone. The orthodox economc-analytcal framework that has been appled to terrorsm may be expected to generate results when appled to the lone wolf terrorstc agent, especally f the utlty functon of the lone wolf s tself a functon of an organsaton wth whch the lone wolf sympathses. The ndvdualstc nature of lone wolf terrorsm may, however, demand more subtlety from any economc-theoretcal framework that s appled to ts analyss. Orthodox Economc Analyss of Lone Wolf Terrorsm The applcaton of a basc ratonal actor expected utlty model to lone wolf s easy and yelds mmedate emprcally testable results. It generates results by treatng the lone wolf as a ratonal actor. It does not, however, penetrate very deeply nto the nature of lone wolf terrorsm. A lone wolf terrorst wth no dstnct sympathes for a partcular terrorstc organsaton may be thought of as an ndvdual attemptng to maxmse an expected utlty functon lke the Becker (1968) or Ehrlch (1973) expected utlty functons for crmnal behavour that were adapted to the analyss of hjackng by Landes (1978): ( P ) U( Z ) + P PU( Z S) + P ( P ) U( Z C) EU = 1 1 (1) a a c a c 9 Also see Bueno de Mesquta (2005), Jacobson and Kaplan (2007) and Sandler and Arce (2007). Publshed by Berkeley Electronc Press,

8 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 Where Pa s the probablty of apprehenson, P c s the condtonal probablty of convcton f apprehended, Z represents the lone wolf s payoff, S s the negatve payoff of a prson sentence and C represents the costs assocated wth apprehenson when the lone wolf s not sentenced (see Landes 1978, pp.5-6). Such a model encapsulates the deterrence effect. In assessng a target or attack type, the lone wolf weghs the probablty of success aganst the probablty of capture and convcton. Harsher sentences or enhanced securty around partcular targets wll decrease the EU assocated wth such targets and deter the lone wolf. Lone Wolf Terrorsm Predcton 1: The mplementaton of hgher securty and harsher penaltes may be expected to deter the lone wolf from a partcular target or attack type. The weakness of a model such as the one depcted n Equaton (1) s that t ultmately says very lttle about the lone wolf. The deterrence result has value when assessng a partcular target or attack type or a terrorstc group but ts value does not translate well to the context of the lone wolf. Predcton (1) should stll be expected to hold. However, the lone wolf places a more onerous burden on securty agences and analysts. Unlke the stream of hjackers analysed by Landes (1978), lone wolves who plan ther operatons ndependently may generate a seres of pont attacks charactersed by once-off partcular attack types on partcular targets. Securty agences may mpose the deterrence effect upon a lone wolf by correctly antcpatng a target or attack type (or by mposng harsher punshments). The sngle attempted or actual strke by a sngle lone wolf on a sngle (unantcpated) target s not, unfortunately, effectvely modelled wth a basc model that has an emphass on deterrence (such as Equaton (1)). A ratonal actor model that ncorporates both the deterrence and substtuton effects s more flexble. Equaton (1) can be thought of as beng appled to a partcular target or attack type. The lone wolf then apples Equaton (1) to a number of alternatves and chooses the alternatve that provdes the hghest expected utlty. The lone wolf wll substtute one target or attack type for another as he re-ranks the alternatves n lght of changng condtons. Adaptng Equaton (1) to explctly ncorporate other targets or attack types s straghtforward: EU = N [ ( Pa ) U( Z ) + Pa Pc U( Z S ) + Pa ( 1 Pc ) U( Z C )] = 1 1 (2) DOI: /

9 Phllps: Lone Wolf Terrorsm In Equaton (2), the subscrpt,, ndcates that the lone wolf s EU s the sum of utlty across each terrorstc (or non-terrorstc) operaton. If the lone wolf acts as f he maxmses EU, nnovatons n the utlty structure of ndvdual operatons affect EU. The lone wolf may be deterred from a partcular operaton but attracted to another. The model depcted n Equaton (2) s not entrely satsfactory but t does explctly encapsulate both deterrence and substtuton effects wthn a sngle tme perod. It s also a slghtly more useful representaton of the lone wolf s decson calculus. By constructon, the model depcted n Equaton (2) can more effectvely handle the pont attacks that mght characterse lone wolves, even f only to the extent that the lone wolf may be expected to rank possble targets or attack types, to re-rank them as crcumstances change and to choose only the best ranked feasble alternatve. Lone Wolf Terrorsm Predcton 2: The mplementaton of hgher securty and harsher penaltes may be expected to deter the lone wolf from a partcular target or attack type and cause hm to substtute one type of attack for another. The weakness of the model s that ts analytcal power does not extend far enough nto the doman of the lone wolf. Attack types or targets that are not feasble or hghly ranked wthn a preference orderng are not undertaken. Wthn a sngle tme perod, the lone wolf must strke wth pont attacks rather than combnatons of attack methods and targets. The deterrence and substtuton effects of predcton (2) must stll be expected to hold. However, securty agences vewng the lone wolf through the analytcal flter of Equaton (2) are left wth lttle advance over Equaton (1) and must stll antcpate the lone wolf s ponts of attack. The problem s essentally one of non-revealed preference. A sngle lone wolf who does not engage n a partcular operaton mght be revealng that such an operaton has been accorded nferor rankng wthn hs preference orderng or he mght be revealng no such thng. On the contrary, the operaton may be planned and ready to execute. Because of the pont attack nature of lone wolf terrorsm, t s only after a preference has been revealed that Equaton (2) becomes more useful to securty agences. The theme of the forgong dscusson s the ndependent and ndvdual nature of lone wolf terrorsm generates a seres of pont attacks whch are dffcult to analyse wthn the standard utlty theoretcal framework. Deterrence and substtuton effects should stll be expected to hold for any ratonal actor but the gudance for securty agences that can be extracted from the analytcal framework s thn because of non-revealed preferences. Ths stands n contradstncton to a terrorstc organsaton that mght more readly (1) reveal preferences through propaganda (for example, Bn Laden s fatwa); or (2) fall nto Publshed by Berkeley Electronc Press,

10 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 the structure of terrorstc ncdences revealed n the tme seres. The ndvdual nature of the lone wolf also presents problems for the applcaton of the endowment effect. The resources and nfrastructure of a terrorstc organsaton may subject to a dmnuton that can be expected to produce a dmnuton n terrorstc ncdences. Lkewse, a dmnuton n the resources endowment of the lone wolf knocks partcular attack types or targets out of the lone wolf s feasble set and may temporarly render all attack types and targets nfeasble. Lone Wolf Terrorsm Predcton 3: A dmnuton n the resources endowment of the lone wolf can be expected to produce a dmnuton n lone wolf terrorstc actvty. The ndvdual and, presumably, largely self suffcent nature of the lone wolf agan presents analytcal challenges. If securty agences can strke a lone wolf s resource endowment, t would seem lkely that under such crcumstances both the dentty and locaton of the lone wolf s known and he may be permanently decommssoned. If not, of course, t seems unlkely that the resource endowment may be struck n any drect way. Securty agences operatng wth the gudance of the orthodox economc analytcal framework must focus on across the board measures that make resources (for example, bomb-makng equpment) more dffcult to source. The analytcal framework and the endowment effect do not translate easly to the ndvdual and self suffcent context of the lone wolf. The rsk preferences of the lone wolf are of crtcal mportance. The level of rsk averson 10 exhbted by the terrorst shapes the choce of attack type and target. Furthermore, f the lone wolf becomes nvolved n a negotaton or barganng process wth the government and ts securty agences, the rsk preferences that the lone wolf exhbts wll certanly shape hs actons wthn such a process. An ncrease n the rsk the lone wolf assocates wth partcular targets or attack types may produce both deterrence and substtuton effects unless the ncreased rsk s accompaned by an ncrease n the expected payoff. Lone Wolf Terrorsm Predcton 4: An ncrease n the rsk assocated wth the payoffs of a partcular terrorstc operaton wll deter the lone wolf from undertakng the operaton unless there s a commensurate ncrease n the expected payoffs. 10 Rsk averson rather than rsk seekng behavour s the startng pont because rsk seekng behavour unrealstcally mples that the terrorst wll gve up unts of payoff to take on more rsk. Rsk averson more realstcally mples that the terrorst wll take on any amount of rsk as long as the payoff s hgh enough. Of course, f the terrorst does happen to be rsk seekng we may say that he has negatve rsk averson. DOI: /

11 Phllps: Lone Wolf Terrorsm The rsk preference effect does not suffer from the same lack of transferablty to the lone wolf context. Ths s because the lone wolf cannot escape the dstrbuton of payoffs that characterses terrorstc operatons n general. The payoffs and the varablty or rsk of the payoffs to terrorstc operatons, partcularly f measured n terms of human tragedy (number of fataltes) or meda coverage (whch s most lkely a functon of the level of human tragedy), are encapsulated n a probablty dstrbuton that apples to all terrorstc organsatons. Only nnovatons n attack type and target not reflected wthn the dstrbuton are unrestraned by the dstrbuton. Governments and ther securty agences may therefore determne the payoffs and rsks assocated wth partcular terrorstc operatons, regardless of whether they are perpetrated by an ndvdual or group. Securty measures that enhance the rsk (wthout ncreasng expected payoffs) assocated wth partcular targets and attack types generate deterrence and substtuton effects. However, wthn a payoff-rsk framework the dosyncrases of the lone wolf do not nterfere wth the analytcal determnaton of the strength of these effects. Wthn a payoff-rsk framework, the lone wolf s constraned by the probablty dstrbuton of payoffs to terrorsm. The rsk preference effect s durable when the lone wolf s consdered wthn a payoff-rsk analytcal framework. Wthn a game theoretcal structure, the nteractons between governments or between securty agences of a sngle government, regardng deterrence measures should stll hold n the context of lone wolf terrorsm. A lone wolf need not operate wthn a domcle and mght, for nstance, perpetrate an attack aboard an arcraft that he has boarded outsde of the jursdcton of the target country. The deterrence and pre-empton decsons of each of two dfferent target countres may have mplcatons for the other country (see Arce M. and Sandler (2005, p.186)) n the context of lone wolf terrorsm but ths, of course, does not provde any addtonal nsghts or predctons that deeply address the dosyncrases of the phenomenon. Although a partcular type of pre-empton or deterrence may be requred for lone wolves, the nteractons of governments n executng such actons seem lkely to follow smlar patterns to those revealed by game theoretcal analyss of terrorsm. It s unclear but unlkely that a lone wolf threat would be treated dfferently by governments than the threat of the terrorstc organsaton. Lone Wolf Terrorsm Predcton 5: The lone wolf terrorst presents challenges smlar to the terrorstc group wth regard to the coordnaton of securty polcy between governments. A lone wolf mght engage n negotatons wth a government, partcularly f the actvty nvolves a hostage-takng stuaton. The strategc nteractons Publshed by Berkeley Electronc Press,

12 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 between governments and lone wolves are lkely to follow smlar patterns to those dentfed by hstorcal analyss and game theoretcal analyss f a negotaton process emerges. In ths nstance, the lone wolf has almost no defnng dosyncrases and game theoretcal analyss as t has been worked out n the context of terrorstc organsatons may be expected to functon. Lone Wolf Terrorsm Predcton 6: The lone wolf terrorst has no defnng dosyncrases wthn a negotaton or barganng context. Game theoretcal analyss apples more easly to both the lone wolf and terrorstc organsaton than expected utlty analyss. Ths apples to models of government-government nteracton and government-terrorst nteracton. Models ncorporatng a thrd party, such as popular support, may be more complex when explored wthn a lone wolf terrorsm context. It seems clear that the popular support modelled n game theoretcal analyss of terrorsm does not apply wth any sgnfcant drect force wthn the lone wolf context. In such models, popular support for terrorsm emerges from (1) economc damage caused by counterterror operatons; (2) the assessment by the populaton of the government s counter-terror operatons; (3) the dverson of government money to counterterrorsm (Bueno de Mesquta and Dckson (2007) and Squera and Sandler (2006)). The lone wolf s unlkely to precptate counter-terror operatons that galvanse publc support aganst the government n the manner envsaged wthn the extant game theoretcal analyss. As such, no predctons for lone wolf terrorsm from the exstng theory can be garnered on ths pont. The applcaton of orthodox economc analyss yelds several conclusons for lone wolf terrorsm. The man nsghts that have been reached by the applcaton of economc analyss to terrorsm may usually be expected to hold n some way or another when appled to lone wolf terrorsm. Governments and securty agences that face the threat of lone wolf terrorsm do not do so wthout the beneft of an exstng analytcal framework. However, the ndvdual, ndependent and self-suffcent nature of true lone wolf terrorsts presents obstacles to the depth of nsght that can be gathered by an applcaton of orthodox methods. The realsaton that even true lone wolves are constraned by the dstrbuton of payoffs that characterses terrorsm s a pont of tracton that mght be exploted to generate deeper results that may be mplemented n an operatonal sense by governments and securty agences. An analytcal framework wthn whch the predctons of the orthodox model hold but whch, at the same tme, encompasses the dosyncrases of the lone wolf wll provde much more tangble analytcal gudance to governments and securty agences. DOI: /

13 Phllps: Lone Wolf Terrorsm A Mean-Varance Framework An analytcal framework that explots the constrant placed upon the lone wolf terrorst by the dstrbuton of payoffs to terrorst ncdences s a mean-varance preference orderng framework. Wthn ths framework, lone wolves order ther preferences for partcular attack types or targets based only on two moments of the dstrbuton: (1) the mean (expected payoff); and (2) the varance (rsk) of the payoffs. Because the lone wolf cannot escape the dstrbuton of payoffs that characterses terrorst ncdences, the applcaton of a mean-varance framework to lone wolf terrorsm may provde computable results nsghts nto lone wolves preference orderngs that cannot be attaned by any other method. The method s a ratonal actor model but one that places a less onerous burden on both the agent and the economst seekng to analyse the agent s behavour. A meanvarance preference orderng s lkely to concde approxmately wth any preference orderng constructed wth full EU methods. If the agent s assumed to be charactersed by a quadratc utlty functon, the agent s mean-varance preference orderng wll be precsely consstent wth a full EU orderng. Although a mean-varance preference orderng may be constructed over any aspect of terrorstc behavour meda coverage, publc support, fnancal payoffs the most mmedately obvous payoff s the level of human tragedy fataltes and njures. Furthermore, the level of human tragedy s the frst and most mportant statstc reported by the press and, at the very least, s lkely to represent a very plausble proxy for the more ntangble poltcal nfluence that s usually consdered to be the ultmate objectve of terrorsts. In many ways, the level of human tragedy determnes the amount of coverage and attenton an ncdent receves. Ths tends to facltate the dssemnaton, although approxmately, of the dstrbuton of fataltes assocated wth partcular attack methods and targets and recent evdence strongly supports the assumpton that terrorsts act to maxmse the level of human tragedy. The ndvdual arrested for the Washngton D.C. Metro bombng conspracy explctly stated ths as the objectve (Fnn, Hsu and Gbson 2010). The assumpton that terrorsts act to maxmse the level of human tragedy s also n accordance wth the very nterestng fndng that the number of vctms n a partcular attack s correlated wth the number of vctms of prevous attacks, mplyng a contest n brutalty among terrorst groups (Caruso and Schneder 2010). Assumpton 1 The lone wolf makes a preference orderng of combnatons of attack methods on the bass of two moments of the dstrbuton of the fataltes assocated wth the partcular attack method combnatons. Publshed by Berkeley Electronc Press,

14 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 The utlty of the lone wolf s a functon of the mean (expected) fataltes, F, and rsk (the standard devaton of the possble dvergence of fataltes from the mean). Formally, ( F, σ ) U = f (3) F The lone wolf terrorst faces the task of constructng a preference orderng based upon the mean and varance of the fataltes assocated wth partcular attack methods. If the lone wolf can combne attack methods, the lone wolf faces the task of constructng a preference orderng across combnatons of attack methods. The expected payoff of a combnaton of attack methods may be stated as: F = n = 1 w F (4) The rsk or varance of the expected payoff of a combnaton of attack methods may be stated as: 2 σ = = n = 1 j= 1 n = 1 n 2 w w ρ σ σ w σ + 2 j n j n = 1 j= 1 j j w w ρ σ σ j j j (5) Where ρ j s the correlaton coeffcent that expresses the degree of correlaton between the fataltes generated by attack method and attack method j and w s the proporton of resources allocated to attack method. It should also be noted that ρ σ σ s equal to the covarance between attack methods and j ( σ ) j j j. The double summaton sgn smply mples that all possble pars of attack methods must be accounted for. Wthn ths framework, the lone wolf wll consder the set of attack method combnatons that have the hghest payoff for each level of rsk. The set of attack method combnatons that have the hghest payoff for each level of rsk s the effcent set. The effcent set may be determned by repeatedly solvng the relevant quadratc programmng problem (Strong 2006, p.155): DOI: /

15 Phllps: Lone Wolf Terrorsm 2 mnσ = n n = 1 j= 1 w w jρjσ σ j Subject to a target F *: F n = w F = F * = 1 (6) And the constrants: n = 1 w = 1 w 0 The consttuton of the effcent set s mportant nformaton for governments and ther securty agences (see Phllps 2009). Because the lone wolf s constraned by the dstrbuton of payoffs that characterses terrorstc ncdences, the lone wolf who constructs a preference orderng of attack methods on the bass of mean and varance s drawn to the effcent set of attack method combnatons. Governments and ther securty agences have a much narrower set of potental attack method combnatons upon whch to focus ther attenton and efforts when the lone wolf s analysed through the flter of a mean-varance preference orderng framework. A dstngushng feature of lone wolf terrorsm s ts lone ndvdual nature. It would seem unlkely, at least wthn a sngle perod, that a lone wolf could deploy a combnaton of attack methods (for example, a combnaton of bombng, assassnaton and armed assault). What s far more lkely s that the lone wolf wll deploy a sngle attack method wthn a perod of analyss. The lone wolf s further constraned to the set of combnatons wthn the effcent set that contan just one attack method. It s to one of these sngle attack method combnatons that the lone wolf wll devote resources n a sngle perod. Formally, Publshed by Berkeley Electronc Press,

16 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 mn 2 σ = σ 2 Subject to a target F *: F = w F = 1 = F * (7) And the constrant: w 1 A mean-varance preference orderng over attack methods does not requre the assgnment of a utlty functon. However, further nsghts can be obtaned from dong so. The assgnment of a quadratc utlty functon guarantees the consstency of any mean-varance preference orderng wth the NM axoms. Although there has been strong debate regardng the deployment of quadratc utlty functons wthn fnancal economcs, a quadratc utlty functon wll closely (locally) approxmate other utlty functons and closely approxmate a full EU preference orderng wth less computatonal burden and wth the advantage of yeldng computable results (the consttuents of a ratonal actor s preference orderng) (see Elton et al. (2003, p.232); Kroll, Levy and Markowtz (1984); Levy and Markowtz (1979); Meyer (1987) and, for a dscusson of theoretcal consderatons, especally the utlsaton of mean-varance orderngs for portfolo problems and the selecton of the optmal choce, Baron (1977, p )). The assgnment of a quadratc utlty functon provdes the mechansm by whch the rsk preferences of the lone wolf may be analysed wthn the mean-varance analytcal framework. Not only wll such an analytcal apparatus provde computable results relevant to the analyss of lone wolf terrorsm that wll closely approxmate any full EU analyss but the specal features of quadratc utlty mght be partcularly useful for the analyss of the lone wolf. Formally, the specfc functonal form of the utlty functon that emerges from a stuaton where the terrorstc agent wth quadratc utlty makes choces solely on the bass of two moments of the dstrbuton (mean and varance) of payoffs may be expressed formally as: U 2 ( F ) c + af df = (8) If the terrorstc agent happens, for a gven payoff, to prefer a smaller varance of payoffs to a larger varance, then d > 0. The applcaton of a DOI: /

17 Phllps: Lone Wolf Terrorsm quadratc utlty functon has a number of dstnct advantages. A quadratc utlty functon permts the analyss of the effect of the rsk averson parameters on the utlty generated by partcular payoffs. It wll do so n a manner that wll locally approxmate other specfcatons of utlty functons. A number of addtonal nsghts nto lone wolf terrorsm may be generated by the applcaton of quadratc utlty. The features of quadratc utlty that are most mportant and relevant are lsted below: 1. The quadratc utlty functon ensures that the equlbrum weghts assgned to partcular attack methods by lone wolf terrorsts are not nfluenced by the fnteness of the mean and varance of the attack method combnatons (see Ohlson 1977). Analyss may proceed, for example, even when lone wolf terrorsts are assumed to face nfnte rsk. 2. The quadratc utlty functon must reach a maxmum at some pont. Ths s a problem wthn fnancal economcs but not for defence economcs. Beyond some pont, addtonal expected fataltes at a constant rsk level wll result n a reducton n the allocaton of resources to rsky attack method combnatons (see Wppern 1971). Ths dmnshng margnal utlty of fataltes past some pont ensures that the mean-varance framework s consstent wth the accepted defntons of terrorsm. 3. The queston of the locaton (wthn the range of payoffs) of the sataton pont s an mportant one. It s possble that sataton occurs wthn a relevant (not extreme) range of payoffs to attack method combnatons. In ths case, whether sataton s nterpreted as encompassng some poltcal aspect of terrorsm beyond merely accumulatng fataltes or as somethng that occurs at a moment of self-destructon, large or extreme payoffs payoffs that are many standard devatons from the mean are not necessarly requred to entce the lone wolf. Governments and ther securty agences may confne ther analyss to the dstrbuton of payoffs to terrorsm. The theoretcal-analytcal framework that has been set down n ths secton yelds a number of predctons for the lone wolf terrorst. The predctons that are generated from ths partcular analytcal framework encompass those of the orthodox expected utlty approach to the analyss of terrorsm. However, the mplcatons are more precse and computable results relevant to the set of attack method combnatons from whch the ratonal lone wolf wll select are obtanable. The predctons that are yelded from the mean-varance analytcal framework wth quadratcty of the lone wolf terrorst s utlty functon are lsted below. Each predcton s accompaned by an example or nterpretaton n order to add more Publshed by Berkeley Electronc Press,

18 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 concreteness to the predctons and provde an ndcaton of ther practcal applcaton and relevance. Predcton 1 The lone wolf terrorst wll be deterred from engagng n terrorstc actvty by an augmentaton n the varance of the expected payoffs. Interpretaton Lone wolf actvty wll decrease when the lone wolf perceves an ncrease n the varablty of the fataltes that can be expected from an attack (and vce versa). For example, random screenng of packages delvered to all government departments wll lkely ncrease the varablty of the fataltes that the lone wolf can expect from a letter bombng campagn. Publcsed securty alerts that heghten awareness among targets wll also lkely have the same effect. Predcton 2 The lone wolf terrorst wll reorder hs preferences for attack method combnatons on the bass of changes to the two moments of the dstrbuton of payoffs. Interpretaton When there s a change n ether the expected fataltes and/or the varablty of the expected fataltes assocated wth a partcular attack method (or combnaton), the lone wolf wll change hs preferences for that attack method. For example, news of a bombng campagn that generates an nordnate number of fataltes may ncrease the expected fataltes assocated wth bombng and reposton the attack method at a hgher poston n the lone wolf s preference rankng. Predcton 3 An ncrease (decrease) n the rsk averson of the lone wolf wll nduce a preference re-orderng. Lkewse, an ncrease (decrease) n the rsk (the second moment of the dstrbuton) wll nduce a preference re-orderng. Interpretaton The quadratcty of the lone wolf s utlty functon mples that the lone wolf wll be observed to allocate more resources (ncludng tme) to the less rsky attack methods (or combnatons) as hs recorded fataltes and njures ncrease. DOI: /

19 Phllps: Lone Wolf Terrorsm Predcton 4 Lone wolf terrorsts wll choose attack method combnatons that are contaned wthn the effcent set of combnatons (those that have the hghest expected payoff for a gven level of rsk). Interpretaton The lone wolf wll be observed to deploy (or exhbt a tendency to deploy) the attack methods (or combnatons) that domnate others n terms of expected fataltes for a gven level of rsk. These attack method combnatons are computable. Ths represents valuable nformaton to the government and ts securty agences. Predcton 5 Lone wolf terrorsts, at least wthn a sngle perod of analyss, wll choose attack method combnatons that are consttuted by a sngle attack method. Interpretaton Lone wolf terrorsts, for the reasons explaned above, wll choose sngle attack methods at partcular ponts n tme. Ths follows logcally from the nature of the lone wolf. Predcton 6 Past some pont, the lone wolf terrorst may experence decreasng margnal utlty from fataltes generated by attacks. Interpretaton After some perod of success, the lone wolf wll be observed to reduce or cease hs actvty. He may resume agan after some tme has elapsed. Predcton 7 The lone wolf wll be found to nhabt a relevant range of the dstrbuton of payoffs to terrorstc ncdences. Interpretaton The lone wolf need not be attracted to the extreme tals of the dstrbuton or to actvty that sts outsde of the dstrbuton of fataltes assocated wth terrorst actvty n general. Lone wolves may be satsfed by very low levels of fataltes and engage n terrorst actvtes that place them well wthn the probablty dstrbuton of fataltes. The nsght that the lone wolf s subject to and constraned by the probablty dstrbuton of payoffs and rsks that characterses terrorstc operatons and the durablty of the rsk preference effect s of crtcal mportance. Publshed by Berkeley Electronc Press,

20 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 It provdes the openng for the constructon of a theoretcal framework that encompasses the ndvdual and pont attack nature of lone wolf terrorsm and generates nsghts nto the payoff-rsk tradeoffs that wll bat the lone wolf. The predctons of the orthodox model wll hold n such a framework but n a manner that provdes much more tangble analytcal gudance to governments and ther securty agences wthn the context of the lone wolf. A mean-varance preference orderng approach to the analyss of terrorsm enhances the tradtonal or orthodox approaches to the expected utlty analyss of terrorsm and generates computable results that may assst governments and securty agences n ther pursut of both terrorsts assocated wth terrorst organsatons and the nsdous lone wolves. Statstcal Analyss and the Lone Wolf s Sngle Attack Method Combnatons The analyss of the lone wolf wthn a mean-varance framework commences wth the dentfcaton of the propertes of the dstrbuton of terrorstc ncdences and, n partcular, the payoffs and rsks assocated wth attack methods. Usng the RAND Corporaton s data for terrorstc ncdences (the MIPT database), the average payoff and the rsk assocated wth each of ten attack methods may be computed for the perod 1968 to The ten attack method types covered by RAND are (1) armed attacks; (2) arson; (3) assassnaton; (4) hostage; (5) bombng; (6) hjackng; (7) kdnappng; (8) other ; (9) unconventonal 11 ; and (10) unknown. Of all of these attack methods, bombng, unconventonal and hostage takng ncdences have the hghest rsk and also the hghest level of expected fataltes per attack per year. 11 The 9/11 terrorst attacks represent the most promnent recorded ncdents of ths class n the RAND-MIPT database. A nuclear or bologcal attack would be recorded as unconventonal were such an attack to occur. DOI: /

21 Phllps: Lone Wolf Terrorsm Table 1. Statstcal Summary 1967 to 2007 of Attack Methods Attack Method Varance Standard Devaton Average Annual Fataltes Per Incdent Armed Attack Arson Assassnaton Hostage Bombng Hjackng Kdnappng Other Unconventonal Unknown The lone wolf terrorst cannot escape ths dstrbuton. Combnatons of these attack methods form the choce set from whch terrorsts and terrorstc organsatons choose. From the complete choce set, lone wolves and terrorstc organsatons select from those attack method combnatons that have the hghest expected payoff for a partcular level of rsk. That s, from the effcent set of attack method combnatons that solve the quadratc programmng problem outlne n the prevous secton. Phllps (2009) presents calculatons of the effcent set usng the RAND data. Attack method combnatons that consttute the effcent set are charactersed by ther weghtng schedules (resource allocatons). For example, 50 percent armed assault, 10 percent kdnappng, 30 percent bombng and 10 percent assassnaton. Unlke a terrorstc organsaton, the lone wolf, at least wthn a sngle perod, s more lkely to be constraned at each gven level of rsk to the corner combnatons that contan a sngle attack method. The determnaton of these sngle attack method combnatons s undertaken n ths secton. For each of the attack methods lsted above, the RAND data for a fortyyear perod s utlsed to compute the expected payoff for ndvdual attack methods over a range of standard devatons and the weght (percentage of resources that would be devoted to the attack method) accorded to the ndvdual attack method at each standard devaton. For each attack method, the weght and expected payoff at levels of standard devaton rangng from 0.05 fataltes per attack per year to 11.5 fataltes per attack per year are computed. Formally, a range of values for Equaton (9) were establshed. Publshed by Berkeley Electronc Press,

22 Peace Economcs, Peace Scence and Publc Polcy, Vol. 17 [2011], Iss. 1, Art. 1 n 2 ( F F ) = 1 σ = (9) n 1 Equaton (9) s the equaton for the standard devaton (rsk) of a sngle attack method,. For the range of values for Equaton (9), the expected payoffs of combnatons consstng of sngle attack method at partcular weghts were computed. The followng quadratc programmng problem, whch s essentally equvalent to the problem above, was solved over the range of standard devatons for attack method combnatons consstng of sngle attack methods ( = 1): max F = w F Subject to a target standard devaton σ *: = 1 σ * = n ( F F ) n 1 2 (10) And the constrant: w 1 The results of the calculatons are presented n Tables Two and Three. The range of standard devatons s contaned wthn the frst column. For each attack method,, the weght (percentage of resources) and expected payoff that s consstent wth each level of standard devaton s presented. For example, at a standard devaton of fataltes per attack per year, fve percent (0.05) of resources allocated to armed attack generates an expected payoff of fataltes per attack per year. DOI: /

23 Phllps: Lone Wolf Terrorsm Table 2. The Lone Wolf s Effcent Set of Sngle Attack Method Combnatons, Part One Armed Hostage Arson Assassnaton Attack Standard Weght Payoff Weght Payoff Weght Payoff Weght Payoff Devaton Publshed by Berkeley Electronc Press,