Institute for Defense Analyses
4850 Mark Center Drive • Alexandria, Virginia 22311-1882
National Institute of Statistical Sciences
Workshop on Statistics
and Counterterrorism
An Empirical Model of the
Psychology of Deterrence:
Reality Does Not Conform to Theory
Robert Anthony
20 November 2004
The views expressed in this talk are solely those of the author and do not
represent an official position of IDA or its sponsors.
Copyright, the Institute for Defense Analyses, 2004
3/23/2016-1
Definition of Deterrence
Deterrence is “the prevention from action by
fear of consequences –
deterrence is a state of mind
brought about by the existence of a
credible threat of unacceptable counteraction.”
(JCS Pub 1-02)
3/23/2016-2
Key Points
• Deterring suicide terrorists
• Deterrence aspects of counter-terrorism (CT)
• Calibrated model of psychology of deterrence
– Opinions of incarcerated drug smugglers
– Peru to Colombia air bridge denial operations
– Caribbean drug smugglers (air or go-fast boat)
– Fisheries enforcement by U.S. Coast Guard
– Early automobile driving – an “extreme” sport
• Failures of risk perception / acceptance theories
– Expected Utility Theory (EUT)
– Others
• Perpetrators consider risks before rewards
• Unique property of IDA model  Universality?
3/23/2016-3
Deter Suicide Attacks?
A careless terrorist is a non sequitur
• What might suicide terrorists fear?
– Failure, arrest, or loss of life without completing the mission
– Dishonoring or bringing retribution upon their families
– Embarrassing their cause and supporters of their cause
– Revealing any larger scheme and their supporting network
• Reframe* the terrorists’ perceptions
– FROM: Avoiding a loss  RISK SEEKING
– TO:
Pursuing a gain  RISK AVERSE
* Tversky and Kahneman (1981)
3/23/2016-4
How Does Deterrence Contribute to CT?
Interdict
Effective interdiction and
protection will deter
Deterrence protects some
unknown vulnerabilities
Deter
Protect
Mitigate
3/23/2016-5
Deterrence is a large force multiplier:
Deterred = 2 to 10 x Interdiction
Rockwell interviews of inmates
• Opinions of incarcerated smugglers:
What else matters?
• Nationality: U.S., Mexican, Colombian
• Ages: 20 to 50
• Education: grammar school to Ph.D.
• Drugs: marijuana, cocaine, heroin
• Experience: 1 to 10 loads
• No rewards for being interviewed
• 254 prisoners eligible; 112 participated
• Experienced drug enforcement interviewers
3/23/2016-6
Willingness to Smuggle - Interview Results
“I would not smuggle drugs into the U.S. if my chances of
getting caught (caught and convicted, or caught, convicted,
and imprisoned) were… ”
Imprisoned
Probability of
Interdiction
1 in 10
1 in 5
2 in 5
4 in 5
Certain*
Respondents
No Answer
Self
83
11
5
2
3
104
5
Convicted
Associate
43
27
13
3
6
92
0
Self
72
16
9
4
3
104
5
Caught
Associate
32
25
26
5
4
92
0
Self
63
17
15
3
6
104
5
Associate
21
29
25
3
14
92
0
* Certain: the last response category combines 1) not willing to smuggle when
faced with certain capture and 2) willing even if certain to be captured.
3/23/2016-7
Inmate Willingness to Smuggle
Fraction of Inmates Willing to Smuggle  W ( PI* )
1.0
Interview data
Associate caught
Assoc. imprisoned
Self caught
Self imprisoned
Deterrence
8.0
threshold
6.0
Willingness Function
 P0 
W ( P )   * 
 PI 
1.03 0.07
*
I
4.0
2.0
“Undeterrable”
residual
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Perceived probability of Interdiction  PI*
3/23/2016-8
Chi-square probability = 0.49
Fisheries Violations & U.S. Coast Guard Effort
Willingness = Violation Rate (VR); Interdiction = Boarding Rate (BR)
y = 0.011x -0.97 ±0.15
0.12
New England
VR (Nnwr)
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
0.8
Boarding Rate [B( Nnwr)/NFV]
Quarterly
October - December 1995
0.14
y = 3E-07x
0.12
VR (Nnwr)
South Atlantic
and Caribbean
Power (Quarterly)
-0.95 ±0.16
0.1
0.08
0.06
0.04
0.02
0
0
0.000005
0.00001
0.000015
BR2[B(Nnwr)/EV]
3/23/2016-9
0.00002
0.000025
Exponents are
indistinguishable
from -1.0.
Early Automobile Use
Percent of U.S. Population Using Automobiles
100
10
1920
1
Note: on log-log plot,
inverse power is 45 line
1910
0.1
1/ PI
tail
1900
0.01
0.000001
0.00001
0.0001
0.001
Fatalities per Person Hour of Exposure
Source: Starr, 1972
3/23/2016-10
Peru to Colombia Air Bridge Denial Operations
Consequences
Observed Willingness to Smuggle
Lethal
1.0
Incarceration
Peru ABD
non-lethal ops
0.8
0.6
Loss of drugs, vehicle, and
chance of imprisonment
Peru ABD
lethal ops
0.4
Transition period
(average)
0.2
0.0
0.0
0.2
0.4
0.6
0.8
Observed Probability of Interdiction
3/23/2016-11
1.0
Operations against Caribbean Smuggling
Consequences
Willingness to Smuggle
Lethal
1.0
Incarceration
Transit zone
air Interdiction
0.8
0.6
Loss of drugs, vehicle, and
chance of imprisonment
Puerto Rico
go-fast ops
Interdicted
fraction of
all smugglers
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Probability of Interdiction
3/23/2016-12
P 
PI W  PI   0 
 PI 
 P0
Wage: What Is Enough?
Factor of Increased Wages
Percent Willing To Smuggle
10
100%
Red = Self
Green = Associate
Saturation
80%
Risk x2
Risk x3
Risk x4
Certain
Risk x2
Risk x3
Risk x4
Certain
60%
40%
Wage
 Risk 2
0.60
9
8
7
6
5
4
3
2
20%
R2  0.990
1
0%
0
0
2
4
6
8
10
Factor of Increased Wages
0
1
2
3
4
Factor of Increased Risk
Traffickers assess risk first, and then ask whether the wage is enough.
3/23/2016-13
5
Expected Utility Theory (EUT)
• Leading EUT method for quantifying the psychology of
risk-taking, the Conjoint Expected Risk (CER), is:
W  a  b  PI  c  PI  L  d  (1  PI )  G 
• Problems with EUT and risk perception theories in general:
– Model coefficients change per experiment (not universal)
– Mathematically inconsistent with willingness function’s 1 PI
– Narrow mid-range of risks in published papers
– Laboratory data (mostly student trials)
– Fundamental unresolved issues in academic community
• Willingness model fits data from one published paper better
than EUT or CER
3/23/2016-14
Willingness Function Contradicts EUT & CER
The general EUT form cannot approximate the willingness
b and c  L become a single
constant, l . And d  G  becomes increasing function, g ( PI ).
function’s form. For a fixed loss,
W  a  PI  l  (1  PI )  g ( PI )
And W = P0 at PI = 1.0 implies
For P0  PI  1.0
a  P0  l
.
Also, W = 1.0 for PI = P0 ; therefore:
W  P0  (1  PI )  (1  g ( PI )  g ( P0 ))  P0  1  PI
Because g ( PI ) is a monotonically increasing function of PI .
To represent the “undeterrable” residual,
neither EUT or CER ever drops below –45 diagonal.
3/23/2016-15
Data from Business Investment Experiment
MBA Student Responses
27 Risky Situations
(Two shown)
Risk Ratings
(Scale 0 to 10)
PI
Gain
Loss
Avg
Std
W
1
0.3
+12
-2
3.14
2.14
0.97
2…
0.5
+13
-3
3.79
1.89
0.95
Range
0.3; 0.7
+2; +48
-2; -48
3.14;
7.42
1.83;
2.50
0.16; 0.97
Accepted
No.
Source: J. Sokolowska, A. Pohorille / Acta Psychologica 104 (2000) 339-369
3/23/2016-16
Comparison of Models
Type
Model Equation for W
RMSE
Adj R2
EUT
0.59  0.02 PI L0.06  1.69  (1  PI )G 0.80
0.10
0.84
Poly
0.56  0.04  PI  L  0.03  G  0.0006  G 2
0.10
0.87
Risk
 0.10  0.01  Risk 2.12  1.04  G 0.07
0.04
0.95
P0 / PI (0.43  0.35  Log10 L  0.24  Log10G) / PI
0.05
0.92

0.09
0.89
P0 / PI
3.14  G 0.46 PI  L0.54

RMSE = Root Mean Square Error
Threshold of P0 / PI required dropping two events with PI  P0  2  RMSE.
3/23/2016-17
Perpetrators Consider Risk First
• Prisoner willingness
 f ( P0 , PI ) no wages mentioned
• Prisoner wage sensitivity ends at willingness asymptote
• Raw risk estimate better than Expected Utility Theory (EUT)
(might also reflect incorrect functional form for EUT)
• “Explains” framing – Focus on fear of loss of control:
A. Unless one takes an extreme risk
B. If one ventures from acceptable position
• Persuasive Argument Theory (PAT) reinterpreted
– “Successes” (attempt rate) is ignored
Weighted
– Number in pool = arguments for attempting
comparison
– Prospects of interdiction = arguments against
3/23/2016-18
Is Willingness Function Universal?
• Real-world data:
– Variety of situations and cultures
– Risks to well being versus monetary rewards
• Wide dynamic range: 0.01  PI  1.0
• Simple inverse function
1 / PI*
• Verified by interview comments:
– Interdiction threshold of deterrence W  1.0 at PI  P0
– “Undeterrable” residual W ( PI  1.0)  P0
• Risk decision preceding reward decision
• Limitations
– Only fits extreme cases assuming sufficient rewards
– Fitted P0 rather than function for consequence severity
3/23/2016-19
Implications for Counterterrorism
• Deterrence leverages interdiction by large factors
• Perpetrators ignore interdiction risks below the deterrence
threshold – implies a minimum investment to be effective
• Undeterrable tail of willingness function:
– A contradiction to current risk assessment theories
– An irreducible threat to interdict?
– Understanding why there is a tail may be key to
understanding the psychology of the perpetrators
• If the willingness function is universal:
– Terrorism is an attempt to deter us (our psychology applies)
– Terrorism can be compared to extortion and ethnic cleansing
3/23/2016-20
Backup Slides
• Compensation for trafficking risks
• Unique Feature of Willingness Function
• Deterrence Theory
• Validate Universality
• Terrorism = Deterring Us?
• Peru Data – Traffic and Interdictions
3/23/2016-21
Judge Risk First, Wage Second
PI W  P0 reveals need for “sufficient wage”.
Willingness x Pi
P
SELF
I
0.05
0.10
Willingness x Pi
PI
ASSOCIATE
Baseline risk
0.04
0.03
Wages
x2
0.02
0.01
0.00
0.00
x3
x4
x5
x10
Po
0.06
Wages
0.04
x2
x3
x4
0.02
0.05
0.10
0.15
0.20
Po
0.08
Po
0.25
0.30
Inferred Probability of Interdiction = P
PiI
x5
x10
Po
0.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Inferred Probability of Interdiction = Pi
PI
“SELF” responses require more wage to maximize willingness.
Willingness judgments assumed a sufficient reward:
risk decision precedes reward decision.
3/23/2016-22
Unique Feature of Willingness Function
Willingness
FI  Fraction Interdicte d
W a n
 PI  W  (i a)  (a n)
1.0
 P0 
 PI   
 PI 
 P0  (i0 n)
0.8
Deter
a  a
i   a  PI
a
i   i0
0.6
0.4
They
Succeed
0.2
i0
P0 
n
Interdict
0.0
0.0
0.2
P0
3/23/2016-23
0.4
PI
PI
0.6
0.8
Probability of
Interdiction
1.0
PI  i a
Deterrence Theory
• Joint IDA / academic research on deterrence theory
(Risk perception / decisions, psychophysics, etc.)
• Need for theory
– Explain “undeterrable” effect and develop CT options
– Preventing terrorists from deterring us
– Understanding communication about risk
– Development of MOPs
» Indirect measures, e.g., communication content
» Find more direct observables
3/23/2016-24
Validate Universality
• Verify and calibrate deterrence model for past cases
– Terrorism – Intelligence Community data
– Populations being terrorized – Open and classified sources
– Professions or sports with extreme risk – Actuarial data
– Other?
• Reanalysis of military surrender
– Casualty rate
– Framing perceptions of battle consequences
3/23/2016-25
Terrorism = Deterring Us?
• Terrorism as deterrence of peoples & governments
– Northern Ireland – western society & years of conflict
– Bosnia & Kosovo – ethnic cleansing displacements
– Afghanistan – casualties, intimidation, & displacements
– Colombia – paramilitary forced relocations, FARC
assassinations of police & politicians
– Criminal extortion – force necessary to gain compliance
• Recasting willingness function from terrorist view
– Verify willingness function based on level of violence
– Thresholds for various consequences
3/23/2016-26
Peru Data – Traffic and Interdictions
Verified Interdictions
Detected Trafficker Flights
180
18
160
16
140
SJ III
SJ IV
FD/SD
14
Interdictions
Flights
120
100
Base Prices
12
10
80
8
60
6
40
4
20
2
0
0
Jan-91
Jan-92
Jan-93
Jan-94
Jan-95
Jan-96
Jan-97
Jan-98
NAS = Narcotics Affairs Section of U.S. Embassy Peru
3/23/2016-27