Game Theory: Why Death Penalty is not the best punishment for rape cases
While there is a huge outcry demanding death penalty for rape
cases, regret analysis helps to explain why it is not the best punishment for
such crimes.
Naturally, losing one’s own life is costlier than life
imprisonment for a person. Therefore the pay-off for a criminal will be higher
if sentenced to death as compared to being jailed for life. For the purpose of
calculations, let us assume the following.
Punishment
|
Payoff
|
Hanged till death
|
10
|
Jailed for life
|
7
|
If a
criminal kills the rape victim, chances of his being caught are reduced because
the victim will not survive to identify him. Therefore naturally the
probability of the criminal being caught is less if he kills the victim as
opposed to if he does not kill her. For the purpose of calculations, let us
assume the following.
Perceived probability of
being caught
|
||
A
|
||
Criminal's actions
|
Kill
|
0.75
|
Do not kill
|
1
|
(Perceived probability of not being caught) = 1 – (perceived
probability of being caught)
Therefore
Perceived probability of
not being caught
|
||
B = 1-A
|
||
Criminal's actions
|
Kill
|
0.25
|
Do not kill
|
0
|
Regret Analysis for the criminal will therefore will be as
per the following table
Table 1: Regret analysis for rapist.
Death Penalty
|
Life imprisonment
|
||||||||
Perceived probability of
being caught
|
Perceived probability of
not being caught
|
Pay-off if caught
|
Pay off it not caught
|
Total Pay-off
|
Payoff if caught
|
Pay off it not caught
|
Total Pay-off
|
||
A
|
B = 1-A
|
C
|
D
|
E=A*C+B*D
|
F
|
G
|
H=A*F+B*G
|
||
Criminal's actions
|
Kill
|
0.75
|
0.25
|
10
|
0
|
7.5
|
10
|
0
|
7.5
|
Do not kill
|
1
|
0
|
10
|
0
|
10
|
7
|
0
|
7
|
|
If death is
the punishment for rape, then the criminal will have to pay less (7.5 as
compared to 10) if he chooses to kill the girl. Therefore he will kill the
girl.
If the
punishment for rape is life imprisonment, the payoff for the criminal will be less
if lets the girl survive (7 as compared to 7.5 if he kills the girl) therefore
he will not kill the girl. Thus we see that death penalty is not the best
punishment for the crime.
Relationship
between death penalty and efficiency of police at catching the criminal
If
perceived probability of being caught
if the criminal kills the girl
|
<
|
Payoff for being hanged
|
perceived probability of being caught
if the criminal does not kill the girl
|
payoff for being jailed for life
|
then the
total payoff for the criminal will be lower if he kills the girl than if he
lets the girl survive. Therefore in this case he will choose to kill the girl
and death penalty in such a situation will be a better punishment.
Death Penalty
|
Life imprisonment
|
||||||||
Perceived probability of
being caught
|
Perceived probability of
not being caught
|
Pay-off if caught
|
Pay off it not caught
|
Total Pay-off
|
Payoff if caught
|
Pay off it not caught
|
Total Pay-off
|
||
A
|
B = 1-A
|
C
|
D
|
E=A*C+B*D
|
F
|
G
|
H=A*F+B*G
|
||
Criminal's actions
|
Kill
|
0.6
|
0.4
|
10
|
0
|
6
|
10
|
0
|
6
|
Do not kill
|
1
|
0
|
10
|
0
|
10
|
7
|
0
|
7
|
|
This means that if the police is more efficient at catching
rapists than murderers, then the rapist will have a tendency to kill the girl.
