Two people have been arrested for a serious crime and since been separated such that they cannot communicate. The prosecutor provides an ultimatum to both of them individually:
You may choose to either
confess or remain silent.
If you both choose to remain
silent, rest assured that we have enough evidence to convict you both of a
crime, albeit one which is less serious and attracts a lesser sentence than
that for which you have been arrested.
If you both confess, you
will both be charged with the crime for which you have been arrested, I will
reward you both with a reduction in your sentences in recognition of that.
If you confess while the
other remains silent, I will set you free.
I will use your evidence to ensure that the other will serve the maximum
sentence possible.
This
scenario clearly has ethical implications, but which ethical principle has
precedence is not so clear. There are
also a number of uncertainties which I have glossed over which makes
determining precedence extremely difficult.
Are the two people long-term friends or strangers? Did they actually commit the crime? Is the prosecutor reliable, that is will the
prosecutor keep her word?
What
is the extent of the difference between the punishments? Is the death sentence involved? Are they part of an organisation which will
punish a confessor on release? What are
the ethical stances of the prisoners – is lying worse than abandoning a
colleague or vice versa?
It
is possible that neither prisoner will be aware whether the other has been
given this ultimatum yet, or indeed ever will be. From that perspective, it can be argued that
the single prisoner may only be playing a game with the prosecutor, not the
other prisoner. Otherwise, in reality,
the prisoner is playing two different games simultaneously – one with the other
prisoner and one with the prosecutor.
In
the standard treatment of the prisoners’ dilemma the following is assumed:
·
Both prisoners act rationally, based on
nothing more than the information provided.
·
Both prisoners consider only the best
possible (short term) outcome for themselves without fear of ethical
constraints or retribution after release.
·
Both prisoners may consider the other as
little more than an abstraction, so no consideration as to the welfare of the
other is necessary. Both are aware that
the other was also taken into custody.
·
The crime in question is sufficiently mundane
that no lasting stigma is attached to admitting to it (at least from the
perspective of the prisoners).
·
The rules of the game are fair and thus the
prosecutor is not lying, provides both prisoners with the same dilemma and will
keep her word.
Furthermore,
the scale of punishments is such that the punishment accorded to a betrayed
prisoner, one who remains silent while the other confesses, is worse than any
punishments meted out to both. We’ll
call this the “Severe Punishment” and arbitrarily set it to 20 years in
prison. The punishment which would be
shared by both prisoners is significantly lighter if both stay silent than if
both confess. We’ll call the former the
“Minimum Punishment” (5 years in prison) and the latter the “Medium Punishment”
(10 years in prison). The reward for
unilateral confession, freedom and immunity from prosecution or “No
Punishment”, is preferable to all other outcomes. (Variations of these scales of punishment are
also studied by games theorists, but we shall not delve quite so deeply.)
The
problem facing each prisoner is that the reward or punishment to be accorded is
not entirely of his own making. Consider
the decision making process only one prisoner, calling him Larry for
convenience. Larry has two choices, to
stay silent or to confess. Larry knows
that his partner in crime (Wally) has the same two choices, but he doesn’t know
for sure what Wally will do and he knows that Wally doesn’t know what he, Larry
will do.
If
Larry chooses to stay silent, two outcomes are possible: Wally stays silent and
they both receive the Minimum Punishment of 5 years or Wally confesses and is
released while Larry receives the Severe Punishment of 20 years.
If
Larry chooses to confess, two outcomes are possible: Wally stays silent and
receives the Severe Punishment of 20 years while Larry is released or Wally
confesses and both receive the Medium Punishment of 10 years.
What
should Larry do?
Because
Wally and Larry’s decisions are effectively simultaneous, Larry can consider
his predicament from two perspectives: if Larry makes a certain decision, what
will be the potential consequences of Wally’s decision? and, if Wally makes a
certain decision, what options are open to Larry?
The
first consideration can be illustrated thus:
Either
Larry
decides to confess
|
|
Wally
decides to confess
|
10
years in jail for both
|
Wally
decides to remain silent
|
Larry
goes free
|
Wally
spends 20 years in jail
|
or
Larry
decides to remain silent
|
|
Wally
decides to confess
|
Larry
spends 20 years in jail
|
Wally
goes free
|
|
Wally
decides to remain silent
|
5
years in jail for both
|
The
second consideration can be illustrated thus:
Either
Wally
confesses
|
|
Larry
decides to confess
|
10
years in jail for both
|
Larry
decides to remain silent
|
Wally
goes free
|
Larry
spends 20 years in jail
|
or
Wally
remains silent
|
|
Larry
decides to confess
|
Wally
spends 20 years in jail
|
Larry
goes free
|
|
Larry
decides to remain silent
|
5
years in jail for both
|
The distinction
between to the two modes of decision making is that the first is predictive (in
which Larry makes a decision and hopes that Wally makes a particular decision)
whereas the latter is reactive (one in which Wally makes or is assumed to have
made a decision and Larry must ensure that his decision obtains the best
result).
Looking
at the predictive consideration:
·
If Larry decides to confess, he stands to
gain freedom at the expense of Wally or to spend 10 years in jail, along with
Wally. Clearly in this instance, Larry
will hope that Wally remains silent.
·
If Larry decides to stay silent, he might
only spend only 5 years in jail together with Wally. However, if Wally was going to stay silent
anyway, then Larry has made a suboptimal decision which would have given him
freedom. Additionally, by remaining
silent, Larry has exposed himself to the risk of spending 20 years in jail.
In
terms of prediction, it appears that Larry’s best option is to confess.
Looking
at the reactive consideration:
·
If Wally confesses, then Larry can either
confess and only spend 10 years in jail along with Wally, or stay silent and
allow Wally to walk free while he himself spends 20 years in jail.
·
If Wally stays silent on the other hand, then
Larry can either confess and be released or stay silent and spend 5 years in
jail along with Wally.
In
terms of reaction, the benefits accruing from confession and irrationality of
staying silent are even starker.
The
“dilemma” revolves around the fact that if the two are going to spend time in
jail together (which seems the likely outcome given that both are rational
agents and both will rationally decide to confess) then it is rational that
they collectively strive to spend as little time in jail as possible – which
they could accomplish by remaining silent.
Therefore, it’s rational to confess and it’s rational to remain silent.
It
is tempting to consider this scenario in terms of ethics, both from the
perspective of allowing ethics to sway the decision making of the prisoners and
also by analysing the scenario to see if a moral structure could be derived
from the hypothetical dilemma.
If
ethics were allowed to sway the decision making of the prisoners, it would be
necessary to decide which standard ethical principle has precedence – “do not
lie” or “do not abandon/betray your colleagues”? To determine this we need to know more about
the prisoners. For instance, we don’t
know whether the prisoners actually committed the crime of which they are
accused. While we stated that the game
is ‘fair’ it was not made clear that the prisoners were guilty or not.
If
the prisoners are career criminals, then it is probable that they will value
unity over honesty. If the prisoners are
innocent (and more, do not know the other prisoner at all), it is probable that
unity will not figure highly. This does
not bode well for a concept of universal morality, at least as derived from the
prisoners’ dilemma, because the morality to be applied is clearly dependent on
the situation.
What
we do see, however, is that the morality of unity does have a benefit in this
situation. It is generally considered
moral to extend and honour trust. In
this instance, bilateral morality will benefit both prisoners. Many natural situations are analogous to the
prisoners’ dilemma and the morality of unity does seem to come into play in
these situations.
An
example is when two ancient warriors first meet, and choose neither to shield
themselves nor to raise their weapons against the other. By extending trust and honouring that
(apparent) trust, each the warriors risk death if the other plans
betrayal. What they avoid is the need to
fight immediately and risk being wounded in an unnecessary battle while
simultaneously standing to gain by potentially making an ally.
In
the prisoners’ dilemma we can see that the morality of unity can reap the
benefits of co-operation in a situation in which choosing not to co-operate
would result in a worse outcome for both.
Is this sufficient basis for a universal morality?
Let
us briefly consider a couple of issues.
First,
who are the prisoners playing against?
Is Larry playing against Wally, or against the prosecutor (potentially
together with Wally)? When the scenario
is framed, it is stated that the prosecutor is ‘fair’ but it is plain that she
may benefit from the situation, or potentially fail to benefit, depending on
the outcome. If she obtains two
confessions, that could be considered a win, possibly her best outcome. However, she may consider one major
conviction with a full sentence served to be preferable – we can reason that
this is quite likely otherwise she wouldn’t make such a generous offer. Her worst outcome is to have both prisoners
remain silent, thus obtaining only two nominal convictions.
If
Larry and Wally confess and remain silent with equal probability (randomly,
rather than rationally), the prosecutor has a 75% chance of getting a
favourable outcome – either two confessions or one major conviction. If Larry and Wally are independent rational
actors playing against each other, then both will almost certainly choose to
confess, a favourable outcome for the prosecutor. It is only when they choose to act ethically
(applying the morality of unity) that the prosecutor will lose.
Therefore,
exactly who it is that Larry plays against should be a vital part of his
considerations. Larry can only win
against the prosecutor by staying silent and hoping that Wally does so
too. If Larry chooses to play against
Wally though, then he should rationally choose to confess. If Wally confesses then a draw results
between the prisoners and the prosecutor secures a minor win. If Wally chooses to play against the “wrong”
person (that is against the prosecutor, and not Larry), then he will stay
silent and Larry will win by walking free while Wally spends the next twenty
years in jail – and the prosecutor secures a major win.
Second,
we should consider other variants of the prisoners’ dilemma. As the dilemma has been framed, it is a
single event and effectively synchronous.
Most real-world situations are neither isolated events nor entirely
synchronous. There are variations of the
prisoners’ dilemma within the discipline of game theory in which this is taken
into account.
If
the prisoners’ dilemma is asynchronous, the decision making processes of each
prisoner will match with Larry’s hypothetical considerations above. The prisoner who makes the first move uses
the predictive consideration while the other uses the reactive. Both prisoners will therefore rationally
choose to confess, unless the first works on the assumption that they are
playing against the prosecutor and not each other. The second prisoner then has the opportunity
to betray the other or to co-operate in order to beat the prosecutor by staying
silent.
If
the specific form of the prisoners’ dilemma is a series of dilemmas, then the
prisoners can look at the problem in a number of different ways. If both prisoners have a tacit agreement that
they are playing against the prosecutor, then they will consistently choose to
stay silent. However, if at least one
prisoner decides that he is playing against the other prisoner then other
strategies arise.
Let
us say that one prisoner is a superiority seeker, who wants no more than to
prevail over a player who plays the game under the same conditions as
himself. To prevail in a recurring
prisoners’ dilemma, a superiority seeker must win at least one more round than
the other prisoner. This can be achieved
either by confessing in the first and all subsequent rounds and hoping that his
opponent remains silent at least once or by staying silent in the first round,
thereby potentially setting up a trust relationship which later be abused for
profit.
The
first option seems to be clearly more rational as the superiority seeker stands
to do no more than come equal if the other prisoner follows the same strategy
and will win otherwise. The second
option is risky with no clear benefit because by acting to set up a situation
of trust, all the superiority seeker does is make it possible for his opponent
to be the betrayer, rather than the betrayed.
The strategy could also fail in the very first round, if the opponent
chooses to repeatedly confess.
It
therefore seems to make little difference whether a prisoners’ dilemma is a
singular event or recurring, or synchronous or asynchronous. Who a player considers to be the opponent
seems to remain the single most important determining factor.