© Paulo Pereira, José Pedro Pontes,1998
Kantians, Selfish and “Nice” agents : some implications for normative public choice
Paulo Trigo Pereira* and José Pedro Pontes
Instituto Superior de Economia e Gestão
Rua Miguel Lúpi 20, 1200 Lisboa, Portugal
Abstract
Public choice theory postulate that agents in a non-market setting are instrumentally rational and
selfish. However, this approach creates some problems related to the raison d’être of the
normative public choice research programme. This paper considers interaction in two different
environments, of instrumental rational agents and moral agents behaving according to kantian
practical reason. The first environment, is a step-level contribution to a pure public good in
repeated single-shot prisoners’ dilemma (PD) games where agents learn the total contribution
after each round. The second is infinitely repeated PD games, where agents are randomly
selected from the same group of individuals. An evolutionary analysis shows that kantians,
although not playing the games, may have an important influence on the evolutionary stability of
the tit-for-tat Nash equilibrium.
JEL Classification: H41, C73
Keywords: Voluntary donations, ethics, public goods, reciprocity
*
Corresponding author. E-mail: [email protected]: Tel: 351.1.3925989; Fax:351.1.3966407. The first
draft of this paper was presented at the 1997 European Public Choice Society Meeting, Prague, Czech
Republic. We would like to thank comments by Charles Blankart, Geoffrey Brennan and João Gata. The
usual proviso apllies.
1. The essential dilemma of normative public choice
Methodological individualism has been very successful in the application to political
science issues, as the development of the public choice research program over the last decades
demonstrates. Today we have a much clearer understanding of the functioning of the political
process, of the importance of different kinds of rules and institutions and on the final outcomes of
this process. We also have a less idealistic assumption about the Homo politicus.
In welfare economics and some strands of political science, government was (and still is)
modelled as pursuing exclusively the “public interest”. According to this approach the government
is considered as a benevolent dictator, which means three distinct things: ”a” suggests an organic
(as opposed to individualistic) approach, “benevolent” that pursues the public interest and
“dictator” that is able to impose its wishes (policies) to a democratic society.
In some sense the public choice approach has assumed that the Homo politicus
(politician, bureaucrat or citizen) is just Homo oeconomicus (rational and selfish) acting in the
public or collective sphere.
The arguments for shifting the behaviour postulates of agents in the political market, from
benevolence to selfishness have been essentially from three different sorts which it is possible to
identify with the positions of Stigler, Buchanan and Schumpeter.
The first type of argument is that selfishness is an accurate description of human
motivation in any context (private or public) and to assume that when selfishness competes with
altruism, in general, selfishness prevails. This argument which will be labelled as descriptive, was
developed among others by Stigler in his Tanner Lectures (1981).1
Another argument defended by the Virginia school (in particular Buchanan) is related to
methodological monism, i.e. the argument that economists should use the same behaviour
postulates when analysing private markets and political markets. If economists have been
relatively successful in analysing private markets with the Homo oeconomicus why should they
shift the behaviour postulates when studying collective choices in a non-market setting? Public
1
“Let me predict the outcome of the systematic and comprehensive testing of behaviour in situations where
self-interest and ethical values with wide verbal allegiance are in conflict. Much of the time, most of the
time in fact, the self-interest theory (as I interpret it on Smithian lines) will win”. Stigler (1981) pg. 176
quoted in A.Sen (1987) pg.17.
2
2
choice scholars have been stressing the need to keep with the same behaviour postulates for
several reasons: (i) the agents behaving in private and political markets are the same (ii)
assuming that the behaviour of political agents is selfish and rational (even if sometimes it is not)
orientates the research in order to devise institutions to protect citizens from the worst outcome
(e.g. tyranny of the majority) (iii) assuming a plurality of motivations (e.g. sometimes benevolence
and other times selfishness) would make positive analysis impossible because no prediction
could be made with some consistency.
There is a different argument, which we might label as an evolutionary argument, that
may support the use of selfishness as the driving motivation in political markets. This argument
endeavours to explain the evolution of selfishness and whether it became or not the dominant
motivation in political markets. However, it is necessary to prove that in a competitive
environment (myopic) selfishness will prevail over reciprocity or even stronger moral beliefs (such
as the kantian categorical imperative).
Selfishness may be supported in an evolutionary perspective if, and only if, it is shown
that “nice” individuals and kantians can be ‘invaded’ by selfish individuals, i.e. if it is shown that
competition exerts a selective process in which politicians driven by a selfish motivation are likely
3
to succeed while the others are likely to drop out of the political scene. This argument, if correct,
is somewhat more robust than the predictive or methodological monism ones since it does not
treat selfishness as a postulate but aims at explaining selfishness.
However, as discussed in this paper, it is not clear that selfishness emerges as the
dominant motivation. Whatever the argument to support the selfishness assumption, there are
several problems emerging from its use, which can be split into three different categories:
prediction problems, persuasion issues and self-reference problems.
Prediction problems have a double nature: failure to make predictions (e.g. what is the
best strategy in a game with multiple Nash equilibria?) and ability to make predictions which are
shown to be wrong. Why do citizens vote if the probability of a vote being decisive in an electoral
outcome is almost nil? Why do political party activists contribute with time and effort for political
campaigns if the likelihood of having a job or other special benefit as a result of successful
2
Buchanan, Tullock, Olson, Downs.
3
political action is irrelevant? Why do some politicians seem to pursue their own conception of the
“public interest”? Why do people abide with the rule of law, if a rational calculus of benefits from
abiding and expected costs from breaking the law would suggest they should do otherwise4?
Experimental economics in the past decades have assembled some empirical evidence
which is consistent with some degree of “altruistic” preferences (Isaac and Walker, 1988;
Andreoni,1993; Ledyard 1995; Sefton and Steinberg, 1996). This research puts into question the
descriptive argument developed by Stigler but leaves untouched Buchanan’s methodological
argument.
The persuasion problem is related with George Stigler’s insight that the economist is
(intentionally or unintentionally) a preacher. What we teach and practice has side effects on
ourselves and students of economics
5
but also in those we can reach with the economic
discourse. In this sense public choice theory, in the measure that is influential, has a persuasive
effect and contributes to selfish behaviour of Homo politicus. The practical consequence of the
exclusive use of the rational and selfish postulates is the “deconstruction” of the democratic
ideal.
6
7
The self-reference problem referred by Witt (1992) among others is the fundamental
dilemma which normative public choice faces today. It can be summarised in the following
question: If selfishness drives political actors what is the point of normative public choice theory in
advising changes in rules and/or institutions if those who are able to implement these changes
could be worst off in the case they were really implemented and therefore would not implement
them? An escape to this dilemma has been tried in a contractarian approach as developed by
Rawls or Buchanan who assume that decision-makers have a great degree of uncertainty on their
future positions in society so that they are not able to identify their self interests and therefore
they can, more or less unanimously, agree on some principles that serve the general or public
interest. Note, however, that fair principles of justice can be developed because the individuals
3
See Schumpeter (1943).
On this, see Hirshleifer ( 1985) among others.
5
It is not by chance that there are more free-riders in students of economics than among students of other
subjects. The idea of the economist as a preacher can be found in Stigler (1982).
6
The relationship between the democratic ideal and reality is well discussed by Norberto Bobbio (1988).
7
This problem was also refered as the “Determinacy Paradox” by Bhagwati. See the whole issue of
Economics and Politics, 1997, vol 9, in particular the paper by O’Flaherty and Bhagwati (1997).
4
4
are unable to materialise their selfishness. The problem with this “original position” as Rawls
labels it or “constitutional stage” as Buchanan and Tullock prefer, is that it is very difficult to put
decision-makers in that framework of decision. As Mueller (1996) points out the body that serves
as a constitutional convention, to draft or amend Constitutions in European and Latin American
countries, is usually constituted by a committee formed by the major political parties of an existing
Parliament and therefore it is predicted that when designing the structure of government, they will
give more weight to the Parliament and to the political parties (particularly the major political
8
parties ) than to other institutions. Even at the Constitutional stage it is difficult to be behind the
“veil of ignorance” which means that the dilemma continues.
9
The above problems have been considered by scholars in different ways. Some just
ignore them which is the “best” way to protect the hard core of a research programme when
empirical evidence refutates predictions from the theory. Others postulate that agents have
altruistic preferences or conclude that “moral” behaviour is a rational strategy (Gauthier, 1986). A
few give importance to social norms even within the rational choice paradigm (e.g. Elster, 1989
and Sugden, 1989).
This paper explores some consequences of interaction when it is postulated
that
different agents have different motivations for action. In section 2, three different types of rules of
conduct (“kantian” “nice” and “selfish”) are discussed in the context of a prisoners’ dilemma
game. Arguments are developed in order to support the postulate that an unknown proportion of
the population are “kantians”. Interaction is considered in two different environments. The first
environment is a step-level contribution to a pure public good in repeated prisoners’ dilemma
(PD) games where agents learn the total contribution after each round (section 3). The second is
a repeated PD game, where agents are randomly selected from the same group of individuals.
An evolutionary analysis shows that kantians, although not playing the games, may have an
important influence on the evolutionary stability of the tit-for-tat Nash equilibrium (section 4).
8
Since Constitutional amendments need a qualified majority of members of Parliament, this is usually
obtained in multiparty systems by a coalition between the two (or three) major parties at the center-left and
centre-right (the neighbourhood of the median voter). Those parties outside the major coalition have no
“voice” concerning Constitutional revision.
9
Another interesting escape to the dilemma is to consider that advice on changes on rules and institutions
should be addressed not to politicians but to scholars and ultimately citizens. However, to reach “rational
ignorant” voters is very doubtful.
5
Finally, section 5 analyses some implications on normative public choice of postulating that some
agents are “kantians”, others “nice” and still others (myopic) selfish.
2. Kantians, Selfish and “Nice” Individuals
The fact that individuals have different rules of conduct in their daily lives is a pervasive
phenomenon. This section constructs three ideal type individuals (kantians, myopic selfish and
“nice”) and clarifies
the respective motivations for action particularly in prisoners’ dilemma
settings. These three ideal type agents will be considered as ontologically different in section 3.
However, section 4 will consider a different context of interaction where there are only two types
of agents: moral agents (kantians) and instrumental rational (IR) agents.
A kantian is an individual who lives according to the ethical categorical imperative: “Act
only according to that maxim by which you can at the same time will that it should become a
universal law”. Therefore actions are not a mean to achieve certain ends (as in instrumental
rationality) but result from the duty to compel with the moral imperative. Rationality for a kantian is
the ability to understand, in a particular situation, what is the maxim that should become an
universal law and which are the actions which result from that maxim.
10
The main motivation
underlying action is good will and not inclination, satisfaction or pleasure. Good will has an
intrinsic value in itself and not because of the intended consequences of this motivation. Actions
resulting from the moral law will often be unpleasant precisely because they are the “obligation”
of a moral imperative and not an instrumental selfish objective. On the other hand, actions that
appear to be in accordance with the moral law are sometimes selfish in nature as can be seen
from an example given by Kant. A dealer who does not overcharge an inexperienced customer
does this in accordance with duty but not from duty. In reality this behaviour is necessary from its
10
Max Weber distinguish two concepts of rationality. Instrumental rationality and rationality towards a
value and this is the interpretation just given in the text. However, it is possible to interpret the categorical
imperative in an instrumental way. Kant does not believe very much in the capacities of instrumental
reason: “Reason is not, however, competent to guide the will safely, with regard to its objects and the
satisfaction of all our needs (which it in part multiplies) and to this end an innate instinct would have led
with far more certainty.” (Singer (ed.) 1994 pg. 125) Thus, it is possible to argue that Kant believes that the
best way to obtain happiness for the individual and welfare for the society is not the use of a rather
imperfect instrumental rationality (within a means-end framework) but that reason is used in a different
context just to understand the moral obligation. The moral duty will function as a self imposed constraint
on behaviour which may lead to pain or pleasure, but in the long run it is expected to increase average well
being.
6
own advantage so that Kant concludes: “Therefore the action was done neither from duty nor
from direct inclination but only for a selfish purpose” (Singer (ed.) 1994 pg. 126). In modern game
theoretic terminology we could adapt this example saying that a tit-for-tat strategy in a repeated
prisoners’ dilemma game is used neither out of a sense of duty or inclination to cooperate but out
of a selfish (enlightened) purpose.
How should kantians behave in the context of the prisoners’ dilemma game? Kantians do
not play games with other individuals because the motivation for action is not to reach the highest
outcome. If the sense of duty leads them to cooperate they cooperate and if not they do not
cooperate. In this paper it will be assumed that the moral duty leads kantians always to cooperate
and that this behaviour holds either when their behaviour is observed or not. Note that it is
precisely because when a kantian cooperates a selfish individual may not cooperate that his
action has moral worth.11
The myopic selfish is the individual who is unable to identify his long run self interests
and which values too much present payoffs with respect to future payoffs. He his what Gauthier
(1986) calls a straightforward maximiser: he defects in single-shot games, and he also defects in
repeated but non observable games.
The reasons why individuals are myopic have to do with bounded rationality coupled with
selfishness. The argument on bounded rationality is well known today and is related to the fact
that individuals, very often, do not behave according to the maximization of an objective function
(even if they want to maximize and not just to “suffice”) because they are unable to acquire the
relevant knowledge and/or unable to make the optimisation calculus.
A selfish (myopic) individual would abide with a rule (e.g. the rule of law) only when the
expected value of violating the rule is lower than the short run benefits of complying with it. He
only considers short run benefits because of the high value attributed to present benefits, and the
difficulty in predicting long run benefits of abiding with the law. This two effects reinforce each
other. The selfish individual does not realise that in the long run a benefit of abiding with the rule
of law is to maintain social order and avoid that society becomes “nasty, brutish and short”. He
11
A similar pattern of moral behaviour has been labeled in the literature as “rational commitment”
(Harsanyi, 1980), “principle of unconditonal commitment” (Sugden,1982) and “everyday kantianism”
7
only understands that possibility, when society is moving very quickly in that direction and is
almost reaching the stage of (under)development or even anarchy.
Finally, the (enlightened) selfish individual, or “nice” individual is the individual who,
although being selfish, has either better information or better ability to process the information
then the myopic selfish individual. The word “nice” was used by Robert Axelrod (1984) to qualify a
group of strategies in repeated prisoners’ dilemma games that share a common characteristic:
the individual is never the first to defect. Although “nice” strategies are unlimited, in the context of
this paper we will consider only two strategies according to the framework of the interaction as
will be clarified below (sections 3 and 4).
3. Voluntary contributions for a pure public good
In this section it is assumed that agents inherit by early age environment, family values
and/or religion, formal education in kindergartens and primary school, a set of values which lead
to a rule of conduct in their daily lives. They are either “kantians”, “nice” or “selfish”. The only
unknown is the proportion of each group within the population.
The environment considered here is interaction in the framework of repeated single-shot
prisoners’ dilemma (PD) game, where individuals decide whether to contribute or not to the
provision of a pure public good but the individual contribution is not observed. Although there are
repeated games, the framework is somewhat similar to the single-shot PD game since individual
behaviour of not cooperating can not be individually punished.
Each individual i=1,2…M may have a fixed and identical contribution ti to the voluntary
i
provision of a pure public good (q )
or may not contribute at all (0). The technology of public
good “production” is the summation technology so that the overall voluntary provision of the
public good is given by:
M
Q = ∑ qi
(1)
i =1
Assuming two individuals, the payoff matrix is given by:
(Elster, 1989). Elster considers “everyday kantianism” as a social norm of cooperation. However, there is
no reason to suppose that it can not be a moral norm.
8
(Insert Figure 1 here)
which is a prisoners’ dilemma when:
t
<q<t
2
(2)
s
The payoff to an individual s who contributes is c :
M
cs = ∑ qi − t
(3)
i =1
and when he does not contribute ds:
M
d = ∑ qi
s
(4)
i≠ s
In each round of the game, individuals decide whether to contribute or not and, at the end
of each round, they all know the overall provision of the public good in that period. This
information is common knowledge in the second round of the game. Therefore, the first round will
1
2
n
produce the quantity of the public good Q , the second round Q and the nth round Q .Individual
behaviour is not observed, thus, it is not possible to punish or reward individuals so that
strategies, such as tit-for-tat, are meaningless in this context. Any punishment in the form of non
cooperation is social in the sense that it is absence of a pure public good contribution.
Let us assume for a start that there are only selfish individuals, i.e. instrumental rational
individuals using a Nash strategic assumption on the behaviour of other individuals. It is a
standard result that the payoff for the individual in not cooperating is higher than when
12
cooperating ( d > c ) for any given number of individuals cooperating. Therefore, no selfish
s
s
individual will contribute and there will be no provision of the public good in any round of the
game ( Q = Q =... = Q =... = 0 ).
1
2
n
Now consider that there are two types of individuals: selfish and “nice”. Nice individuals
behave according to the norm of reciprocity which in the present context of interaction can be
stated as follows: they cooperate initially and if they find out that at least a proportion p of other
individuals also cooperate they keep cooperating. Otherwise they defect.
12
Note that c =
s
∑q
i
i
− t = ∑ q i + (q s − t ) and (q s − t < 0)
i≠s
9
After round one, nice individuals will have information on the level of public good
1
provision Q and, taking into account the amount of public good that would be provided if all the
individuals cooperate (Q*), they can compute the proportion p =
Q1
Q*
of individuals actually
cooperating. Therefore, there are only two possible equilibria under this situation. If the proportion
of nice individuals is superior or equal to p then the level of provision will be given by the sum of
(n)
the contributions from nice individuals Q . On the other hand if it is inferior to p, they will defect
after the first round and the level of provision will collapse to zero. The two equilibria are thus
either Q
(n)
or 0, which are stable if there is no change in the composition of the population.
Finally, assuming there is a proportion k of kantians and n of nice individuals,, the rules
of conduct clarified in the last section lead to the conclusions that kantians will cooperate and
selfish individuals will defect. “Nice” individuals will have a conditional strategy. They will
cooperate if at least a proportion p of individuals in society also cooperate, i.e.:
k+n≥ p
(5)
and they will not cooperate otherwise.
In practice, under the assumptions used, there will be only three levels of public good
provision: Q* when all contribute, Q
(nk)
when only selfish do not contribute and Q
(k)
when only
kantians contribute.
Q* is the Pareto efficient level of provision of the public good, but will never be achieved
given the behaviour of selfish individuals. The equilibrium level of the public good will be either
Q
(nk)
or Q
(k)
depending on the proportion of non selfish individuals in the population and the critical
level p necessary for “nice” individuals to cooperate.
Some conclusions can already be made. Kantians are always “exploited”. They assure a
minimum level of provision of the public good. Their contribution is also important because they
increase the likelihood that nice individuals will cooperate.
In this section it was postulated that motivations underlying individual behaviour are fixed
within each of the three groups so that changes in the equilibrium level of public good provision
can only occur either as a consequence of migration or different rates of reproduction of the three
groups. If there is immigration of “selfish” individuals their proportion among the population
10
increases and may become higher than the accepted level of non-cooperative agents by “nice”
individuals (1-p). In this case there will be a shift from Q
(nk)
(k)
to Q .
Another way to change the equilibrium level of public good provision is through diferent
rates of reproduction. The argument developed by Bergstrom and Stark (1993) that “altruists”
(those who cooperate in PD games) reproduce faster does not seem to hold here because we
assume global interaction in the provision of a pure public good while they assume that
descendants of “altruists” only interact with each other so that they receive higher payoffs and
reproduce faster. There is no a priori reason to believe that the rate of reproduction of “kantians”
or “nice” agents is superior to the “selfish” agents since there are two contradictory effects. The
darwinistic effect will lead selfish to reproduce faster (since they receive the highest payoffs in this
game) on the other hand the cultural effect will lead selfish to reproduce slower (because they are
also selfish in what concerns procriation).
From a normative point of view, the presence of kantians leads always to a lesser
suboptimality in the provision of the public good. However, this means that punishment to
defectors is not so great as in the case where there are only selfish and nice individuals. This
might be important if we consider, instead of fixed motivations (as in this section), learning in an
evolutionary framework as considered in the next section.
4. Repeated Prisoners’ Dilemma games: instrumental rational and kantians
In this section we consider only two types of individuals, playing repeated PD games,
which are distinguished according to rationality. There are kantians and instrumental rational (IR)
agents, but now IR agents can choose among three main strategies: to be “nice” and adopt tit-fortat (N), always cooperate (C) and always defect (D). The main difference with respect to the
previous section is that now there is not a unique public good, but players are randomly selected
from a population and play infinitely repeated 2x2 PD games.
First (figure 2), we present the evolutionary game theory predictions, assuming that all
individuals are instrumentally rational and adopt either a “nice” or a “selfish” strategy. Secondly
(figure 3), we consider the existence also of kantians and analyse the effects on equilibrium
selection.
11
(Insert Figure 2 about here)
This figure shows the payoffs associated with different pairs of strategies assuming that the
behaviour can be observed and agents can punish others from no cooperation. Note first that cell
I (tit-for-tat playing against tit-for-tat) is a Nash equilibrium provided that
2q − t
> q which is the
1− r
case if future benefits are not heavily discounted at the discount rate r. Playing defection against
tit-for-tat leads then to a lower payoff, since defectors only payoff is the benefits (q) they can get
from meeting a nice agent in one round. In future encounters nice agents will not cooperate
assuming they memorize who was this previous defector.The other Nash equilibrium is mutual
defection. If this strategy is adopted no individual can unilaterally increase his payoffs by adopting
a different strategy. Therefore, although cell I Pareto dominates cell IV, there is no presumption
that being mutually nice will emerge as the selected equilibrium. In the presence of a coordination
game any of the equilibria can emerge and the problem is precisely to know which one is likely to
emerge.
There is also a Nash equilibrium in mixed strategies (NEMS) where players randomize
the strategies used with a probability n' of using a nice strategy which is given by:13
n' =
(1 − r )( t − q )
r ( 2q − t )
(6)
Note, however that this is not a stable strategy since if n > n' the game develops to the pure
Nash equilibrium of both players using the tit-for-tat strategy and if n < n' the expected value of
defecting is higher than tit-for-tat and therefore the game will converge to the pure Nash
equilibrium of always defecting.
Consider now a different type of behaviour - always cooperate. In order to understand the
new situation it is important to establish the difference between the ‘always cooperate’ strategic
behaviour adopted by an IR agent, and the ‘always cooperate’ behaviour adopted by a kantian.
13
The value n ’ is the one that solves the identity:
E ( N | n) = E ( D| n) ⇔
2q − t
. n + (q − t )(1 − n) = q. n , where E ( N | n ) and E ( D| n ) mean the
1− r
expected payoffs of being “nice” and “selfish” (respectively), when there is a proportion n of individuals
adopting a “nice” strategy.
12
An IR may adopt the C strategy if he believes it yields higher payoffs. A kantian adopts the
always cooperate behaviour even when she receives lower payoffs.
First, let us assume that all agents are IR, and that they can adopt three main strategies:
nice, selfish or cooperate. The payoff structure is given by figure 3 and there are some standard
results in the literature which should be considered at this stage. First, there are again two pure
Nash equilibria in playing N/N (if
2q − t
> q ) and D/D. Second, playing always cooperate is not
1− r
rational if there is at least a defector among the population since the expected payoff of a “nice”
agent would be higher than the expected payoff of a co-operator.
(Insert Figure 3 about here)
14
Third, and more important, tit-fot-tat is not an evolutionary stable strategy (ESS) , immune to
invasion by agents playing different strategies, while ‘always defect’ is an ESS. The reason why
tit-for-tat is not an ESS is intuitive. As shown in figure 3 the payoffs of nice agents and agents that
always cooperate are the same. This means that a population of nice agents can be ‘invaded’ by
a ‘always cooperate’ strategy in the sense that individuals that initially adhere to the tit-for-tat
strategy in order to enhance cooperation can adopt a ‘always cooperate’ strategy. There is,
however, an important difference between being “nice” and ‘always cooperate’ which is that the
former is immune to selfish defectors while the latter is not. The important point to note is that to
be nice is not an ESS because nice individuals can be ‘invaded’ by cooperators who, on the other
hand, can be invaded by defectors. This transitivity explains how cooperation among nice agents
can breakdown.
15
14
On evolutionary stable strategies see Maynard Smith (1982) and Sugden (1989) which defines an ESS
and a convention as follows. “An evolutionary stable strategy (ESS) is a pattern of behaviour such that, if it
is generally followed in the population, any small number of people who deviate from it will do less well
than the others. This, then, is a state of rest in the evolutionary process. I shall define a convention as any
ESS in a game that has two or more ESS’s. The idea here is that a convention is one of two or more rules of
behaviour, any one of which, once established, would be self-enforcing” (pg. 91).
15
Sugden (1986) has shown that although tit-for-tat is not an ESS, a strategy very similar to tit-for-tat,
where small mistakes are allowed for, is an ESS. Therefore, we have again a coordination game, now with
two ESS (being mutually nice with mistakes or always defect) and the remaining problem which is to
predict which convention will be adopted. There is no reason to suppose that the inefficient convention
(always defect) will not be adopted just because it is inefficient. As Sugden (1989) argues conventions are
not chosen, they evolve and an inefficient convention may become more prominent.
13
Let us assume now that we have two different types of individuals. Instrumental rational
(IR) individuals who may choose among a tit-for-tat and a ‘always defect’ strategy and kantians
who adopt the categorical imperative to always cooperate.
As clarified in section 2 kantians do not play games, do not adopt strategies because
they are not IR agents. They behave from duty and they just cooperate so that they are, by
definition, immune to invasion. The payoff matrix to analyse this situation is the same as in figure
3 but the main difference is in reading the matrix. Always cooperate is not a strategy but a
behaviour resulting from moral duty.
This means that a small hard core of kantians will foster cooperation with IR agents who
might adopt a tit-for-tat strategy. It is possible to prove that, if the proportion of kantians among
the population is not too high, IR agents playing “nice” is an evolutionary stable strategy. In fact
we only need to guarantee that the expected payoff of being “nice” when there are no defectors,
E ( N |0, n ) , is strictly greater than the expected payoff of a “mutant” which considers to adopt a
“always defect” strategy in the same situation E ( D|0, n ) i.e.:
E ( N |( 0, n) > E ( D|(0, n) ⇔
2q − t
q
>
(1 − n) + q . n
1− r
1− r
(7)
Solving with respect to n, yields:
n>
t−q
≡ n*
qr
(8)
Therefore, n * is the minimum number of “nice” individuals ( 1 − n * , the maximum number of
kantians) within a mixed population with no defectors, in order that being nice is an ESS.
The idea that there is a maximum of kantians to guarantee the evolutionary stability of the
cooperative strategy is intuitive. If there are too many, being a defector becomes very atractive
since the expected payoff is higher than being “nice”.
On the other hand, it is easy to verify that the presence of kantians also reinforces the
evolutionary stability of the always defect strategy because the expected payoff of always defect
without kantians is nil, while with a proporton k of kantians is positive ( k. q / 1− r ).
14
Therefore, the presence of kantians among the population seems to have two
contradictory effects in what cooperation concerns since it reinforces both the Nash equilibrium
of mutual “nice” agents and mutual defection.
To sum up, the tit-for-tat Nash equilibrium in a population composed only of IR individuals
choosing among three strategies (N, C, D) is not an ESS. However, it may become an
evolutionary stable strategy
16
in a mixed population of IR and kantians. The presence of an
appropriate number of kantians (not too great) makes possible that playing tit-for-tat can now be a
convention which, by definition, is evolutionary stable.
5. Avoiding error type I and error type II
Welfare economists, commit the fallacy of considering governments and political agents
pursuing exclusively the “public interest” (error type I). If taken to its extreme, a corollary of this
position would be that any constraints on the behaviour of governments or political actors would
be unnecessary. This is a position that few political scientists would subscribe.
Most public choice scholars, on the other hand, model political behaviour as driven
exclusively by private interests (error type II). Taking this postulate to its full consequences this is
tantamount to say that there is no raison d´être of the normative public choice research
programme. Normative public choice scholars would be preaching in the desert if decisionmakers were exclusively selfish because they would not listen to them. This is what we have
labelled, in section 1, the essential dilemma of normative public choice.
The research programme on Constitutional political economy (CPE) developed by
Buchanan and others seems to be an attempt to deal with the unpleasant consequences of error
type II. However, its validity is based on the presumption that the “veil of ignorance” or the “veil of
uncertainty” is high (so that selfish agents can not identify the meaning of selfishness). In the
domain where this is the case, CPE normative results are likely to be persuasive. However, when
the degree of uncertainty is low CPE is embodied also with the “essential” dilemma.
16
A Nash equilibrium is a necessary but not sufficient condition to be evolutionary stable.
15
If the different rules of conduct were fixed and given, the presence of kantians who were
assumed to cooperate in PD games would be always positive according to the efficiency
criterium. If a subset of individuals (IR agents) choose their strategies, the presence of a (not too
great) number of kantians, reinforces both conventions: always cooperate or always defect.
Which one would be adopted is uncertain but our presumption is that the design of appropriate
rules and institutions may favour one or the other.
Assuming, as we do, that the motivations of politicians are diverse, directs the normative
research agenda to the following problem : “How to devise rules and institutions so that politicians
who want to serve the ‘public interest’ may survive?”. This is the problem addressed by Buchanan
17
(1993) but which has no easy answer . It deserves more scrutiny if we want to solve the
normative political economists’ essential dilemma.
17
Note that Buchanan assumes implicitly, that there are some politicians who want to serve the public
interest. This is somewhat different from early public choice writings. The essential merit of Buchanan´s
paper (1993) is to have introduced the problem. However, the research towards a solution depends on the
particular institutional environment and therefore has only started.
16
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st
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18
Player B
Player
A
C
D
C
D
(2q − t ,2q − t )
(q − t , q )
(q , q − t )
(0,0)
Figure 1 The prisoners’ dilemma
19
Player B
Nice (TfT)
Player
A
Nice
(TfT)
Defect
(
Defect
2q − t 2q − t ( q − t , q )
,
)
1− r 1− r
(q , q − t )
(0,0)
Figure 2 Payoff matrix of repeated games with two strategies (tit-for-tat and ‘always
defect’)
20
Player B
Nice (TfT)
Nice
(TfT)
Player
A
K/C
Defect
2q − t 2q − t
,
)
1− r 1− r
2q − t 2q − t
(
,
)
1− r 1− r
(
(q , q − t )
K/C
2q − t 2q − t
,
)
1− r 1− r
2q − t 2q − t
(
,
)
1− r 1− r
(
(
q q−t
,
)
1− r 1− r
Defect
(q − t , q )
(
q−t q
,
)
1− r 1− r
(0,0)
Figure 3 Payoff matrix of repeated games and three strategies (tit-for-tat, ‘always
cooperate’ and ‘always defect’)
21