Multi-candidate Political Competition and the Industrial Organization of Politics 

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A static model of child rearing

In this section, we present a canonical model of cognitive development through intergene-rational rearing interactions. We define cognition by an Aumann structure (Fagin, Halpern, Moses, and Vardi (2004, p. 37)) enriched by reasoning abilities and action rules contingent on this structure. As defined in Fagin, Halpern, Moses, and Vardi (2004, p. 37), an Aumann structure is a tuple (S, P1, . . . , Pm) where S is the set of states of the world and Pi is a partition of S for some agent i. The cognition of an agent corresponds to two things. First, a representation of the world by a finite set of possible states of the world. Any state of the world is empirical in the sense that any wki can be defined as “the state of the world where action a(wki) must be performed”. We assume the set of possible actions A to be convex and bounded. Second, the cognition of an agent implies reasoning. Empirical frequencies for instance can be built upon the knowledge structure and the varied experiences so as to make Bayesian reasoning feasible.
The preceding formalization encompasses the definition of cognition of the American Psychological Association Dictionary, “all forms of knowing and awareness such as perceiving, conceiving, remembering, reasoning, judging, imagining, and problem solving.” Awareness, perception, conception and memory subsume to a subjective structure of knowledge while reasoning, judging and problem solving relate to the ability to link the subjective states and act contingently. As a simple illustration, a state in the knowledge structure can be “it is raining ». Two agents can differ in their evaluation of the state, as well as in their action upon having the same knowledge. In that example, rain can be associated with a state “the Gods are angry » for one (which could also be associated with other meteorological events) and alternatively with “this is a meteorological event called rain » for another for instance. Those two events will most certainly trigger different behaviors. Knowledge structures are subjective and give the prism of agents’ perception.

The child-rearing interaction

Consider now a parent engaging in early inter-generational rearing. I will use the pronouns she for the parent and he for the child. For the parent, there are n· states of the world that are worth being transmitted. We can think of those states as corresponding to the transmission of language and standard norms of behavior for example. Thus, the set of states of the world that are worth being transmitted is a subset of the knowledge structure of the parent, Ω· = {Ê1, . . . , Ên· } ™ Ω with Ω the knowledge structure of the parent. Instead of making specific assumptions on the structure of reasoning, I will simply assume that for the parent, for each state Êk· that is worth being transmitted, there exists only one best possible action for the child a(Êk· ).
Consistently with our previous discussion, through rearing, the child has the ability to distinguish experiences and build subjective concepts. Furthermore, the child knows that his caregiver as well distinguishes subjective states of his own, given that he apprehends her as an intentional being. Thus, we can formalize a rearing interaction between the caregiver and the child as a principal agent model where the parent seeks to mold the cognition of her child.
Before turning to the transmission of Ω· , we highlight the underpinnings of the transmission of a single state Êk œ Ω· . When the state of the world is wk, the parent believes that the correct action to perform aú is distributed according to a normal distribution centered on a(wk) with precision sp. The ability to know that when the state is wk the correct action is normally distributed with mean a(wk) could be the result of the parent’s own building of state recognition during her childhood for example. Similarly, we assume that a priori, the child believes that the correct way to act in state wk is normally distributed with mean a(wk) and precision f(e). Contrary to the parent however, the child does not know a(wk). He has a prior on a(wk) that is normally distributed with mean a0 and precision s0. The main novelty of our framework is to consider f(e), the precision of the child’s own beliefs on the correct action, to be endogenous to his recognition effort e invested during the rearing interaction. In other words, the precision of the child’s recognition of the best possible action – and thus of the state of the world – depends on his own investments during the rearing interaction.

The dynamics of child rearing and child develop-ment

We have been concerned so far with the transmission of a single state of the world w from a parent to her child. Doing so allowed us to introduce a simple mechanism of inter-generational transmission and to study how the parent’s characteristics (e.g. income and various preference parameters) affect her degree of authoritarianism as well as her pecuniary investments in child rearing. However, such a static theory can not answer for the emergence of behavioral norms through early rearing interactions. In this section, we intend to fill this gap by studying the formation of a cognitive capital through repeated child rearing interactions aiming at transmitting norms. Definition 1. Any agent that possesses a behavioral norm A recognizes a series of states of the world ΩA = {w1A, . . . , wpA } where norm A prescribes a specific collection of behaviors a(ΩA) = {a(w1A), . . . , a(wpA)}. Any norm has an internal consistency, i.e. there exists a common perception of the world associated with the states in ΩA.
A behavioral norm is associated with both a perception of different states of the world and contingent action rules (i.e. a(ΩA)). Take the example of patience. This norm – broadly defined – relates to the delaying a present activities, say consumption, given that one foresees the long-term benefits of the delay. Foreseeing the future stream of benefits is the perception of the world associated with the norm patience. This perception applies for a plethora of situations (i.e. states of the world). There exists empirical evidence that shows that few norms guide human behaviors. Almlund, Duckworth, Heckman, and Kautz (2011) for instance show that stable character skills exist and are predictive of many behaviors. Similarly, analyses of the World Value Surveys, e.g. Inglehart and Welzel (2010), reveal two major dimensions of cross-cultural variations in beliefs and values, (i) a traditional versus secular-rational dimension and (ii) a survival versus self-expression dimension. 10 Besides patience, important behavioral norms that are taught early in life include self-control, trust, attentiveness or self-esteem (Heckman and Kautz (2013)).
In order to explain how child rearing creates endogenous preferences, we rely on a powerful idea in the literature that can be traced back at least to Gary S. Becker and co-authors. It says that preferences can be understood as a capital in the standard sense used in the economic literature and that the agents build progressively a taste for this capital. In their study of addictive behaviors for instance, Becker and Murphy (1988) writes “[. . .] smoking of cigarettes, drinking of alcohol, injection of heroin, or close contact with some persons over an appreciable period of time, often increases the desire (creates a craving) for these goods or persons, and thereby cause their consumption to grow over time”. Similarly, one tends to appreciate being patient as one acts in a way that is consistent with this norm.

Child maltreatment and toxic stress as impediments to chil-dren cognitive development

The environments children grow up in shape how the brain develops. One powerful influence on brain development that we can not approach with the theory set in the previous section is children toxic stress. Toxic stress refers to events that produce strong, frequent, or prolonged activation of the body’s stress management system that can physically damage brain architecture and lead to the underdevelopment of certain parts of the brain that are necessary for emotional control, memory and learning and problem-solving (National Scientific Council on the Developing Child (2005a), Shonkoff, Garner, Siegel, Dobbins, Earls, Garner, McGuinn, Pascoe, and Wood (2011)). A poor response to stress in early childhood has long lasting consequences since it affects brain development (Shonkoff, Garner, Siegel, Dobbins, Earls, Garner, McGuinn, Pascoe, and Wood (2011)). In their report on the subject, Shonkoff, Garner, Siegel, Dobbins, Earls, Garner, McGuinn, Pascoe, and Wood (2011) write “many adult diseases should be viewed as developmental disorders that begin early in life and that persistent health disparities associated with poverty, discrimination, or maltreatment could A healthy nurturing environment can reduce the amount of stress children face in their early years as well as help them to cope with it. The quality of the interactions between children and caregivers is then critical in buffering children against toxic stress (National Scientific Council on the Developing Child (2004)). For instance, children whose relationships are insecure or disorganized demonstrate higher stress hormone levels and the presence of sensitive and responsive caregiver can prevent elevations in cortisol among toddlers, even in children who tend to be temporamentally fearful or anxious (National Scientific Council on the Developing Child (2005a)).
Child maltreatment and other forms of toxic stress such as domestic violence or disasters ne-gatively affect brain development. One typical emotional functioning induced by maltreatment is the Persistent Fear Response (National Scientific Council on the Developing Child (2005a)). Children with a persistent fear response may lose their ability to differentiate between danger and safety, and they may identify a threat in a nonthreatening situation. In turn, this may be the foundation of future anxiety disorders such as PTSD (National Scientific Council on the Developing Child (2005b)). Other behavior and emotional malfunctioning associated with child maltreatment and early stress include hyperarousal, increased internalizing symptoms, diminished executive functioning, delayed developmental milestones, weakened response to positive feedback and complicated social interactions (National Scientific Council on the Developing Child (2005b)).
In order to see how maltreatment and toxic stress affect the development of cognitive abilities, we extend the model of the previous section and assume that the parent chooses three actions during the rearing interaction. She still chooses the pecuniary reward ”t and the level of permissiveness ‘t, but can as well impose a cost pt on her child when he does not behave as expected. This cost models the corporal punishments and the other maltreatments that the parent can impose on her child. We assume that it must be that pt is such that the vc(et) = ”t ⁄≠‘t Ú 2fit exp(≠2 stu2)du ≠ c(et) ≠ pt(1 ≠ ⁄≠‘t Ú 2fit exp(≠2 stu2)du) + u(et, St≠1), ‘t 1 ‘t 1 s s (1.26).

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Beyond the epistemological debate

The epistemological conflict literature assumes that “religion and science are inherently incompatible and that a growth in science leads to decline in religion because they are competing ways of establishing truth” Engstrom and N. Engstrom (2008, p. 91). Abstracting from the possibility of collusion between politics and religion then, if religions do not adapt to the higher truth of science, they are doomed to disappear. The preceding ideas were strongly influenced by the works of Max Weber in The Protestant Ethic and the Spirit of Capitalism (1904) and Economy and Society (1933), and have been advanced in the works of leading sociologists in the 1960s and 1970s such as Peter Berger, David Martin and Brian Wilson. 6 Summarizing, in the words of Norris and Inglehart (2004, p. 7), according to the preceding school of thoughts, “the era of the Enlightenment generated a rational view of the world based on empirical standards of proof, scientific knowledge of natural phenomena, and technological mastery of the universe. Rationalism was thought to have rendered the central claims of the Church implausible in modern societies, blowing away the vestiges of superstitious dogma in Western Europe”.
If science and religion are incompatible, it should be apparent in the data. More precisely, as emphasized by Iannaccone, Stark, and Finke (1996, 1998), we should expect (i) a decline in religion as scientific progress grows and lower levels of religiosity among (ii) more educated people, (iii) scientists and (iv) in “hard sciences” relative to “soft” sciences within the academic community. These predictions find mixed empirical evidence. Iannaccone, Stark, and Finke (1996, 1998) provide evidence that contradicts the four preceding predictions. Evans (2011) shows that Protestant and Catholics differ from secular Americans in their propensity to seek out scientific knowledge only on the few issues where religion and science make competing claims. By contrast, Ecklund and Scheitle (2007) find that academic scientists are much less religious than the general public (consistently with (iii)), while field-specific and interdisciplinary differences are not important predictors of religiosity (in contrast to (iv)). See as well Ecklund, Park, and Veliz (2008) for similar predictions. Relatedly, Bénabou, Ticchi, and Vindigni (2015) show that religion is associated with negative attitudes toward scientific progress at the individual level.
Other lines of research have advanced the precise opposite idea that religion influenced positively science. Merton (1970, 1938) argues that certain dominant cultural values expressed in Puritanism contributed to the rise of science. Such cultural values included profitable education, empiricism and experimentation over idle contemplation (see Engstrom and N. Engstrom (2008) for a thorough discussion on the subject). This view has found supporting evidence in the work of Becker and Woessmann (2009) for example, since they find a positive effect of Protestantism on the diffusion of human capital. 7
To conclude, the preceding series of evidence show that the epistemological conflict rationale for explaining the co-evolution of religion and science finds mixed empirical evidence in the literature. In this paper, I propose an alternative and follow a functionalist approach.

The process of secularization on a Danish Island

By contrast with an epistemological definition, a functionalist approach emphasizes that religions form a system of actions involving formal rituals and symbolic ceremonies, regular celebrations and the provision of social services. Religions are not primarily about explaining the physical world, but rather about coordinating social behaviors and maintaining viable communities. This view is consistent with the literature on religious clubs initiated in the seminal work of Iannaccone (1992). Norris and Inglehart (2004) argue relatedly that religions strive because they provide security and make people less vulnerable to risks. Consistently with this approach, Samuelson and Swinkels (2006) show that religion and welfare state spending are substitute mechanisms that insure individuals against adverse life events.
In a functionalist interpretation, understanding the interaction between science and religion implies studying how science modifies the organizational capacity of religious communities. Our key premise in that respect – which is inspired of a unique case study of secularization – is that science affects religious communities primarily when it broadens agents’ economic opportunities.
Becker (1996) studies the process of religious change in a single Scandinavian county, the rural Danish island of Mors. Starting in the 1960s, the island experienced a steady decline in religiosity while scientific education and the welfare state have grown. On the surface, this dynamics seemed to confirm the standard epistemological conflict rationale for secularization. By contrast, the author shows that the decline in religiosity followed an agricultural mechanization program undertaken by Denmark shortly after the second World War. According to Becker (1996, p 439), “mechanized tractors, harvesters, feeders, and other equipment replaced most human labor in the countryside, boosting productivity. At the same time, they devastated the social system in the villages. Beginning around 1960, agricultural employment on Mors began rapidly disappearing, driving workers and their families into the town and cities in search of work. Local shops began to close, as did the voluntary associations that formed the heart of village social life”.

Competitive equilibrium when the religious are conservative

In order to derive the competitive equilibrium in any period t, we will proceed in three steps. First, we will derive the optimal production scheme given that output and technology producers act optimally. Next, we will study agents’ optimal contributions to the religious good g at a given value of qt, the share of conservative agents in the economy. Finally, we will combine the preceding findings in order to deduce the allocation of labor as a function of the share of conservatives in the economy.
Optimal production: The goods are produced with labor and technology, given that the levels of technology in the two sectors are endogenous to monopoly producers, e.g. artisans and scientists. I denote y (resp. 1 ≠ y) the labor demand in sector 2 (resp. 1). The technical level in sector i is denoted ai so that the production frontier is given by Yi = ai— yi1≠— (2.5).
with 0 < — < 1. Let fi(ai) be the inverse demand function of technologies in sector i. The profits of a monopoly supplying sector i-specific technologies can be written as Zi(ai) = (fii(ai) ≠c)ai where c denotes a constant marginal cost (that we take equal in both sectors for simplicity). The complete derivation of the competitive equilibrium is provided in the online Appendix 1. The formalization follows Acemoglu (2002). When the firms and the agents behave optimally, we find that the relative wage in sector 2 verifies w2 = [( 1 ≠ – )‡( 1 ≠ y )]1/‘(1≠—). (2.6).

Table of contents :

1 Parental Rearing Practices, Cultural Transmission and Cognitive Development
1.1 Introduction
1.1.1 Related literature
1.2 A static model of child rearing
1.2.1 The child-rearing interaction
1.2.2 Television viewing for rearing purposes
1.3 The dynamics of child rearing and child development
1.4 Extensions
1.4.1 Child maltreatment and toxic stress as impediments to children cognitive development
1.4.2 The persistence of television viewing of young children
1.5 Conclusion
1.6 Appendix
1.6.1 Proof of Proposition 1
1.6.2 Proof of Proposition 2
2 A Theory on the Evolution of Religious Norms and Economic Prohibition 
2.1 Introduction
2.1.1 Related Literature
2.2 Motivating examples
2.2.1 Beyond the epistemological debate
2.2.2 The process of secularization on a Danish Island
2.2.3 The Sunni Revival
2.3 The Model
2.3.1 Competitive equilibrium when the religious are conservative
2.3.2 The dynamics of religious preferences
2.3.3 Perfectly forward looking religious leader
2.3.4 Collusion between political and religious authorities
2.4 Conclusion
2.5 Appendix
2.5.1 Competitive equilibrium
2.5.2 The dynamics of religious preferences
2.5.3 Proof of Proposition 2
2.5.4 Proof of Proposition 3
2.5.5 Proof of Proposition 4
3 Multi-candidate Political Competition and the Industrial Organization of Politics 
3.1 Introduction
3.1.1 Literature review
3.2 The canonical model
3.3 Axiomatic approach to probabilistic voting
3.4 Applications
3.4.1 Application 1: Special interest politics with heterogeneous voters and homogeneous entrants
3.4.2 Application 2: Special interest politics with homogeneous voters and heterogeneous entrants
3.4.3 Application 3: Endogenous entry and coalition formation in the legislature in proportional systems
3.4.4 Application 4: Redistributive policies under alternative voting rules
3.4.5 Application 6: Peaceful franchise extension in Democracy
3.5 Conclusion
3.6 Appendix
3.6.1 Proof of Theorem 1
3.6.2 Proof of Theorem 2
3.6.3 Proof of Proposition 1
3.6.4 Proof of Proposition 2
3.6.5 Proof of Proposition 4
3.6.6 Proof of Proposition 5
3.6.7 Proof of Proposition 6
3.6.8 Proof of Lemma 2
3.6.9 Proof of Proposition 7
3.6.10 Proof of Proposition 8
Main conclusion
References 

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