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An article on conversion.
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  Qual Quant (2013) 47:1163–1171DOI 10.1007/s11135-011-9615-x A Bayesian model of religious conversion Vikas Kumar Published online: 5 October 2011© Springer Science+Business Media B.V. 2011 Abstract  The Economics of Religion literature is of two minds on whether conversion ismore likely to occur between close or distant religions. The religious capital model suggeststhat conversion should involve sufficiently close religions whereas cognitive considerationssuggestthatconversionshouldinvolvesufficientlydistantreligions.Wereconciletheseseem-ingly contradictory insights about conversion for the class of non-instrumental, intrinsicallymotivated conversions within a Bayesian framework. We show that religious conversionshould involve moderately distant religions. Keywords  Cognitive constraints  ·  Conversion  ·  Decision  ·  Economics of Religion  · Religious capital JEL Classification  C44 · D80 · Z12 1 Introduction Over the last few decades economists have gradually acquired interest in religion. The is-sue of religious conversion has received some attention in the growing body of literatureknown as the Economics of Religion, mostly in connection with the role of habit in reli-gious sphere, inter-generational transmission of religious affiliation, and the impact of inter-religious marriage on religious affiliation (Kumar 2008).Of all the models that deal with conversion the religious capital model is the best-known.Religious capital consists of “familiarity with a religion’s doctrines, rituals, traditions, andmembers” (Iannaccone 1990, p. 299). With regard to denominational mobility this model The author is Assistant Professor at Azim Premji University, Bangalore.V. Kumar ( B )Azim Premji University, Hosur Road, Bangalore 560100, Indiae-mail: vikasprithvipur@gmail.com; vikas.kumar@azimpremjifoundation.orgURL: http://works.bepress.com/vikas_kumar/   1 3  1164 V. Kumar suggests that “the likelihood of conversion between particular religious groups should begreater the more similar the groups, and overall rates of conversion to and from a particulargroup should be lower the more nearly unique the group” (ibid, p. 300). A convert couldcompletely forfeit religious capital when converting to a dissimilar religion. For instance,a pious Muslim or Jew, who accumulated religious capital by abstaining from prohibitedfoods, has to forfeit the entire capital when converting to Christianity.But the reasonable assumption of cognitive limitation goes against the religious capitalargument. In Ferrero’s spatial model of religious competition there is a continuum ofdegreesof behavioural strictness that membership-maximizing religious firms could demand of theirmembers. People have their ideal locations along this continuum. They subscribe to thereligion closest to their ideal location. However, firm locations are constrained by a “mini-mum critical distance” they need to maintain among themselves, which is in turn assumedto be governed by the “the inability for ordinary people to appreciate doctrinal subtleties andbehavioural differences beyond some point” (Ferrero 2008, p. 84). In other words, the laity cannot be expected to distinguish between sufficiently close religions. While Ferrero is notdirectly concerned with conversion (which in his framework will be equivalent to a shift intheideallocationofanindividual),hisinsightregardingcognitivelimitationsisequallyvalidin case of conversion.Inshort,thereligiouscapitalapproachsuggeststhatconversionshouldtakeplacebetweensufficientlyclosereligionswhereascognitiveconsiderationssuggestthatthereligionsshouldbe sufficiently distant. We argue that believers face cognitive constraints because acceptablestandards of proof can limit individual capacity to distinguish among nearby religions. Wethenreconciletheseeminglycontradictoryinsightsaboutconversionmentionedabovefortheclass of non-instrumental, intrinsically motivated conversions by showing that conversionsshouldinvolvemoderatelydistantreligions.Restofthediscussionisorganizedasfollows.InSect.2weintroducenon-instrumental,intrinsicallymotivatedconversionsandotherspecificsof the setting in which individuals operate. Section 3 reconciles the two different approachesdiscussed above within a decision-theoretic setting. Section 4 provides concluding remarks. 2 The setting Conversions can be characterized according to the source of motivation (intrinsic vs. extrin-sic) and nature of motivation (instrumental vs. non-instrumental). We use ‘instrumental’ inthe narrow materialistic sense. Instrumental conversions are rational in the sense that onehas some material objectives and conversion is undertaken to meet those objectives subjectto constraints. However, the same is not necessarily true of non-instrumental conversions.We will concern ourselves only with non-instrumental, yet rational conversions. Individualswant to follow the “true” religion and convert whenever they learn that their own religion isnot the “true” one. Even though religion has a material dimension, material gain, if any, fromconversion is superfluous to the problem of choice in our analysis. To keep things simple wefurther narrow down our scope by focussing on intrinsically motivated conversions so thatwe can work within a decision-theoretic framework. Intrinsically motivated conversion is aprocess involving just one individual, in particular, his beliefs and preferences. We intendto model the process of non-instrumental conversion at this level. We further assume stablepreferences and restrict our focus to beliefs, which are updated with the help of Bayes’ Rule.In short, we will engage with non-instrumental, intrinsically motivated conversions.Further assume that all individuals who believe in some god or the other also believethat there is no afterlife and that depending on religious practice god dispenses rewards/   1 3  A Bayesian model of religious conversion 1165 punishments entirely during one’s life, in fact, in the current period itself. We will not dealwith religions with positive belief in afterlife because the difficulties faced while modellingsuch religions within a rational choice framework are insurmountable. Even a cursory dis-cussion of the conceptual problems will take us far from our present remit. But three keyproblems bear mentioning here: (a) infinite pay-offs associated with afterlife, (b) absolutelyinscrutable character of afterlife, and (c) inapplicability of Bayesian updating to changes inbelief in religion with afterlife because there is no observable outcome on which to base theupdating of beliefs.Havingdiscussedwhyweareunabletoengagewithreligionsthatsupportapositivebelief in afterlife we will next advance a justification for engaging with religion sans afterlife. Notonly are there religions which have no conception of afterlife but also religions in whichthe quality of afterlife is unrelated to actions chosen and beliefs held in the current life. TheHumanRelationsAreaFiles(HRAF)provideinformationregardingthenatureofbeliefaboutafterlife in a large number of cultures. According to HRAF, in 37% of the cultures peoplebelieve that either there is no afterlife or it is same for all and does not require any effort orfaith while in 63% of the cultures people believe in an afterlife, whose quality depends onindividual effort and faith (Hull and Bold 1994, pp. 456–457). While it is important to note that modern industrial cultures are not represented in HRAF(ibid) we should also keep in mind that liberal Christian sects (we can add Reform Judaism)in the advanced West are de-emphasizing afterlife (Sherkat 2001, pp. 1485–1486). Also, historically strict forms of Calvinism posited an entirely unimpressionable, inscrutable God,whosedecisionregardingafterlifecannotbeinfluencedbyhumans.ThesameistrueofVaish-navism,asectofHinduism(Patnaik2008).Inshort,religionsansafterlifeorreligionwithan afterlife that does not depend on actions taken in this life is not a hypothetical construct and,actually, has empirical support. Further, if the quality of afterlife is independent of actionstaken in this life then we can say that the afterlife dimension of religion is superfluous as faras rational choice analysis is considered.However, like other religions that have a non-trivial afterlife dimension, the aforesaidreligions posit a relationship between material well-being and religious practice in this life.The material and religious spheres are related as follows. Economic output depends on sec-ular effort, assumed to be identical across individuals,  and   religious practice, which variesacross individuals. Believers interpret spatio-temporal variations in material well-being asdivine verdict on righteousness of human conduct. Material setbacks are attributed to divinepunishment for transgressions while gains are treated as rewards for righteousness. In otherwords,itisbelievedthatrightreligiouspractice,whichinturndependsonreligiousaffiliation,accentuates output and vice versa. We assume that all individuals put in optimal religiouseffort in accordance with their religious beliefs since god is believed to be omniscient. Wewill, therefore, not concern ourselves with the possibility of shirking in the religious sector.The substance of our discussion remains unchanged if we assume, alternatively, that the dis-tribution of shirkers in the population is known. In each period individuals form expectationsabout the aggregate output based on their religious beliefs and religious demography (i.e.,share of different religions in the society). At the end of a period, individuals adjust theirbeliefs after observing actual output, which is believed to contain information about the truestate of the world. For the sake of simplicity we assume that individuals update beliefs everyperiod. However, all our results will go through even if individuals update beliefs once inmany periods, with the frequency being determined by limitations of memory or religiousdoctrine. We also assume that religious demography and economic output are known to all.Before we present the model in the next section, three issues bear elaboration, namely, the  1 3  1166 V. Kumar nature of our explanation of conversion, the objective of individuals in the religious sphere,and the relationship between the states of world and religions.First note that we are not following the Marxist approach, which treats changes in thereligious sphere as manifestations of deeper material changes. In our framework, outputdepends on the true state of the world which in turn is governed by the true religion. Recallthat by assumption secular effort is fixed across individuals irrespective of religious affili-ation. So, when individuals change religion by observing output they are not switching toa new brand of opium due to “deeper” material changes. Rather they are correcting theirbeliefs in accordance with “revelation”, conveyed in material terms. For instance, consider asociety consisting of two religions  A  and  B , with  a  and  b  adherents, respectively. Accordingto religion  A (  B )  the aggregate output will suffer because of the wrong religious practices of the followers of religion  B (  A ) , which will attract the displeasure of god. The followers of religion  A  expect the overall output in a society with  a  + b  population to be A after takinginto account the fact that  b  individuals do not worship properly: each follower of religion  A  obtains  x  / a  while each follower of religion  B  obtains  y / b (<  x  / a )  because of wrongreligious practice, where  a  (  x  / a ) + b (  y / b )  =  A. Likewise the followers of religion  B  expectthat the output would be B. If observed aggregate output, say,  C   is sufficiently close to A ( B ) then the followers of   B (  A )  re-think the validity of their srcinal belief and consider convert-ing to religion  A (  B ) . (Note that in the current setting, religious practice of followers of areligion does  not   generate negative externalities for followers of other religions. But such apossibility can be easily incorporated in the model without affecting the key results.) In restof the discussion we will deal with aggregate output as a medium of revelation of the truestate of world that is governed by the true religion.Further note that our individuals are not after optimal decision  a la  Knightian or Bayesiandecision-makers driven by cost-benefit analysis, who try to minimize expected loss (Greene2003, p. 434) or trade-off the cost of data collection and loss from not knowing the “truth”(Cyert and De Groot 1987; Iversen 1984). Our individuals are not instrumentalist because they do not convert to achieve material gains rather they want to ascertain the truth contentof various beliefs and switch to the right one. Inference about the true state of the world isan end in itself.Last but not the least note that the application of the states of world approach for nor-mative purpose requires that the states should be (a) mutually exclusive, (b) exhaustive, and(c) should represent “nature’s exogenous uncertainty” that cannot be affected by individual’schoice of action (Machina 2003). In our discussion, the states of nature (corresponding to different possible true religions) are assumed to be mutually exclusive and exhaustive andthe society is assumed to be sufficiently large so that given the choices of all others an indi-vidual’s choice insignificantly affects aggregate output, the medium of revelation regardingthe state of the world. Note that the set of religions to which our analysis applies triviallyincludes atheism, the belief that output is  not   influenced by god-like agencies. Also, notethat the assumption of mutually exclusive states of nature does not restrict our discussionto exclusivist religions. It can be argued that if followers of different religions can worshipseveral gods (some of them potentially common), one can infer nothing from the observedstates of the world. To see why this is not the case consider a society with two religions,  A (worship god  u ) and  B  (worship gods  u  and  v ). According to religion  A (  B ) , if one worshipsmore or less than one (two) god(s) then ones efforts are misguided and that negatively affectsones material well-being. In other words, it is sufficient for us that the states of nature andassociated religions are mutually exclusive in terms of expected output. The last claim willnot hold if polytheistic pantheons have redundancy, i.e., gods of a polytheistic religion arenot mutually complementary, which has not to my knowledge been shown.  1 3
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