Clngng to Belefs: A Constrant-satsfacton Model Thomas R. Shultz (shultz@psych.mcgll.ca) Department of Psychology; McGll Unversty Montreal, QC H3C 1B1 Canada Jacques A. Katz (jakatz@cnbc.cmu.edu) Department of Psychology; Carnege Mellon Unversty Pttsburgh, PA 15213 USA Mark R. Lepper (lepper@psych.stanford.edu) Department of Psychology; Stanford Unversty Stanford, CA 94305-2130 USA Abstract Belefs tend to persevere even after evdence for ther ntal formulaton has been nvaldated by new evdence. If people are assumed to ratonally base ther belefs on evdence, then ths belef perseverance s somewhat counterntutve. We constructed a constrant-satsfacton neural network model to smulate key belef perseverance phenomena and to test the hypothess that explanaton plays a central role n preservng evdentally challenged belefs. The model provdes a good ft to mportant psychologcal data and supports the hypothess that explanatons preserve belefs. Introducton It s perhaps surprsng that people are so often reluctant to abandon personal belefs that are drectly contradcted by new evdence. Ths tendency to clng to belefs n the face of subsequent counterevdence has been well demonstrated for opnons (Abelson, 1959), decsons (Jans, 1968), mpressons of people (Jones & Goethals, 1971), socal stereotypes (Katz, 1960), scentfc hypotheses (T. S. Kuhn, 1962), and commonsense deas (Glovch, 1991). Belef perseverance s puzzlng because t s commonly assumed that belefs are based on evdence. If t s ratonal for people to form a belef based on evdence, then why s t not equally ratonal for them to modfy the belef when confronted wth evdence that nvaldates the orgnal evdence? Debrefng Experments Some of the clearest cases of apparently rratonal belef perseverance come from debrefng experments. In these experments, subjects learn that the ntal evdental bass for a belef s nvald. For example, Ross, Lepper, and Hubbard (1975) frst provded subjects wth false feedback concernng ther ablty to perform a novel task. Ther subject s task was to dstngush authentc from fake sucde notes by readng a number of examples. False feedback from the expermenter led subjects to beleve that they had performed at a level that was much better than average or much worse than average. Then, n a second phase, subjects were debrefed about the random and predetermned nature of the feedback that they had receved n the frst phase. There were three debrefng condtons. In the outcome debrefng condton, subjects were told that the evdence on whch ther ntal belefs were based had been completely fabrcated by the expermenter. Subjects n the process debrefng condton were addtonally told about the procedures of outcome debrefng along wth explanatons about possble mechansms and results of belef perseverance. Subjects n ths condton were also told that belef perseverance was the focus of the experment. Fnally, subjects n a no-debrefng control condton were not debrefed at all after the feedback phase. Subsequently, subjects n all three condtons rated ther own ablty at the sucde-note verfcaton task. Ths was to assess the perseverance of ther belefs about ther abltes on ths task that were formed n the feedback phase. The mean reported belefs for the three debrefng condtons are shown n Fgure 1. There s an nteracton between debrefng condton and the nature of feedback (success or falure at the note-verfcaton task). The largest dfference between success and falure feedback occurs n the nodebrefng condton. In ths control condton, subjects who were ntally led to beleve that they had succeeded contnue to beleve that they would do better than subjects ntally led to beleve that they had faled. After outcome debrefng, there s stll a sgnfcant dfference between the success and falure condtons, but at about one-half of the strength of the control condton. The dfference between success and falure feedback effectvely dsappears after process debrefng. Ths sort of belef perseverance after debrefng has been convncngly demonstrated for a varety of dfferent belefs and debrefng technques (Jennngs, Lepper, & Ross, 1981; Lepper, Ross & Lau, 1986). One explanaton for such belef perseverance s that people frequently explan events, ncludng ther own belefs, and such explanatons later sustan these belefs n the face of subsequent evdental challenges (Ross et al., 1975). For example, a person who concludes from ntal feedback that she s very poor at authentcatng sucde notes mght attrbute ths nablty to somethng about her experence or personalty. Perhaps she has had too lttle contact wth severely depressed people, or maybe she s too optmstc to empathze deeply wth a sucdal person. Then n the second
phase, when told that the feedback was entrely bogus, these prevously constructed explanatons may stll suggest that she lacks the ablty to authentcate sucde notes. Analogously, a subject who s ntally told that he dd extremely well at ths task may explan hs success by notng hs famlarty wth some depressed frends or hs senstvty to other people s emotons. Once n place, such explanatons could noculate the subject aganst subsequent evdence that the ntal feedback was entrely bogus. Predcted future number correct 22 20 18 16 14 12 10 None Outcome Process Debrefng Feedback Success Falure Fgure 1: Mean predcted ablty n the Ross et al. (1975) experment after debrefng. The assumpton s that even though contradctory evdence may weaken a belef, t s unlkely to alter every cognton that may have derved from that belef, such as explanatons for the belef' s exstence. The well -known frame problem emphaszes the computatonal ntractablty of trackng down every mplcaton of an altered belef (Charnak & McDermott, 1985). People generally do not have the tme, energy, knowledge, or nclnaton to decde whch other belefs to change whenever a belef s changed. In contrast to the vew that people have dffculty dstngushng explanatons from evdence (D. Kuhn, 1991), recent research suggests that people can dstngush explanatons from evdence and that they tend to use explanatons as a substtute for mssng evdence (Brem & Rps, 2000). In ths paper, we report on our attempt to smulate the belef perseverance phenomena reported by Ross et al. (1975). Our basc theoretcal premse n desgnng these smulatons s that belef perseverance s a specal case of a more general tendency for people to seek cogntve consstency. Strvng for consstency has long been consdered to cause a wde varety of phenomena n socal psychology (Abelson, Aronson, McGure, Newcomb, Rosenberg, & Tannenbaum, 1968). In the case of belef perseverance, we assume that people form percepts that are consstent wth external evdence, then acqure belefs that are consstent wth these percepts, and fnally construct explanatons that are consstent wth these belefs. We vew resstance to new evdence that contradcts exstng percepts, belefs, or explanatons as part of an attempt to acheve overall consstency among current cogntons, gven that not all mplcatons of contradctory evdence are actvely pursued. There was a smulaton usng non-monotonc logc of how belef can be preserved despte ordnary debrefng, but t dd not cover the quanttatve dfferences between condtons n the Ross et al. experment (Hoenkamp, 1987). Neural Constrant Satsfacton Our smulatons use a technque called constrant satsfacton, whch attempts to satsfy as many constrants as well as possble wthn artfcal neural networks. The present model s closely related to models used n the smulaton of schema completon (Rumelhart, Smolensky, McClelland, & Hnton, 1986), person percepton (Kunda & Thagard, 1996), atttude change (Spellman, Ullman, & Holyoak, 1993), and dssonance reducton (Shultz & Lepper, 1996). Constrant satsfacton neural networks are comprsed of unts connected by weghted lnks. Unts can represent cogntons by takng on actvaton values from 0 to 1, representng the strength or truth of the cognton. Connecton weghts can represent relatons between cogntons and are assgned postve or negatve values representng the sgn and strength of the relatons. Connecton weghts are bdrectonal to permt cogntons to mutually nfluence each other. External nputs to unts represent nfluences from the envronment. Bases are represented by nternal nputs to a gven unt that do not vary across dfferent network nputs. Networks attempt to satsfy the soft constrants mposed by fxed nputs, bases, and weghts by changng actvaton values of the unts. Unt actvatons are updated accordng to these rules: a t + 1 = a t + net celng a t, when net 0 (1) a ( ) ( ) ( ( ) ( t ) = a ( t) + net ( a ( t) floor) + 1, when net < 0 (2) where a (t + 1) s the updated actvaton value of unt, a s the current actvaton of unt, celng s the maxmum actvaton value for a unt, floor s the mnmum actvaton value for a unt, and net s the net nput to unt, as computed by: net = n wja j bas + ex( nput ) + (3) j where n and ex are parameters that modulate the mpact of the nternal and external nputs, respectvely, wth default values of 0.1, w j s the connecton weght between unts and j, a j s the actvaton of sendng unt j, bas s the bas value of unt, and nput s the external nput to unt. These update rules ensure that network consstency ether ncreases or stays the same, where consstency s computed as: consstenc y = w a a + nput a + bas a (4) j j j When a network reaches a hgh level of consstency, ths means that t has settled nto a stable pattern of actvaton
and that the varous constrants are well satsfed. In such stable solutons, any two unts connected by postve weghts tend to both be actve, unts connected by negatve weghts tend not to be smultaneously actve, unts wth hgh nputs tend to be more actve than unts wth low nputs, and unts wth hgh bases tend to be more actve than unts wth low bases. Increases n consstency and constrant satsfacton occur gradually over tme. At each tme cycle, n unts are randomly selected for updatng, where n s typcally the number of unts n the network. Thus, not every unt s necessarly updated on every cycle and some unts may be updated more than once on a gven cycle. Unusual Smulaton Features The foregong characterstcs of neural constrant satsfacton are qute common. In addton, the present modelng has a few somewhat unusual features. Perhaps the most mportant of these s a two-phase structure that accommodates the two man phases of belef perseverance experments. It s more typcal for neural constrant satsfacton models to operate n a sngle phase n whch networks are desgned and updated untl they settle nto a stable state. Our two phases correspond to the feedback and debrefng phases of these experments. After a network settles n the ntal feedback phase, new unts can be ntroduced, and nputs, connecton weghts, and bases may be changed n a second, debrefng phase. To mplement contnuty between the two phases, a smple type of memory was ntroduced such that actvaton values from the feedback phase would be partally retaned as unt bases n the debrefng phase. Fnal actvatons n the feedback phase were multpled by 0.05 to transform them nto bases for the debrefng phase. Ths s not a detaled mplementaton of a memory model, but s rather a convenent shorthand mplementaton of the dea that there s a faded memory for whatever conclusons were reached n the prevous, feedback phase. Two other unusual features derved from our earler smulatons of cogntve dssonance reducton (Shultz & Lepper, 1996): a cap parameter and randomzaton of network parameters. The cap parameter s a negatve self-connecton weght for every unt that lmts unt actvatons to less than extreme values. The purpose of ths actvaton cap s to ncrease psychologcal realsm for experments about belefs that reach no more than moderate strength. Robustness of smulaton results was assessed by smultaneously randomzng all network parameters (.e., bases, nputs, and connecton weghts) by up to 0%, 10%, 50%, or 100% of ther ntal values accordng the formula: { rand ( abs [ x rand% ] ) } y = x ± (5) The ntal parameter value x s multpled by the proporton of randomzaton beng used (0,.1,.5, or 1) and converted to an absolute value. Then a random number s selected between 0 and the absolute value under a unform dstrbuton. Ths random number s then randomly ether added to or subtracted from the ntal value. Ths parameter randomzaton allows effcent assessment of the robustness of the smulaton under systematc varatons of parameter values. If the smulatons succeed n matchng the psychologcal data, even under hgh levels of parameter randomzaton, then they do not depend on precse parameter settngs. Ths randomzaton process also enhances psychologcal realsm because not every subject can be expected to have precsely the same parameter values. Unts Network Desgn Unts represent external nput and the three types of cogntons that are crtcal to belef perseverance experments,.e., percepts, belefs, and explanatons. Percept unts represent a subject s percepton of external nput, n ths case feedback provded by the expermenter. Belef unts represent a subject s belefs, and explanaton unts represent a subject s explanatons of partcular belefs. In each case, the larger the actvaton value of a gven unt, the stronger the assocated cognton. Actvaton values range from 0 to 1, wth 0 representng no cognton, and 1 representng the strongest cognton. All unt actvatons start at 0 as a network begns to run. Unt names nclude a sgn of +, -, or 0 to represent the drecton of a gven cognton. For example, n these smulatons, +percept refers to a percepton of dong well on a task, -percept to a percepton of dong poorly on the task, and 0percept to not knowng about performance on the task. Percept unts sometmes have an external nput, to reflect the feedback on whch the percept s based. A 0percept unt s requred for smulatng debrefng experments, where nformaton s encountered that explctly conveys a lack of knowledge about performance. Analogously, +belef represents a belef that one s performng well at a task, belef represents a belef that one s performng poorly at a task, +explanaton represents an explanaton for a +belef, and - explanaton represents an explanaton for a belef. Connectons Unts are joned by connecton weghts that have a sze and a sgn. The sgn of a weght represents a postve or negatve relaton between connected unts. A postve weght sgnals that a cognton follows from, leads to, s n accordance wth, or derves support from another cognton. A negatve weght ndcates that a cognton s nconsstent wth or nterferes wth another cognton. Decsons about sgns are based on descrptons of psychologcal procedures. Intal nonzero connecton weghts are + or - 0.5 n our smulatons. Connecton weghts of 0 ndcate the absence of relatons between cogntons. All connecton weghts are bdrectonal to allow mutual nfluences between cogntons. The general connecton scheme n our smulatons of belef perseverance has external nputs feedng percepts, whch are n turn connected to belefs, whch are n turn connected
to explanatons. For falure condtons, a -percept unt receves external nput and s connected to a -belef unt, whch s n turn connected to a -explanaton unt. For success condtons, a +percept unt receves external nput and s connected to a +belef unt, whch s n turn connected to a +explanaton unt. Connecton weghts between ncompatble cogntons, such as between +belef and -belef or between -percept and 0percept, are negatve. The prncpal dependent measure n many belef perseverance studes s a subject s self-rated ablty on a task. Ths s represented as net belef, computed as actvaton on the +belef unt mnus actvaton on the -belef unt, after the network settles n the debrefng phase. Ths technque of usng two negatvely connected unts to represent the dfferent poles of a sngle cognton was used by Shultz and Lepper (1996) n ther smulaton of cogntve dssonance phenomena. Networks for Feedback Phase Fgure 2 shows specfcatons for the negatve feedback condton. Negatve feedback, n the form of external nput, wth a value of 1.0, s postvely connected to the percept unt. Ths same network desgn s used for the no-debrefng condton of the debrefng phase. Fgure 2: Network for negatve feedback. Postve connecton weghts are ndcated by sold lnes; negatve connecton weghts by dashed lnes. A feedback phase represents the presentaton of nformaton on how a subject s dong on a task. It s assumed that ths nformaton forms the bass for a belef about ablty and to explanatons of that ablty. Because of the connecton scheme and the fact that all unt actvatons start at 0, percept unts reach actvaton asymptotes frst, followed by belef unts, and fnally by explanaton unts. Networks for Debrefng Phase -explanaton Input 1.0 -percept -belef +belef Fgure 3 shows network specfcatons for the debrefng phase. Ths network was used for both outcome debrefng and process debrefng. The partcular network shown n Fgure 3 shows a debrefng phase that follows negatve feedback. As noted earler, an unusual feature here s the ncluson of bases for percept, belef, and explanaton unts from the earler, feedback phase. These based unts are represented by bolded rectangles around unt names, and mplement a faded memory of the feedback phase. There s also a new unt, the 0percept unt, wth an nput of 1.0, to represent that nothng vald s known about task performance. Ths unt has no bas because t was not present n the prevous phase. It s negatvely connected to the or + percept unt to represent the dea that the feedback data from the prevous phase are false, and thus convey no nformaton about task ablty. Input 1.0 -percept 0percept Fgure 3: Network for outcome and process debrefng followng negatve feedback. Unts that have bases from the feedback phase are ndcated by bolded rectangles. We mplemented the stronger, process debrefng by multplyng bas values by a factor of 0.1. Ths reflects the dea that process debrefng s so thorough that t severely degrades all cogntons that were created n the precedng feedback phase. Networks n the no-debrefng condton were dentcal to those descrbed n Fgure 2, wth no topology changes after the feedback phase. However, as n all debrefng condtons, bases of.05 of fnal actvatons were used for any unts beng carred over from the feedback phase. Networks were run for 120 update cycles n each of the two phases; by ths tme they had typcally settled nto stable states. Prncples of Network Desgn -explanaton -belef +belef In summary, network desgn can be summarzed by 13 prncples: 1. Unts represent cogntons. 2. The prncpal cogntons n belef perseverance experments are nput feedback, percepts, belefs, and explanatons. 3. The sgn of unt names represent the postve or negatve poles of cogntons. 4. Unt actvaton represents strength of a cognton (or a pole of a cognton). 5. The dfference between postve and negatve poles of a cognton represents the net strength of the cognton. 6. Connecton weghts represent constant mplcatons between cogntons. 7. Connecton weghts are b-drectonal, allowng possble mutual nfluence between cogntons or poles of cogntons. 8. Cogntons whose poles are mutually exclusve have negatve connectons between the postve and negatve poles.
9. Sze of external nput represents strength of envronmental nfluence, such as evdence or feedback. 10. External nputs are connected to percepts, percepts to belefs, and belefs to explanatons, representng the assumed chan of causaton n belef perseverance experments. That s, envronmental feedback creates percepts, whch n turn create belefs, whch eventually lead to explanatons for the belefs. 11. Networks settlng nto stable states represent a person's tendency to acheve consstency among cogntons. 12. Fnal unt actvatons from the feedback phase are converted to unt bases for the start of the debrefng phase of belef perseverance experments, representng the partcpant's memory of the feedback phase. 13. Multplyng actvaton bas values by 0.1 represents thorough, process debrefng. Results We focus on the fnal net belef about one s ablty after the debrefng phase. Ths s computed as actvaton on the +belef unt mnus actvaton on the -belef unt. Here, we report only on the 10% randomzaton level, but smlar results are found at each level of parameter randomzaton. Net belef scores were subjected to a factoral ANOVA n whch debrefng condton (none, outcome, and process) and feedback condton (success, falure) served as factors. There was a man effect of feedback, F(1, 114) = 29619, p <.001, and an nteracton between debrefng and feedback, F(2, 114) = 9102, p <.001. Mean net ablty scores are shown n Fgure 4. For success feedback, net belef scores were hgher after no debrefng than scores obtaned after outcome debrefng, whch were n turn hgher than scores obtaned after process debrefng. The opposte holds for falure feedback. Predcted ablty 1.5 1 0.5 0-0.5-1 -1.5 None Outcome Process Debrefng Feedback Success Falure Fgure 4: Mean predcted ablty n the smulaton after debrefng. To assess the ft to human data, we computed a regresson F wth regresson weghts based on the pattern of the Ross et al. (1975) results. The regresson weghts were 2, -2, 1, -1, 0, and 0 for the no debrefng/success, no debrefng/falure, outcome debrefng/success, outcome debrefng/falure, process debrefng/success, and process debrefng/falure condtons, respectvely. Ths produced a hghly sgnfcant regresson F(1, 114) = 47558, p <.001, wth a much smaller resdual F(4, 114) = 67, p <.001. The regresson F accounts for 99% of the total varance n net belef. As wth human subjects, there s a large dfference between success and falure wth no debrefng, a smaller but stll substantal dfference after outcome debrefng, and very lttle dfference after process debrefng. To assess the role of explanaton n the smulaton, we subjected actvatons on the explanaton unt after the debrefng phase to the same ANOVA. There s a man effect of debrefng, F(2, 114) = 3787, p <.001, a much smaller man effect for feedback F(1, 114) = 15.37, p <.001, and a small nteracton between them, F(2, 114) = 6.76, p <.005. The mean explanaton scores are presented n Fgure 5. Explanatons are strong under no-debrefng, moderately strong under outcome debrefng, and weak under process debrefng. But because explanatons had been strongly actve n all three condtons at the end of the feedback phase, these postdebrefng results reflect relatve dfferences n mantenance of explanatons. Explanatons are mantaned under no debrefng, partally mantaned under outcome debrefng, and elmnated n process debrefng. Mean explanaton 1 0.8 0.6 0.4 0.2 0 None Outcome Process Debrefng Fgure 5: Mean explanaton scores n the smulaton after debrefng. Dscusson Feedback Success Falure The tendency for belefs to persevere even after evdence for them has been fully nvaldated challenges some basc assumptons about human ratonalty. If people reasonably base ther belefs on evdence, then why s counter-evdence not suffcent to elmnate or change belefs? We used constrant-satsfacton neural networks to test the dea that explanaton plays a key role n sustanng belefs n
these crcumstances. The model provdes a good ft to exstng psychologcal data from debrefng experments n whch subjects are nformed that that the prncpal evdence for ther belefs s no longer vald (Ross et al., 1975). Smulated belefs reman strong wthout debrefng; belef strength s reduced after standard outcome debrefng, and elmnated after more thorough, process debrefng. Ths pattern of results matches the psychologcal data, wth about halfstrength belefs under outcome debrefng and elmnaton of belefs by process debrefng. As n our earler smulatons of cogntve dssonance phenomena, the neural constrantsatsfacton model s here shown to be robust aganst parameter varaton. Even a hgh degree of parameter randomzaton does not change the pattern of results. The smulatons further revealed that belef perseverance s mrrored by strength of explanaton. Explanatons reman strong wth no debrefng, and decrease progressvely wth more effectve debrefng. Although t s obvous that debrefng reduces the strength of erroneous belefs, the fndng that t also reduces explanatons s perhaps less obvous. In our smulatons, explanaton s reduced by effectve debrefng va connectons from external evdence to percepts, percepts to belefs, and belefs to explanatons. People spontaneously generate explanatons for events as a way of understandng events, ncludng ther own belefs (Kelley, 1967). If an explanaton s generated, ths explanaton becomes a reason for holdng an explaned belef, even f the belef s eventually undercut by new evdence. Future work n our group wll extend ths model to other belef perseverance phenomena and attempt to generate predctons to gude addtonal psychologcal research. Acknowledgments Ths research was supported by a grant to the frst author from the Socal Scences and Humantes Research Councl of Canada and by grant MH-44321 to the thrd author from the U.S. Natonal Insttute of Mental Health. References Abelson, R. P. (1959). Modes of resoluton of belef dlemmas. Conflct Resoluton, 3, 343-352. Abelson, R. P., Aronson, E., McGure, W. J., Newcomb, T. M., Rosenberg, M. J., & Tannenbaum, P. H. (Eds.) (1968). Theores of cogntve consstency: A sourcebook. Chcago: Rand McNally. Brem, S. K., & Rps, L. J. (2000). Explanaton and evdence n nformal argument. Cogntve Scence, 24, 573-604. Charnak, E., & McDermott, D. (1985). Introducton to artfcal ntellgence. Readng, MA: Addson-Wesley. Glovch, T. (1991). How we know what sn t so: The fallblty of human reason n everyday lfe. New York: Free Press. Hoenkamp, E. (1987). An analyss of psychologcal experments on non-monotonc reasonng. Proceedngs of the Tenth Internatonal Jont Conference on Artfcal Intellgence (Vol. 1, pp. 115-117). Los Altos, CA: Morgan Kaufmann. Jans, I. (1968). Stages n the decson-makng process. In R. P. Abelson, E. Aronson, W. J. McGure, T. M. Newcomb, M. J. Rosenberg, & P. H. Tannenbaum (Eds.) (1968). Theores of cogntve consstency: A sourcebook. Chcago: Rand McNally. Jennngs, D. L., Lepper, M. R., & Ross, L. (1981). Persstence of mpressons of personal persuasveness: Perseverance of erroneous self-assessments outsde the debrefng paradgm. Personalty and Socal Psychology Bulletn, 7, 257-263. Jones, E. E., & Goethals, G. R. (1971). Order effects n mpresson formaton: Attrbuton context and the nature of the entty. In E. E. Jones et al. (Eds.), Attrbuton: Percevng the causes of behavor. Morrstown, NJ: General Learnng Press. Katz, D. (1960). The functonal approach to the study of atttudes. Publc Opnon Quarterly, 24, 163-204. Kelley, H. H. (1967). Attrbuton theory n socal psychology. In D. Levne (Ed.), Nebraska Symposum on Motvaton. Vol. 15. Lncoln: Unversty of Nebraska Press. Kuhn, D. (1991). The sklls of argument. Cambrdge: Cambrdge Unversty Press. Kuhn, T. S. (1962). The structure of scentfc revolutons. Chcago: Unversty of Chcago Press. Kunda, Z., & Thagard, P. (1996). Formng mpressons from stereotypes, trats, and behavors: A parallel-constrant satsfacton theory. Psychologcal Revew, 103, 284-308. Lepper, M. R., Ross, L., & Lau, R. R. (1986). Persstence of naccurate belefs about self: Perseverance effects n the classroom. Journal of Personalty and Socal Psychology, 50, 482-491. Ross, L, Lepper, M. R., & Hubbard, M. (1975). Perseverance n self-percepton and socal percepton: Based attrbutonal processes n the debrefng paradgm. Journal of Personalty and Socal Psychology, 32, 880-892. Rumelhart, D. E., Smolensky, P., McClelland, J. L., & Hnton, G. (1986). Schemata and sequental thought processes n PDP models. In D. E. Rumelhart & J. L. McClelland (Eds.), Parallel dstrbuted processng: Exploratons n the mcrostructure of cognton (Vol. 2). Cambrdge, MA: MIT Press. Shultz, T. R., & Lepper, M. R. (1996). Cogntve dssonance reducton as constrant satsfacton. Psychologcal Revew, 103, 219-240. Spellman, B. A., Ullman, J. B., & Holyoak, K. J. (1993). A coherence model of cogntve consstency: Dynamcs of atttude change durng the Persan Gulf war. Journal of Socal Issues, 49, 147-165.