Keskustelualotteta #58 Joensuun ylopsto, Talousteteet Do norms and procedures speak louder than outcomes? An exploratve analyss of an excluson game Tmo Tamm ISBN 978-95-9-3-6 ISSN 795-7885 no 58
Do norms and procedures speak louder than outcomes? An exploratve analyss of an excluson game * Tmo Tamm Faculty of Law, Economcs and Busness Admnstraton Unversty of Joensuu Abstract Economsts have recently produced theores and evdence concernng the role of socal preferences n varous crcumstances of economc behavour. Ths has meant that n addton to selfsh preferences for one s own materal payoffs, economsts have become ncreasngly nterested also n nvestgatng one s preferences for materal and nonmateral payoffs of the opposng sde, or the partes nvolved, n general. A recent branch n ths research s bult on the contractaran aspect of behavour: are we wllng to follow the rules we have collectvely agreed upon? A case n pont s the work by Saccon and Fallo (005) whch shows that a remarkable porton of the players n an excluson game shfted from a selfsh strategy towards an equal dvson of monetary payoffs after they jontly agreed upon the sharng rule (of an equal dvson) and had good reasons to expect that ther opposng players also agreed upon the rule. Ths paper studes the Saccon-Fallo model by takng nto account the players process-regardng preferences n selectng the sharng rule. It also llustrates the measurement of procedural farness wth an analyss of emprcal data gathered n a small-scale plotng experment. Keywords: conformst preferences, process-regardng preferences, behavoural economcs, expermental economcs JEL classfcaton: C7, C9 * I would lke to thank Marco Fallo, Ismo Lnnosmaa and Nko Suhonen for ther helpful comments on earler versons of ths paper.
. Introducton Let me predct the outcome of the systematc and comprehensve testng of behavour n stuatons where self-nterest and ethcal values wth wde verbal allegance are n conflct. Much of the tme, most of the tme n fact, the selfnterest theory wll wn (Stgler 98, 76). Durng the last two decades economc theorsts and expermental economsts have produced emprcal evdence and theores whch cast, at least when nterpreted broadly, serous doubts on Stgler s predcton above. Indeed, n most of the reports on experments, self-nterest motvaton s outrun by varous types of other-regardng motvaton, such as rewardng and punshng, contrbutng to a publc good, as well as recprocty and altrusm. Recently, a more felctous counterexample to Stgler s asserton s stated n terms of the conformst preference theory by Grmalda, Saccon and Fallo (Grmalda and Saccon 00; Fallo and Saccon 007). The theory sees ndvduals as seekng complance wth a moral prncple condtonal to the belef that also other ndvduals seek smlar complance. The theory has mplcatons for many real-world problems predomnated by ncomplete and/or nformal contracts. These problems are often charactersed as socal dlemma stuatons typcal n economc actvtes under labels such as educaton, health care, natural and recreatonal resources, publc televson, regulaton, organzatonal performance and other uses of shared resources where the ndvdual and collectve nterests are at odds. Ths paper contrbutes to the research agenda commenced by Fallo, Grmalda and Saccon. The major am here s to show, f only tentatvely, that, n stuatons where conformty to a norm s a crucal source of ndvdual motvaton, people may also value the farness of the processes n whch the norm s jontly agreed. The vew adopted n ths paper emphaszes the so called voce-dmenson of collectve decson-makng. Ths refers to the extent to whch those who are affected by a decson have an opportunty to contrbute to, or be nvolved wth, the decson-makng procedure (Dolan et al. 007; Anand 00). Presumably, ths dmenson has a bearng on the felds and topcs mentoned above n the context of the conformst preferences theory. 3 Another purpose of the paper s to study, n the context of the excluson game, other factors of behavour than conformty and farness namely, other-regardng preferences (altrustc motvatons), relance on the ratonalty of Conformst preference theory s appled to non-proft organzaton analyss by Grmalda and Saccon (005) and to corporate socal responsblty problem by Saccon (007). See Grmalda and Saccon (005), Fallo and Saccon (007) and Saccon and Grmalda (007). 3 Benz (005) mentons () consumpton, () work and employment, () democratc partcpaton, (v) publc good allocaton, (v) taxaton, (v) redstrbuton and nequalty, (v) organzatons, and (v) law as areas of emprcal relevance. 3
others, and the esteem of ndependence of others behavour. To be sure the man nterest s n a prelmnary analyss and n plotng the devces that were appled n measurng these factors.. Theores of socal, procedural and conformst preferences.. Overvew In response to the outcomes n experments where the behavour of subjects has qute often devated from the self-regardng preferences model of standard economc theory 4, economsts have formulated theores of what they call socal preferences. The followng smplfed scheme llustrates the overall conceptual structure of utlty functons n these new theores: Utlty materal payoff + s x (averson to dsadvantageous dfference n payoffs) + s x (averson to advantageous dfference n payoffs) + s 3 x (kndness expectaton of the other s behavour) + s 4 x (conformty to a shared norm expectaton of the other s conformty). The scheme suggests that a person experences utlty, or derves pleasure, from the components n her utlty functon. In the utlty theory s manner of speakng the person assgns real numbers (utls) to () tems n her own materal payoffs or consumpton bundle, to () the dstance of her payoffs from the far level of payoffs, to () kndness (or malcousness), condtonal to her expectatons consderng the ntentons of the other player(s), and to (v) her conformty to an deal or a shared norm, condtonal to her belef of the conformty of the other player(s) to the deal. 5 In addton, the scheme suggests that the mpact of the other components of the functon except the materal payoffs are medated by the correspondng senstvty coeffcent, labelled as s,..s 4 and n the scheme. Ths ndcates that the strength of the mpact of one partcular component can vary between ndvduals and across stuatons. It may also take the value of zero, whch means that n a partcular stuaton, or for a partcular person, the mpact of that component n the utlty functon s zero. Accordngly, when a senstvty coeffcent becomes hgh enough, a person may choose to take another course of acton than f she were motvated solely, or domnantly, by her self-nterested materal outcomes. 4 The term self-regardng preferences model comes from Cox (004). The term makes t easer to see that expermental or other emprcal fndngs whch are nconsstent wth ths model need not be nconsstent wth standard economc theory as utlty functons can be defned as ncludng others payoffs n addton to one s own payoffs. 5 Note that tems () and (v) are modeled on the psychologcal games framework by Geanakoplos et al. (989) where utltes are derved drectly from belefs. 4
In addton to the above scheme we can add a ffth component n the utlty functon by consderng the fact that people often have process-regardng preferences. Ths means that people care how thngs and outcomes come about. A qute well-known demonstraton of ths s Machna s mom example where a mother who has one candy to be gven ether to her son or to daughter, and who decdes to flp a con to decde whch one of the chldren wll receve the candy (Machna 989; 3-4; also Trautmann 007). In the example the mother regards con-flppng as a far procedure of makng a decson whereas the son sees t as unfar. As s the way wth socal preferences, the strength of the mpact of process-regardng preferences vares between ndvduals and across stuatons. Fgure. Theores of preferences Preferences Tastes/valuatons of thngs Selfsh preferences A person s own materal payoffs/ consumpton bundles Socal preferences How a person ranks dfferent allocatons of materal payoffs to themselves and to others Procedural preferences How thngs/outcomes come about Standard EUT and GT Inequalty averson theores One s own payoff compared to relatve payoffs. Farness (recprocty) equlbrum theores One s belefs on other s kndness Varous auxlary hypotheses type of arguments. Bolton 99; Fehr and Schmdt 999; Bolton and Ockenfels 000; Rabn 993; Sally 00; Falk and Fschbacher 998 Conformty wth a shared rule Fallo and Saccon 007; Saccon and Fallo 005; Grmalda and Saccon 005 Bowles 004; Anandt 00; Ben-Ner and Putterman 999 Some examples tppng charty votng voluntary unpad work workng harder wthout money ncentves than wth money ncentves contrbutng to publc goods costly punshng of free-rders makng generous offers n ultmatum games (and rejectng ungenerous offers) punshng and rewardng the opponent player accordng to hs/her behavour cooperaton n a prsoner dlemma game punsh those who volate a shared norm pure altrusm (mprovng the wealth of others) There s currently an array of theores of socal preferences. Fgure s an attempt to organze these theores nto a tentatve typology accordng to the followng crtera: () are preferences related to 5
one s own materal payoffs, to the allocaton of materal payoffs, or to the process from whch the payoffs come about; () does a theory account for nteractve expectatons or not, and (3) do the preferences concern moral and ethcal values or not. Ths typology helps us n understandng the man dfferences n the theores and n seeng the procedural and conformst preferences wthn a broader theoretcal context. Although a detaled account of the typology les outsde the scope of ths paper, t can be notced that all exstng theores are based on methodologcal decsons to focus on partcular components of utlty and to gnore the other components. For example, recprocty theores focus on materal payoffs and recprocty consderatons whle nequalty averson theores focus on materal payoffs and dfferences n payoffs. A related fact s that so far as more psychology s brought n to these theores there emerges the dvdng lne between fxed vs. constructed preferences. That s, thngs such as farness and norm complance can be brought nto the model of economc behavour by assumng that people have ready-made preferences towards these thngs. Thus, when people enter varous decson-makng stuatons they then consult exactly these ready-made preferences to make ther decson. The standard expected utlty theory and game theory, as well as many nequalty averson theores, operate just n ths manner. On the contrary, Rabn s farness equlbrum theory and the conformst preference theory operate by assumng that context matters. In other words, the theores assume that people have preferences that depend on what the others expect her to thnk or do (see, for nstance Hargreaves Heap and Varoufaks 004, ch 7 and Brun and Sugden 007). An mportant fact s that experments have had an mportant role n the development of the theorzng on socal preferences. As has been argued by Sugden (005) and Santos (006), these experments can be charactersed as experments as exhbts aka behavoural experments. These charactersatons pont to the fact that typcal experments, where socal preferences are nvestgated, nclude causal factors and mechansms that are not bult nto the theory that s currently tested (n addton to the factors and mechansms whch are ncluded nto the theory). Therefore, these experments produce new knowledge on human behavour and they result qute often n new fndngs, devatons, anomales etc. Ths capacty of behavoural experments explans why there are currently several theores of socal preferences as explanatons of human behavour whch devates from the predctons of the standard theory. The characterstcs of behavoural experments motvate also the study reported n ths paper vz., the operaton of causal factors other than conformty n the context of the excluson game. The dscusson on theoretcal approaches and modellng prncples contnues to be vvd and also new theoretcal deas and extensons of theores and models appear almost all the tme. Therefore 6
the above account excludes some of these new deas. A recent hybrd model s Trautmann s (007) process farness model combnng process-regardng preferences to the orgnal Fehr-Schmdt model of nequalty averson. Another such model s presented by Charness and Rabn (00) who combne socal welfare preferences and recprocty preferences wth the player s materal preferences to conceptually map the behavoural patterns found n experments. A more radcal vew s that by Gold and Sugden (007) whch outlnes a model for team reasonng n explanng some puzzles of game theory... Process-regardng preferences Lke socal preferences also process-regardng preferences have been known to economsts for a long tme, although they have been almost totally neglected n economsts theores and models. The term process-regardng preferences s here taken to mean that people do not only care about outcomes but they also, and sometmes manly or even exclusvely, value the processes and condtons where the outcomes come about. For example, consder the Machna s mom example ntroduced above. In the example, the mother cares about the farness of the process (of allocatng a candy to one of her two kds) whle the kd who was left wthout a candy consders the outcome farness, and also, f complanng of the way the mother made her decson, also the process farness 6. The relevance of ncludng process-regardng preferences nto the theores of socal preferences s apparent. Indeed, there s a shortage of models that could explan the data that cannot be accommodated by nequalty averson theores or recprocty theores (Sen 997; 000; Frey et al. 003; Bolton et al. 005; Trautmann 007). An llustratve example s provded by Lnd et al. (993; see also Frey et al. 003), who nvestgated a stuaton where ltgants faced a conclaton procedure n the end of whch the court orders an award. The dsputng partes can accept the award or reject t and go to tral. The ltgants therefore balanced nstrumental outcomes of the process aganst the farness of the arbtraton procedure. The result of the nvestgaton was that the ltgants who regarded the conclaton procedure as far were more lkely to accept the court-ordered award (bd.). 6 As for another example, consder Sen s (997, 758-9) Chnese doctor case, where Dr. Chang, who works n a remote rural area n Chna and has one unt of medcne to be gven ether to sck chld A or B. The medcne unt would save A s lfe wth a slghtly hgher probablty than t would save the lfe of chld B. Dr. Chang s most preferred opton s not to make a personal decson that would deny the medcne to one of the two chldren. What would be a proper mechansm or process through whch a far decson s to be made? 7
Another llustratve example of procedural farness concerns the health care ratonng. Thnk about prorty settng decsons whch are made by doctors and health care authortes and the outcomes of whch nfluence patents and publc. Doctors and authortes are here strong actors whose preferences and nteracton determne the outcomes the patents, the weak actors, get from the operaton of the health care organzaton. In Waloo and Anand s (005) survey research the respondents (who represented patents and publc) agreed that procedures are mportant, especally they emphaszed the dea that patents and publc should be consulted before makng health care prorty settngs. Ths suggests that the customers of health care organzatons do not only care about the health consequences of the operaton of the organzatons but also about the farness of the procedures from whch the outcomes come about. By ncludng nto hs vew the dea of conformst preferences and ethcal rules of takng care of also the weak actors n the socety, we come to the followng queston: can the deas of procedural farness and conformst preferences be ncluded nto socety s attempt to desgn nsttutons and organzatons that reflect the preferences of all partes concerned? Furthermore, could the consderaton of processes and conformty brng about better socal benefts than nsttutons and organzatons desgned only by the strong actors? Consder then a more abstract case called a three-person excluson game wth a sharng rule 7. In a basc excluson game two actve players make ther own ndvdual decsons to take a share of the cake. The passve thrd player gets the rest of the cake, possbly nothng. The stuaton rases the followng consderatons: would you take as much as possble wthout thnkng the other two players; or would you guess what the other actve player wll do and do the same; or would you take less to yourself to ensure that the passve thrd player gets somethng? In the game wth a sharng rule, the players frst agree collectvely, and wthout knowng ther roles n the later phases n the game, on a rule accordng to whch the problem of cake-sharng should be solved. Then each player makes her ndvdual decsons n stuatons where each player solves the cake-sharng problem ndvdually wthout any feedback on other s decsons, or possblty to sgnal or negotate. As a player of such a game you probably would lke to draw on the collectvely agreed sharng rule, at least f you expect the others wll do the same. Ths, ndeed, s the contractaran element of the game: are you wllng to follow the rule whch you have jontly agreed wth others? A three-phase excluson game combnes the above sequences: frst, playng the game wthout any explct rule; second, collectvely selectng a rule (and consttutng a socety ); and thrd, playng the game wth the selected rule (n a socety just consttuted). It s hypotheszed that not only () a 7 Ths example conceptually descrbes the experment whch s reported below. In the conceptual descrpton we nvestgate what causal factors would work n such a smplfed stuaton whle n the experment we study, what wll happen when real people behave n such a smplfed but real stuaton. 8
player s belefs of how the other players wll behave (follow the collectvely chosen rule or to devate from t) nfluence on a player's behavour but also () her percepton of the farness of the process of collectvely choosng the rule wll affect on what she beleves the others wll do and on what she herself wll do. As wll be explaned n secton.3, the frst nfluence s added to an ndvdual's utlty functon n the conformst preferences theory by Grmalda and Saccon. The second nfluence s prelmnary explored n subsecton 3.5.3. The dea, that ndvdual behavour s affected by the percepton of the farness of the procedure by whch a group makes ts decson, needs to be theoretcally justfed. At least one should comment on the psychologcal plausblty of the argument. A short justfcaton provded here refers to the orgnal nstrumental value of a partcular procedure whch, however, has transformed durng the (socal) evoluton of the procedure so as to have both an nstrumental and nherent value, and even only an nherent value (Anand 00; see also Sen 997, 749). For example, a con-flppng method has ts orgnal value as a means to make decsons but t also has an nherent farness-value. 8 The general pont, however, s that the concept of procedural farness s observable and falsfable: ts nfluences can be measured and t s possble to fnd stuatons where t does not play a role. 9.3. Conformst preferences theory In the context of socal and economc nteracton conformty refers to one s adjustng to norms, deals, prncples, or standards. That s, shared norms (and ts counterparts mentoned) help us n stuatons where we do not solely, or at all, act to satsfy our desres. A tellng example s the traffc rule sayng that gve way to traffc comng from the rght. 0 Ths rule, when shared by all drvers (and known by pedestrans) coordnates perfectly the traffc at crossroads. The pont s that when you are n a bounded ratonalty stuaton, where you cannot use your computatonal power to form expectatons of what the others wll do (by regressng n the style thnk what others thnk you are thnkng what they are thnkng and so on), the shared norm makes the formng of your expectaton possble. Conformty wth the norm s often a good response for all partcpants of the game and t s often, but not always, secured by laws and nformal rules wth or wthout sanctons (see Bowles 004, 47-48). Bccher (006), for nstance, argues that even f the conformty wth a norm leads to choces that are aganst the person s self-nterest, the person conforms to the norm f () she s aware 8 For example, Pommerehne et al. (997) studed people s atttudes towards varous collectve decson mechansms n a hypothetcal stuaton of placng a nuclear waste repostory. They found that nearly 60% of the respondents were n favor to engneerng mechansm and only 6% to a lottery mechansm. 9 On a more profound account, see Benz (005). 0 Ths example comes from Hargreaves Heap (99). 9
of the norm, () she thnks a suffcent number of other players obey the rule, () other players thnk the person ought to conform or a suffcent number of other players are ready to sancton her for not obeyng the rule. In the traffc rule example above there are clear materal benefts (the avodance of a crash and ts losses) whch gve a reason to a drver to conform the rule. The lterature on why ndvduals devate from the standard theory of ratonal choce, ponts, however, to the fact that very often the devatng behavour s n contrast wth the self-regardng materal preferences of ndvduals. Accordngly, these theores typcally focus on varous socal dlemma stuatons, where ndvduals pursut of self-nterest s contradctory to the common nterest of a group, organzaton or socety. In ths context the role of a rule s contractaran: whch rule should be selected collectvely, and how t should be selected n order to get people to cooperate for mutual beneft. If we assume that ndvduals are ratonal, each player of the game prefers the outcome where her ends are accepted by everyone; but snce ths would usually not lead to an agreement, ndvduals can be seen as wllng to make concessons to reach agreement (Sugden 993). Therefore, ndvduals would trade-off ther own materal payoffs aganst benefts from reachng agreement. These benefts may come from varous sources, such as avodance of penaltes, enjoyment of soldarty, or pleasure of complyng wth a rule and so on. The above account of some dmensons of norms gves a proper background to understand the so called conformst preference theory by Grmalda and Saccon. Grmalda s and Saccon s thrust for ther theory s n combnng a player s ntrnsc motvaton to act accordng to a shared prncple wth the player s consequentalst (selfsh and materal) preferences. They then construct what they call a comprehensve utlty functon where the utlty depends on the player s materal payoffs and the (ds)utlty comng from the degree of one s conformty to a shared prncple. Thus, the utlty functon conssts of a non-consequentalst aspect n the sense that the preference to conform the shared deal need not consult the player s preferences for her materal payoffs. Instead, ones preference to conform s contextual that s, t depends on what the other party expects her to thnk and do. In consequence, the conformst preference theory explans why subjects n an excluson game experment change ther behavour after they have jontly agreed a norm. Ths behavoural pattern s not explaned by the nequalty averson theory or the farness equlbrum theory. Grmalda and Saccon present the general form of ther comprehensve utlty functon as follows : Regardng the role of norms n the self-regulaton by network-effects, see Avram (003). The presentaton of the model follows Saccon and Fallo (005) and Fallo and Saccon (007). 0
V ( σ ) = U ( σ ) λ F[ T ( σ )], where + σ = actons for the players; U (σ ) = player s materal, consequentalst utlty; λ F[ T ( σ )] = player s deal (non-consequentlst) utlty whch reflects s concern to the conformty wth the shared norm n the functon T; λ 0 = weght parameter whch expresses how mportant the conformst component s for ; F = functon whch transforms socal normatve crteron nto ndvdual deal utlty; T = socal welfare functon (takes a value for each state σ ). The authors then present the defnton of T wth a Nash socal welfare functon. The dea n ths defnton s to provde metrcs for calculatng the values of possble states of affars. Ths results n an orderng of the possble states of affars an mpartal spectator would gve on the bass of the socal normatve crteron (also Grmalda and Saccon 005). Furthermore, t s assumed that the orderng s shared by all actors who are nvolved nto the game. The excluson game example makes ths dea more concrete. There players select the socal normatve crteron (the sharng rule) n phase two. Let us smplfy the selecton by assumng that there are two rules, hgh (h, whch means here as much as possble to two actve players ) and low (l, whch means here equal shares to all three players the passve one ncluded ). If the players jontly select the rule low, the rule low serves as the bass of the metrcs calculaton on the grounds of the Nash welfare functon. Ths metrcs then produces the orderng N(l, l) > N(l, h) > N(h, h), where the expressons N(.,.) refer to the values the welfare functon assgns to the actve players strategy choces. (Ths procedure, when appled to the excluson game, yelds the payoff matrx shown n Fgure 4 n secton 3. 3 ) The next step n constructng the model s the defnton of the functon F by usng ndexes of conformty to (two) players. Frst, player s condtonal conformty ndex measures s degree of 3 Formally, T s gven by the Nash socal welfare functon N: T(σ ) = NU (,... UN ) = ( U c ), where c s the = dsagreement utlty resultng from the breakdown n the negotaton. In an excluson game the two actve players and ask ether hgh, d h = R, or low, d l = R 3, where =, and R s the amount of money to be dvded n the game. Hence, the thrd player s payoff s s = R ( d + d), and, n partcular, f both actve l l players ask low, s = R ( d + d) = R 3. By assumng that c = 0, the Nash product yelds the orderng l l h l l h h h dds > d ds = dd s > d d s, based on max l l l l l l () T ( d, d ) = N ( d, d ) = d d R 3, h l h l h l s l h l h () T ( d, d ) = N( d, d ) = d d = N( d, d ) = d d R 6, and mn h h h h h h () T ( d, d ) = N( d, d ) = d d 0 = 0. See the detals n Saccon and Fallo (005). N
devaton from the pure condtonal conformty wth the norm. The ndex, whch vares from 0 (no devaton) to - (maxmal devaton), s defned as follows (Saccon and Fallo 005): max ( T ( σ, ) ( ) b T b f σ, b ) =, where max mn T ( b ) T ( b ) b = player s belef concernng j s choce; T max ( b ) = maxmum attanable value of T gven j s choce accordng to s belef; T mn ( b ) = mnmum attanable value of T gven j s choce accordng to s belef; and T ( σ, ) = actual value of T when chooses strategy σ gven her b belef about j s behavour. In other words, the devaton ndex s composed of the dfference between the value attached to s actual choce n the socal welfare metrcs and the hghest value of the socal welfare metrcs calculated on the bass of collectvely chosen rule scaled by the dstance between the hghest and the lowest welfare metrcs values. Although the selected socal welfare crteron (the sharng rule) was assumed to be shared by all players of the game, the above formula of the condtonalty of an actor s conformty adopts the perspectve of an ndvdual actor. Ths s just the dea that an actor s devaton from the socal welfare crteron reflects how much she wants to generate the fulfllment of the outcome mpled by the crteron, gven the actor s belefs of the other player s choce (see Grmalda and Saccon 005). Second, player j s expected recprocal conformty ndex measures j s degree of devaton from complete recprocty n complyng wth the deal prncple T. Ths vares from 0 (no devaton at all) to - (maxmal devaton). The ndex s seen through player s belefs about j s acton and about her belefs concernng s choce. The ndex s defned as follows: ~ f ( b j, b max T ( b, b ) T ( b ) ) =, where max mn T ( b ) T ( b ) b = player s frst order belef about j s acton, whch s formally dentcal to the strategy of player j; b = player s second order belef about j s belef about the acton of, whch s formally dentcal to s strategy predcted by player j. Also ths formula presents an actor s perspectve to the socal welfare crteron. The formula shows how player sees that the player j thnks about s conformty to the norm. Ths brngs the prncple
of mutualty to the model n that t assumes that an actor s motvaton to comply wth the norm ncreases the closer she thnks the other player comples wth the norm. The condtonalty and recprocty ndexes above are then entered nto the deal component of the utlty functon. Ths s now defned n the followng way: ~ λ [ + f ( b, b )][ + j f ( σ, b )]. Ths defnton states that f player conforms perfectly to the deal and f expects that player j does the same, then the values of the two ndexes are zero. In ths case the resultng utlty value of the deal component s λ. In other words, the player s utlty value s the same as the mportance of the deal component to the player. On the contrary, f the player does not entrely conform and does not expect the player j to conform ether, then both ndexes take negatve values, possbly -, whch yelds a smaller utlty value than λ. Fnally, the comprehensve utlty functon V, consstng of a materal and an deal component, can be wrtten as follows (bd.): ~ V ( σ, b, b ) = U ( σ, b ) + λ [ + f ( b, b )][ + j f ( σ, b )]. Ths functon mples that a player adopts the agreed rule f she expects that the other player acts n the same way. Ths also means that conformst preferences (utlty from conformng) can nduce players to choose strateges they would not choose f they consder ther materal utltes only. The model can be summarsed n the followng way. In the begnnng there s a materal game 4 n whch only the player s own materal payoffs matter. Ths game s adequately captured by a utlty functon consstng only of a player s own consequentalst payoffs. Consder, then, the case that the game has a socal dlemma structure: f the players would contrbute to the common nterest, then everyone would be better off than f everyone only pursues her own self-nterest. Several new components can be added nto the utlty functon to account for the altered structure of the game. The conformst preferences model alters the structure of the game n the followng specfc way. It assumes that an deal game s nvolved wth the materal game n the sense that the nteracton of strong players has nfluences on the weak players who, however, can not partcpate n the actual 4 The terms materal and deal game come from Grmalda and Saccon (005). 3
game as actve players. Therefore a strong player s descrpton of the game now ncludes also a weak player s payoffs and the utlty the strong player derves from the deal component of the utlty functon defned above. In prncple, the normatve crteron T can be any prncple of takng care of other players, especally the weak ones. The model, however, makes a stylsed case by assumng that the players of the game commonly, and as mpartal spectators, select a rule to be shared by all players of the game. In addton, not only the complance to the rule but also players expectatons of others complance enter the pcture as sources of utlty. Recall now the dea of process-regardng preferences ntroduced n secton.. Clearly, such preferences reflect the players acceptance of the procedure by whch the selecton of the rule was accomplshed. In addton, they may have nfluences on the players behavour and belefs and t can be hypotheszed that f a player sees that the selecton of the rule was far (n that t reflects her preferences) t s more lkely that the player conforms to the rule and beleves that the other players also conform to the rule. Ths hypothess s studed n secton 3.5.3 below. 3. Analyss of an exploratve experment 3.. The outlne of the Saccon and Fallo (005) experment and the predctons of the model Saccon and Fallo (005) conducted an excluson game experment to assess emprcally the conformst preferences model. The experment conssted of three phases n the followng way: n phase one the subjects played three rounds of excluson game wth a reassgnment of the player roles n the begnnng of each round; n phase two the subjects were dvded nto three-member groups and each group voted the sharng rule accordng to whch the sum of money ( euros) should be dvded; n phase three the excluson game was agan played n two rounds and the actve players made publc predctons of the other player s behavour just before ther own choce. Fgure. The excluson game payoff matrx (Saccon and Fallo 005) G 3 4 6 3 3, 3, (6) 3, 4, (5) 3, 6, (3) G 4 4, 3, (5) 4, 4, (4) 4, 6, () 6 6, 3, (3) 6, 4, () 6, 6, (0) 4
The expermental excluson game payoff matrx s shown n Fgure. Two actve players (G and G) make ther own decsons and the passve player (G3) gets the sum whch depends on what the actve players decde. Fgure 3. Sharng prncples and rules n the SF experment (bd.) Prncples Rules Prncple Every player should share the benefts, n partcular, who has not the possblty to choose should not receve less than the others. G G G3. 33 % 5 % 4 %. 5 % 33 % 4 %.3 33 % 33 % 33 % Prncple. People who play under a decsonal role could clam a hgher share of benefts. G G G3. 50 % 33 % 7 %. 33 % 50 % 7 %.3 50 % 50 % 0 % In votng the sharng rule the subjects voted one of two general prncples and among sx specfc sharng rules derved from the prncples (Fgure 3.). In the votng procedure the anonymty was mantaned and no communcaton among subjects was allowed. Fgure 4. Payoff matrx when the conformst preference model s appled (bd.) 3 G 4 6 G 3 3, 3 3+ 3 3 λ, 4+ λ 3, 6 4 4 4+ 3 λ, 3+ 3 λ 4+ λ 4, 4+ λ 4, 6 6 6, 3 6, 4 6, 6 Fgure 4 s based on the conformst preferences model and the socal welfare metrcs explaned n secton.3. It shows the ndvdual comprehensve utlty values for the excluson game payoff matrx n Fgure, on the condton that n each state the player s belefs recprocally predct the strategy chosen by the opponent. The dagnoss of the game goes now as follows: () f λ > 6-4 = then player one prefers, n terms of her comprehensve utlty functon, strategy ask for 4 to strategy ask for 6 as well as player two; we can defne that the combnaton ask for 4, ask for 4 s a psychologcal equlbrum f λ > ; 5
() f player one beleves that player two does not choose accordng to the shared prncple, she does the same and player two decdes symmetrcally so that both choose ask for 6 ; we can defne that the combnaton ask for 6, ask for 6 s also a psychologcal equlbrum. Saccon and Fallo then produce the followng predctons of ther model 5 : () Because the possbly nnate conformst preferences are nactve n phase one of the game almost all players choose ask for 6 ; () A sgnfcant part of subjects choose the sharng rule that assgns equal payoffs to all three players; (3) After havng selected the sharng rule, a sgnfcant number of players generate expectaton of recprocal conformty and choose accordng to t; (4) A sgnfcant part of players choose ask for 4 ; (5) Informaton that confrms belefs about conformty of others does not change the wllngness to conform. Saccon and Fallo found evdence n support of the conformst preferences model. As they argue, not only the fact that the players changed ther behavour between the phases one and three, but also the fact that many players expressed the same strategy choce between the phases, s consstent wth ther theory (gven ther choce n phase two and ther belefs). In other words, the latter fact does not serve as an anomaly of the theory. But, as we shall see, ths s not the whole story. The ntroducton of dfferent collectve decson-makng mechansms nduces some dfferences n the behavour of subjects n the experment. 3.. An exploratve experment: desgn and ts evaluaton The exploratve experment, whch ths paper s based on, was conducted n January 008 at the Unversty of Joensuu (hereafter J08 experment). The desgn of the experment reproduces the man structure of the Saccon-Fallo experment (hereafter SF experment) but t also extends t by varyng the procedures wth the help of whch the collectve decsons were carred out. 5 As notced n secton.3, the nequalty averson theory by Fehr and Schmdt and the farness equlbrum theory by Rabn do not predct correctly n the context of the excluson game. That s, both of them predct (although for dfferent reasons), that the players choose ether ask 4 or ask 6 both n phase one and n phase three. 6
Fgure 5. Outlne of SF and J08 experments and of ther comparson SF experment: J08 experment NrOXrO O b NrOXrO NrOXrO NrOXrO O a In Fgure 5 above N refers to non-randomzed assgnment of subjects to the treatment group (snce there s only the treatment group). The Os n the fgure ndcate that certan varables are measured both before the treatment (X) and after the treatment. The small letters r, n turn, refer to the fact that the consttuton of the sub-groups was randomsed before each observaton. The symbols O b and O a refer to measurements done before and after the actual excluson game experment. In SF experment there was one treatment and one measurement before and one measurement after the treatment. The J08 experment, on the other hand, adds two more treatments. In addton, t ncorporates measurements before the excluson game experments and after these. The whole experment conssted of three stages and stage two conssted of three sessons (Fgure 6.) Fgure 6. Structure of the experment Stage one Stage two Sesson one Sesson two Sesson three Lottery Majorty votng Negotaton Stage three O N O X O N O X O N O X O O Dctator game Secure game Three rounds before he treatment Three rounds after the treatment As n sesson one As n sesson one and two Evaluaton tasks It s also worth of notcng that none of the three treatments n J08 are dentcal to the SF treatment. In other words, when SF employed the three-person group unanmty votng procedure n selectng the sharng rule, J08 made use of the followng three procedures: () lottery, () a whole-group majorty votng and () a three-person group negotaton 6. The desgn allows the constructon of several derved varables, such as dstrbuton of payoffs, dfferences between choces before and after the treatment, and dfferences between the sharng rule payoff and a players choce. Although the sample sze s small (8 subjects/36 54 choces) due to the prelmnary nature of the experment, some qualfed results can be reported from the 6 Before negotaton, the subjects were dvded nto three-person groups. Each group negotated wthn the group and selected the sharng rule. No nformaton on the outcomes of the negotaton was dstrbuted to other groups. After the negotaton, the same groups played the excluson game and the roles of the players wthn the group were changed between each round. 7
experment. Although exact statstcal tests correct the bases the sparse and unbalanced data may cause n the use of asymptotc tests, t can not be ruled out that another sample of subjects would possbly produce dfferent results. The expermental desgn rases the queston of unwanted maturaton effects. Ths means that when the subjects enter n sesson two (and three, respectvely) they already are affected by the treatment n sesson one (and two). Table shows that the possblty of these effects cannot be ruled out: the choces labelled E ( equty-orented, that s, choce values up to 4) progress n an ascendng way n before treatments choces,, and 3, whle choces labeled S ( self-nterest-orented choces, namely choces 5 and 6) progress n a descendng way. However, the Cochran exact test sees no statstcally sgnfcant dfferences n the before-treatment choces between the sessons (p =.48). The same holds for the after treatment choces (p =.84). On the other hand, the ch-square test shows that although the choce dstrbutons n the after-treatment choces n sesson one and n the before-treatment choces n sesson two are dfferent and skew to opposte drectons, the dfference s not statstcally sgnfcant (p =.06). The same holds between the after-treatment choces n sesson two and the before-treatment choces n sesson three (p =.36). Snce maturng effects are obvous, at least n the sense that the end of a sesson s too smlar to the begnnng of the next sesson, we must keep n mnd that these effects may ncrease the occurrences of the behavoral patterns predcted by the conformst preferences theory. At the same tme, the maturng effects may obscure the effect-sze that can be leveled aganst each treatment. Table. Evaluaton of the maturng effects Frequences p-values E S Ch-Square Ch-Square Cochran Cochran Exact.06 Exact.36 Exact.48 Exact.84 Before treatment 4 X After treatment 5 X X Before treatment 5 X X After treatment 5 X X Before treatment 3 7 9 X X After treatment 3 9 7 X It s also worth of notcng that the treatment n sesson three (group-negotaton) was substantally dfferent from the other two treatments. The treatment allowed that each group selected a sharng rule of ts own. In consequence, there emerged selectons of the actve players dvde the whole cake rule, whch meant that also the number of choces labelled S ncreased from the conformst reasons and not (maybe) from the maturng effects. 8
3.3. Hypotheses The man purpose of the experment was to fnd out whether the dfferent collectve decsonmakng procedures have dfferent nfluences on the behavour of subjects. As was suggested n the theoretcal secton of the paper, t s reasonable to argue that dfferent procedures work dfferently and gve brth to dfferent stuaton-specfc perceptons of farness. Hence, we can set the followng two hypotheses: () Although the subjects stll exhbt conformst motvatons, there are dfferences n how many decsons are changed when moved from the before treatment to the after treatment phase; () The subjects perceptons of the farness of the selecton procedures matter; n partcular, f a subject sees that her own preferences are taken nto account, she s more lkely to conform to the selected rule than otherwse. 3.4. Expermental procedures The subject pool of the experment conssted of the students n the faculty of Busness, Law and Economcs at the Unversty of Joensuu. The subjects, 8 n total, were recruted by an e-mal message. Subjects were pad 5 euros for partcpaton and up to ten euros accordng to ther decsons n the experment. The experment sessons were run manually and the whole experment lasted approxmately 45 mnutes. Subjects were gven the nstructons (ncludng the nformaton n Fgure and Fgure 3) before the experment. The progress of the experment was conducted by the expermenter by usng sldes and by dstrbutng separate answerng sheets n stages. The frst stage of the experment conssted of a dctator game and a secure game (see Appendx.). In each man sesson n the experment a subject played the excluson game for sx rounds three rounds before the treatment and three rounds after the treatment. The total number of rounds n stage two was eghteen. The subjects were told, that for each subject one round was selected at random and subject earnngs were derved from t. Regardng stage one, t was told that for each task separately, one of the subjects was selected at random for payng for real. In the excluson game sessons the subjects were assgned to three-member groups before every three-round set. The roles of the players changed so that each player took each of the roles G, G, and G3 n turn. In fve out of sx three-round sets the group membershp was anonymous. That s, 9
although the subject knew her group label n each three-round set, she ddn t know who the other members n the group were. In the last three-round set the subjects knew the other members n the group as the treatment was based on face-to-face negotaton wthn each group. The treatments n stage two were conducted n the followng way. In the frst sesson the subjects were told that one of the sx sharng rules n Fgure 3 wll be selected at random by throwng a dce. The dce was thrown by the expermenter, and the outcome was announced for the subjects. In the second sesson the subjects were nvted to vote for the sharng rule. Before votng t was told that the 50% majorty rule wll be appled and that new rounds of votng wll be conducted untl the result fulfls the majorty condton. The votng was carred out by a secret ballot procedure and the wnnng rule, as well as the scores of the alternatves, was announced to the subjects. In the last treatment based of group-negotaton the subjects were frst gven ther group symbols and then nvted to stand up and to search the group co-members and to negotate and select the sharng rule together. Table shows the dstrbuton of votes n the second sesson and the dstrbuton of the group-negotated selectons n the thrd sesson. Table. Votes n sesson two and selected rules n sesson three Sesson two: majorty votng Sesson three: group negotaton Sharng rule (fgure 3) Frequency Percent Frequency Percent (..) (..) 3 (.3) 4 (..) 5 (..) 6 (.3.) - 0-6 - 5,6 55,6-5,6 33,3 - - 5 - - 3 - - 83,3 - - 6,7 Total 8 00 8 00 3.5. Results 3.5. Choce dstrbutons The J08 experment replcated the major outcomes of the SF experment. The bar charts n Fgure 7 show that the dstrbutons of payoffs changed both when moved wthn the sesson (from decsons before to decsons after the treatment) and between the sessons. We can see that n all rounds before the treatment the mode value was sx (euros) but after the treatment four (euros). Ths ndcates, f only at a very general level, that the shft n the behavour of players wthn each sesson was to the drecton predcted by the conformst preference theory. It s worth of notcng, however, 0
that the bar charts below nclude also the payoffs of the passve players. These are accumulated on the low values of horzontal axs and also on value four but not on value sx. (%) Before treatment 60 After treatment 50 Lottery selecton Majorty votng Group-negotaton 40 30 0 0 0 L0 L L L3 L4 L5 L6 V0 V V V3 V4 V5 V6 N0 N N N3 N4 N5 N6 Payoffs Fgure7. Players choces n the experment 3.5. Behavoural patterns and effect-sze evaluaton Fgure 8 shows the percentage values of the after-treatment behavoural patterns n dfferent sessons. Our focus s here on conformst patterns, whch are defned as rule-choce-expectaton patterns (RCEs, n short) that fulfl the followng condton: R = C = E 7, where R refers to the payoff mpled by the agreed rule, C to the payoff related to the strategy chosen and E to the other player s payoff due to her expected acton. Defned n ths way, there are two conformst patterns n our data. The frst one occurs when the jontly agreed rule s the equalsplt rule and a player s strategy choce and expectaton concde wth the rule. The second conformst pattern occurs, when the players agree on the rule called two actve players dvde the whole cake, and a player s strategy choce and expectaton concde wth the rule. Let us label the former one R es and the latter one R us. In the J08 experment, the R us = C = E patterns occurred only n sesson 3 (wth the group-negotaton procedure). 7 One can read ths conformer s reasonng n the followng way: My choce pays me out the same amount of money that pays out the choce I expect my opponent player wll make and, n addton, ths amount of money equals the payoff mpled by the sharng rule I and my co-player(s) have selected.
(%) 60,0 50,0 40,0 30,0 0,0 0,0 0,0 5,8 Lottery slecton Majorty votng Group-negotaton 4,7 30,6 5,0 5,0,,, 6,7,, 8,3 5,6 0,0 0,0 0,0 0,0,8 Res=C=E Rus=C=E R<C>E R=C<E R=C>E R<C=E Res=C=E Rus=C=E R<C>E R=C<E R=C>E R<C=E Res=C=E Rus=C=E R<C>E R=C<E R=C>E R<C=E Patterns Fgure 8. RCE-patterns n dfferent sessons One man concern of the expermental analyss was the number of decsons that changed between the before-treatment and after-treatment choces. Related to ths, the frst hypothess n secton 3.3 suggested that there are dfferences between the treatments. The McNemar test was performed to study the dfference between before-treatment and after-treatment behavour. The dfference s sgnfcant only n the case of the lottery-treatment (p =.006). The dsappearance of the sgnfcance n the other two treatments s a lkely result of the unwanted maturaton effects mentoned n secton 3.. Accordngly, as Fgure 9 shows, the number of equty-orented choces ncreases n the beforetreatment phases when movng from sesson one to sessons two and three. A straghtforward (but statstcally debatable) nterpretaton of the McNemar test ndcates the followng effect-szes 8 : Lottery treatment: 4,7 (%) Majorty votng treatment: 47,6 (%) Group negotaton: 6,5 (%) The effect szes above should be taken wth reservatons, snce the obvous maturng effects decrease the row sum of cells c and d (see footnote 8). Note also, that the group-negotaton procedure allowed the agreement on the group-specfc sharng rule. Indeed, one group agreed on the rule.3 (the actve players dvde the cake and the passve player gets nothng). The choces of ths group are removed from the effect-sze calculaton. 8 There s no standard measurement of the effect-sze n McNemar test. The effect-sze e s here calculated from the formula e = c/(c + d)x00 when the x table s: a b c d
After Before E S E S 0 4 McNemar p =.006 Lottery selecton procedure After Before E S E 4 S 0 McNemar p =.090 Majorty votng procedure After Before E S E 4 3 S 5 4 (6)* McNemar p =.363 Group negotaton procedure *The fgure n the brackets shows the number of S-choces by players who agreed on the.3. rule n ths sesson. Fgure 9. Comparson of equty-orented (E) and self-nterest-orented (S) dstrbutons of choces before and after the sharng rule selecton Taken together, the analyss of conformst patterns and the evaluaton of the effect-szes suggest that the porton of conformst patterns ncreased when movng from sesson one to sessons two and three. In addton, the effect-sze ncreased respectvely (although only symptomatcally). There can be (at least) two reasons to ths: maturaton effects and procedural farness consderatons. Maturaton effects are obvous, especally the effects of nformaton spreadng, snce the majorty votng procedure revealed nformaton on how the votes on the sharng rules were dstrbuted. As wll be shown n subsecton 3.5.4, the relaton between the behavour n the dctator game (and the secure game) and the behavour n the excluson game changed substantally after the completon of the majorty votng procedure. The expermental desgn does not allow, however, a closer analyss of the nformaton effects. Instead, the nfluence of farness perceptons s analyzed below. 3.5.3 The nfluence of farness perceptons The second hypothess n secton 3.3 suggests that f a player sees that the procedure of jontly selectng the sharng rule s far, she s more lkely to exhbt conformst preferences than otherwse. Ths means that a player s farness percepton nfluences on what she beleves the others wll do and on what she herself wll do. Ths was nvestgated by measurng the subjects perceptons by two devces vz. by a questonnare type Lkert scale measurement and by the so called IOS scale (Incluson of Other n the Self scale). The Lkert-scale measurement was appled by askng the subjects to ndcate whether they thnk a gven procedure was very far, far, unfar, or very unfar. The tems whch they were asked to rank were dfferent decson procedures n general (lottery, negotaton, majorty votng, and expert system) and the decson procedures used n the experment. The IOS-scale, on the other hand, measures the subject s concepton of her standng relatve to the other partcpants n the decson-makng (see De Cremer et al. 005). The method s based on the dea that a subject s gven dfferent descrptons of her standng wth the help of 3