Social Image and the 50-50 Norm :A T h e o r et ica l a n d Ex pe rimenta l An a ly sis o f A u dien c e Effects∗James A ndreoni, University of California, San DiegoB. Douglas Bernheim, Stanford Univ ersity and NBERApril 6, 2009AbstractA norm of 50-50 division appears to have considerable force in a wide range ofeconomic environments, both in the real w orld and in the laboratory. Even in settingswhere one party unilaterally determines the allocation of a prize (the dictator game),many subjects voluntarily cede exactly half to another individual. T he hypothesis thatpeople care about fairness does not by itself account for key experiment al patterns.We consider an alternative explanation, which adds the hypothesis that people liketo be perceived as fair. The properties of equilibria for the resulting signaling gamecorrespond closely to laboratory observations. The theory has additional testableimplications, the validity of which we confirm through new experiment s.∗We are indebted to the following people for helpful comments: Iris Bohnet, Colin Camerer, NavinKartik, Antonio Rangel, three anonymous referees, and seminar participants at the California Institute ofTechnology, NYU, and Stanford University’s SITE workshop in Psychology and Economics. We acknowledgefinancial support from the National Science Foundation through grant numbers SES-0551296 (Andreoni),and SES-0452300 (Bernheim).Forthcoming, Econometrica, 2009.1 IntroductionEqual division of monetar y rew ar ds and /o r costs is a widely observed beha viora l norm . F ifty-fifty sharing is commo n in the con te xt of joint ventures among corporations (e.g. Veuglers andKesteloot [1996], Dasgu p ta and Tao [1998], and Hauswald and Hege [2003]),1share tenancyin agriculture (e.g. De Wea ver and Roum a sset [2002], Agraw al [2002]), and bequests toc h ildren (e.g. Wilhelm [1996], Menchik [1980, 1988]). “Splitting the difference” is a frequentoutcome of negotiation and conven tiona l arbitration (Bloom [1986]). Business partners oftendivide the earnings from join t projects equally, friends split restaurant tabs equally, and theU.S. go vernment splits the nominal burden of the payroll tax equally between employers andemployees. Complian ce with a 50-50 norm has also been duplicated in the laboratory. E venwhen one party has all the bargaining pow er (the dictator game), ty pica lly 20 to 30 percentof subjects v olun tarily cede half of a fixed pa yoff to another individual (Camerer [1997]).2Our object is to develop a theory that accounts for the 50-50 norm in the dictator game,one w e hope will prove applicable more generally.3Experimental evidence sho w s that asignificant fraction of the population elects precisely 50-50 division ev en when it is possibleto give sligh tly less or slightly more,4that subjects rarely cede more than 50% of the aggregatepa y off, and that there is frequently a trough in the distribution of fractions ceded just below50% (see, e.g., Forsythe et al. [1994]). In addition , choices depend on observability: greateranonymityforthedictatorleadshimtobehavemoreselfishly and w eakens the norm,5as dotreatments that obscure the dictator’s role in determining the outcome, or that enable himto obscure that role.6Agoodtheoryofbehaviorinthedictatorgamemustaccountforall1Where issues of control are critical, one also commonly sees a norm of 50-plus-one-share.2The frequency of equal division is considerably higher in ultimatum games; see Camerer [2003].3Our theory is not necessarily a good explanation for all 50-50 norms. For example, Bernheim andSeverinov [2003] propose an explanation for equal division of bequests that involves a differen t mechanism.4For example, according to Andreoni and Miller [2002], a significant fraction of subjects (15 to 30%)adhered to equal division regardless of the sacrifice to themselves.5In double-blind trials, subjects cede smaller amounts, and significantly fewer adhere to the 50-50 norm(e.g. Hoffman et al. [1996]). However, when dictators and recipients face each other, adherence to thenorm is far more common (Bohnet and Frey [1999]). Andreoni and Petrie [2004] and Rege and Telle [2004]also find a greater tendency to equalize payoffs when there is an audience. More generally, studies of fielddata confirm that an audience increases c haritable giving (Soetevent [2005]). Indeed, charities can influencecontributions by adjusting the coarseness of the information provided to the audience (Harbaugh [1998]).6See Dana, Cain, and Dawes [2007], Dana, Weber, and Kuang [2007], and Broberg, Ellingsen, Johannesson1these robust patterns.The leading theories of behavior in the dictator game invok e altruism or concerns forfairness (e.g., Fehr and Schmidt [1999], Bolton and Ockefels [2000]). O ne can reconcilethose hypotheses with the observed distribution of choices, but only by making a w kward as-sumptions — for example, that the utility function is fortuitously kink ed, that the underlyingdistribution of preferences con tains gaps and atom s, or that dictators are boundedly ratio-nal. Indeed , with a differen tiable utility function, the fairness hypothesis cannot explainwh y anyone w ou ld choose equal division (see Section 2, below ). Moreover, neither altruismnor a preference for fairness explain s why observability, and hence audiences, play such animportant role in determining the norm’s strength.This paper explores the im plica tion s of supplementin g the fair ne ss hy pothesis with anadditional plausible assumption : people lik e to be perceiv ed as fair. We incorporate that de-sire directly into the utility function; alternativ ely, one could depict the dictator’s preferenceas arising from concerns about subsequen t interactions.7Our model giv e s rise to a signalinggame wherein the dictator’s choice affects others’ inferences about his taste for fairness. D ueto an in trinsic failure of the single-crossing propert y, the equilibriu m distribution of transfersreplicates the choice patterns listed abo ve: there is a pool at precisely equal division, andno one giv es either more or slightly less than half of the prize. In addition, consistent withexperimental findings, the size of the equal division pool depends on the observability of thedictator’s c h oice. T hus, while our theory does leave some experimental results unexplained(see, e.g., Oberholzer-Gee and Eic henberger [2008], or our discussion of Cherry et al. [2002]in Section 2), it nevertheless