A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas visit our wbsit at http://businss.mit.du or contact th Cntr dirctly at businss@mit.du or 67-53-754
Analyzing th conomic fficincy of Bay-lik onlin rputation rporting mchanisms Chrysanthos Dllarocas Sloan School of Managmnt Massachustts Institut of Tchnology Cambridg, MA 39, USA dll@mit.du Abstract This papr introducs a modl for analyzing marktplacs, such as Bay, which rly on binary rputation mchanisms for quality signaling and quality control. In our modl sllrs kp thir actual quality privat and choos what quality to advrtis. Th rputation mchanism is primarily usd to induc sllrs to advrtis truthfully. Buyrs bas thir ratings on th diffrnc btwn xpctd and actual quality. Furthrmor, ratrs ar lnint and do not post ngativ ratings unlss transactions nd up xcptionally bad. It is shown that, in such a stting, th fairnss of th markt outcom is dtrmind by th rlationship btwn rating lnincy and corrsponding strictnss whn assssing a sllr s fdback profil. If buyrs judg sllrs too strictly (rlativ to how lnintly thy rat) thn, at stady stat, sllrs will b forcd to undrstat thir tru quality. On th othr hand, if buyrs judg too lnintly thn sllrs can gt away with consistntly ovrstating thir tru quality. An optimal judgmnt rul, which rsults in outcoms whr, at stady stat, buyrs accuratly prdict th tru quality of sllrs, is thortically possibl to driv for all lnincy lvls. Furthrmor, if buyrs judg sllrs using that rul, thn th mor lnint buyrs ar whn rating sllrs, th mor likly it is that sllrs will find it optimal to sttl down to stady-stat quality lvls, as opposd to oscillating btwn good quality and bad quality. Howvr, it is argud that this optimal rul dpnds on svral paramtrs, which ar difficult to stimat from th information that Bay currntly maks availabl to its mmbrs. It is thrfor qustionabl to what xtnt unsophisticatd buyrs ar currntly using Bay fdback information in an optimal way. This is work in progrss. Suggstions and commnts vry wlcom. Plas addrss corrspondnc to dll@mit.du
. Introduction Onlin rputation rporting systms ar mrging as an important quality signaling and quality control mchanism in onlin trading communitis (Kollock 999; Rsnick t. al. ). Rputation systms collct fdback from mmbrs of an onlin community rgarding past transactions with othr mmbrs of that community. Fdback is analyzd, aggrgatd and mad publicly availabl to th community in th form of mmbr fdback profils. If on accpts that past bhavior is a rlativly rliabl prdictor of futur bhavior, thn ths profils can act as a powrful quality signaling and quality control mchanism, ssntially acting as th digital quivalnt of a mmbr s rputation. Bay rlis on its rputation mchanism almost xclusivly in ordr to both produc trust and induc good bhavior on th part of its mmbrs. Bay buyrs and sllrs ar ncouragd to rat on anothr at th nd of ach transaction. A rating can b a dsignation of prais, complaint or nutral, togthr with a short txt commnt. Bay maks th sums of prais, complaint and nutral ratings submittd for ach mmbr, as wll as all individual commnts, publicly availabl to all its usrs. Ancdotal and mpirical rsults sm to dmonstrat that Bay s rputation systm has managd to provid rmarkabl stability in an othrwis vry risky trading nvironmnt (Dwan and Hsu ; Rsnick and Zckhausr ). Th rising practical importanc of onlin rputation systms not only invits but rathr ncssitats rigorous rsarch on thir functioning and consquncs. Ar such mchanisms truly rliabl? Do thy promot fficint markt outcoms? To what xtnt ar thy manipulabl by stratgic buyrs and sllrs? What is th bst way to dsign thm? How should buyrs (and sllrs) us th information providd by such mchanisms in thir dcision-making procss? This is just a small subst of unanswrd qustions, which invit xciting and valuabl rsarch. Th study of rputation as a mchanism for inducing good bhavior in markts with asymmtric information is crtainly not nw. Svral conomists hav publishd important works analyzing its proprtis (Rogrson, 983; Schmalns, 978; Shapiro, 98; Smallwood and Conlisk, 979; Wilson, 985, just to nam a fw). Nvrthlss, although past work in conomics has studid som of th ovrall ffcts of rputation, it has paid vry littl attntion to th analysis of spcific mchanisms for forming and communicating rputation, in part bcaus in traditional brick and mortar socitis such mchanisms ar largly informal (thy ar oftn rfrrd to as word-of-mouth advrtising ) and dfy dtaild modling. Th fw publishd rsults focusing on th ffcts of spcific proprtis of rputation mchanisms clarly mak th point that such proprtis can hav significant ffcts on th markt outcom. For xampl, Rogrson (983) shows that rputation basd on subjctiv binary ratings (.g. good/bad, prais/complaint) crats an xtrnality, which affcts th ntir markt. Shapiro (98) shows that, unlss th mchanism by which rputation is formd satisfis crtain proprtis, sllrs may find it optimal to continuously oscillat in quality, priodically building good rputation and subsquntly milking it. On th othr hand, th dsign and implmntation of onlin rputation systms has so far bn th rsarch domain of computr scintists (s Brs t. al., 998; Sarwar t. al., ; Schafr t. al. for ovrviws of past work). Th mphasis of past work in th ara has bn on dvloping algorithms and systms for collcting, aggrgating and xtracting usful information from sts of usr ratings, drawing from work in information rtrival, data mining and collaborativ filtring. Th analysis and valuation of th proposd algorithms is typically don in trms of computational complxity and statistical mtrics, such as thir running tim, mmory rquirmnts, avrag rcall and prcision, avrag bias, tc. W bliv that thr is a nd for work that bridgs th two disciplins: rsarch, which taks into account th algorithmic dtails of spcific rputation systms but also modls how ths systms ar mbddd insid trading communitis and invstigats thir ffctivnss and impact, not only in trms of computational and statistical proprtis, but rathr in trms of thir ovrall impact in th fficincy of th markt and th wlfar of th various classs of markt participants. Givn that rputation systms wr concivd in ordr to assist choic in nvironmnts of imprfct information, thir impact in thos lattr
markt dimnsions should b th ultimat dtrminant of succss of any nw proposd nw algorithm and systm. This papr contributs in this dirction by proposing a modl for analyzing th conomic fficincy of binary rputation systms, such as th on usd by Bay. Sction introducs th modl and its undrlying assumptions. W assum that buyr satisfaction on Bay is a function of th diffrnc btwn th advrtisd and tru quality of an itm. In such a stting, th rputation mchanism is primarily usd to induc sllrs to advrtis truthfully. Sction 3 formalizs this intuition into a numbr of proprtis that Bay-lik rputation mchanisms should satisfy, in ordr to b considrd wll functioning. Sction 4 applis our modl in ordr to dtrmin undr what circumstancs such mchanisms can indd b wll functioning. It is shown that th fairnss of th markt outcom is dtrmind by th rlationship btwn rating lnincy and judgmnt strictnss whn assssing a sllr s fdback profil. An optimal judgmnt rul, which rsults in outcoms whr, at stady stat, buyrs accuratly prdict th tru quality of sllrs, is thortically possibl to driv for all lnincy lvls. A rathr surprising conclusion of our analysis is that, if buyrs us this optimal judgmnt rul, thn th mor lnint buyrs ar whn rating sllrs, th mor likly it is that sllrs will find it optimal to sttl down to stady-stat quality lvls, as opposd to oscillating btwn good quality and bad quality. In that sns, ratr lnincy bnfits th ovrall stability of th systm. Howvr, it is argud that this optimal rul dpnds on svral paramtrs, which ar difficult to stimat from th fdback information that Bay currntly maks availabl to its mmbrs. It is thrfor qustionabl to what xtnt unsophisticatd buyrs ar currntly using Bay fdback information in an optimal way. Sction 5 considrs th implications of rlaxing som of th simplifying assumptions on which our analysis is basd. Finally, Sction 6 summarizs th contributions and conclusions of th papr.. A modl of rputation-mdiatd marktplacs with binary fdback This sction introducs a modl for analyzing marktplacs, which rly xclusivly on a binary rputation mchanism for quality signaling and quality control. A binary rputation mchanism is a mchanism whr ratrs ar givn th opportunity to rat past transactions using on of two valus, commonly intrprtd as positiv (i.. satisfactory) and ngativ (i.. unsatisfactory, problmatic). Our intntion is to us this modl in ordr to study th conomic impact of rputation mchanisms similar to th on usd by Bay (s Rsnick and Zckhausr for a dtaild dscription). In our modl, qualitis ar non-ngativ ral-valud quantitis, which subsum aspcts of both product quality and srvic quality. W assum that ach sllr producs itms, whos ral quality q is unknown to buyrs and can only b dtrmind with accuracy aftr consumption. W furthr assum that all buyrs prfr highr quality to lowr quality, although thy might diffr in th xtnt to which thy ar prpard to pay for an xtra unit of quality. Finally, w assum that although th ral quality of itms is not communicatd to buyrs, sllrs do inform buyrs by advrtising. On Bay, advrtising corrsponds to th sllr-supplid dscription, which accompanis all itms. Th advrtisd quality of an itm is compltly controlld by th sllr (i.. thr is no validation of any kind by a third party) and may or may not corrspond to its ral quality. q a r In addition to positiv (prais) and ngativ (complaint) ratings, Bay s rputation mchanism also supports nutral ratings (which, howvr, ar rarly usd in actual practic). As will bcom apparnt blow, our modl subsums ratrs who would submit nutral ratings on Bay into th st of ratrs who don t submit any rating at all.
Sllrs aims to maximiz th prsnt valu of thir payoff function π ( x, q, q ) = G( x, q, q ) c( x, q ) r a r a r whr x is th volum of sals, G(.) is th gross rvnu function and c(.) is th cost function. W assum that c / q and π / q for all sllrs. r a Undr th abov assumptions, sllrs hav an incntiv to ovr-advrtis quality. Th markt would thn dgnrat to a markt for lmons (Akrlof 97). In ordr to avoid this from happning, buyrs ar givn th option to rat ach transaction using a positiv or ngativ rating. A rputation systm, opratd by a trustworthy third party, accumulats all ratings into a fdback profil R Σ, Σ, ) for ach sllr, whr Σ is th sum of all positiv ratings rcivd for that sllr during th most rcnt tim window, and = ( Σ no rating Σ no rating Σ is th sum of all ngativ ratings rcivd during th sam priod is th numbr of transactions for which no rating was submittd. Tim windowing is usd in ordr to addrss th possibility that sllrs may improv or dtriorat thir bhavior ovr tim. For xampl, on Bay, fdback profils display th sums of ratings rcivd during th past 6 months only. Buyr utility from purchas of a singl itm is modld by U =θ q p, whr p is th pric, θ is a buyr s quality snsitivity and q is th lvl of quality prcivd by th buyr aftr consumption. Whn considring a purchas, buyrs combin all th information that is availabl to thm, i.. an itm s advrtisd quality and a sllr s fdback profil, in ordr to form a subjctiv assssmnt of an itm s stimatd quality, whr: q q = f (, R) q a () Armd with knowldg of prics and stimatd qualitis, buyrs procd to purchas on of th availabl itms, prsumably th on which maximizs thir xpctd utility U = θ p. Following a purchas, buyrs obsrv th itm s prcivd quality q = q r q ε, whr ε is a normally distributd rror trm with standard dviation σ. Th introduction of an rror trm is intndd to collctivly modl a numbr of phnomna, which occur in actual practic. For xampl: buyrs may misintrprt a sllr s advrtisd quality (this should b modld as q q ε, howvr, our analysis is idntical if w add th rror trm to q instad) sllrs may xhibit small variations in actual quality from on transaction to anothr buyrs may hav small diffrncs in thir prcption of quality basd, say, on thir moods that day som aspcts of prcivd quality dpnd on factors byond a sllr s control (.g. post-offic dlays) Finally, buyrs dcid whthr to rat a transaction as wll as what rating to giv. Our modl assums that ratings ar a function of a buyr s satisfaction rlativ to hr xpctations. W dfin a buyr s satisfaction from a givn transaction to b th diffrnc btwn prcivd and xpctd utility. That is, S U U = θ ( q q ε). Undr th abov assumptions, S is a normally distributd random variabl = r ( r with man θ q q ) and standard dviation θ σ. On intrsting proprty of Bay, which has bn rportd on svral mpirical studis, is that most buyrs giv vry fw ngativ ratings to sllrs. Rsnick and Zckhausr () rport that lss than.5% of buyrs and.% of sllrs post nutral or ngativ fdback about thir trading partnrs (s Figur ). Thy tntativly conclud that ratrs ithr rat gnrously or prfr to rfrain from rating at all aftr bad xprincs. = a Bay dos not currntly publish Σ no rating. Th rsults of this papr mak a strong cas that thy should.
Buyr of Sllr Sllr of Buyr Frquncy Prcnt Frquncy Prcnt Ngativ.3 353. Nutral 6. 6. Positiv 8,569 5.,56 59.5 Non 7,49 48.3 4,6 39.4 Total 36,33 36,33 Figur : Frquncis of fdback in Rsnick and Zckhausr s data st. Rsnick and Zckhausr () rfr to this phnomnon as a high courtsy quilibrium and offr svral spculativ xplanations: Bay allows rciprocal ratings (that is, sllrs also rat buyrs) and buyrs ar oftn afraid that posting a ngativ rating for a sllr will lad to rtaliatory bad ratings, harassing mails tc. Bay dos not provid mchanisms to prvnt or assist such situations. Furthrmor, it has bn rportd that sllrs oftn communicat with buyrs via mail and ngotiat sttlmnts to transaction problms, whil xplicitly plading with thm to not post ngativ ratings. Finally, Bay has cratd a cultur of prais, whr th vast majority of ratings and commnts ar xtrmly positiv. In such a stting, most buyrs fl a moral obligation to conform to th prvailing social norms and b nic and rlativly forgiving to thir trading partnrs. Our modl uss a rating function r(s), which attmpts to modl th abov mpirically obsrvd bhavior. Mor spcifically, w ar assuming that buyrs rat a transaction as positiv if thir actual utility from th transaction xcds thir xpctd utility (i.. if S>). On th othr hand, buyrs only rat a transaction as ngativ if thir actual utility falls short of thir xpctd utility by mor than a lnincy factor λ, that is, if S < λ. Finally, for transactions, which nd up bing slightly bad but not too bad (i.. whr λ < S ), w ar assuming that buyrs prfr to simply rfrain from rating at all 3. To summariz: " " if S > r( S) = " " if S λ () no rating if λ < S whr S = U U = θ ( q q ε ), ε ~ N(, σ ), r To simplify th initial analysis, w ar making th assumption that θ, σ and λ ar constant across th ntir population of buyrs and sllrs. In Sction 5, w will rlax thos assumptions and study how thy impact th rsults drivd in Sctions 3 and 4. 3. Wll functioning rputation mchanisms Th following sctions will us th modl dvlopd in Sction, in ordr to xplor undr what circumstancs binary rputation mchanisms can b wll functioning. Bfor doing that, howvr, in this sction w will discuss what it mans for a rputation mchanism to b wll functioning in marktplacs with privat quality information. W dfin a wll-functioning rputation mchanism to b on, which satisfis th following two proprtis: WF: If thr xists an quilibrium of prics and qualitis undr prfct information (i.. in sttings whr q q = q ) thn, in nvironmnts whr q is privat to sllrs, th xistnc of th = a r r rputation mchanism maks it optimal for sllrs to sttl down to a stady-stat pair of ral and advrtisd qualitis, rathr than to oscillat, succssivly building up and milking thir rputation. 3 On Bay, som buyrs would post a nutral rating in this cas.
WF: Assuming WF holds, undr all stady-stat sllr stratgis ( q r q ) th quality of sllrs as stimatd by buyrs bfor transactions tak plac, is qual to thir tru quality (i.. q = )., a q r Bfor w procd, lt us justify th abov dfinition by providing a brif rational for th dsirability of proprtis WF and WF. First, th valu of rputation mchanisms in gnral rlis on th assumption that past bhavior is a rliabl prdictor of futur bhavior (Wilson 985). If oscillations wr optimal, th prdictiv valu of cumulativ functions of past ratings, such as Σ,, would b gratly diminishd. In nvironmnts whr th primary Σ (or only) mchanism for crtifying and controlling sllr quality is basd on rputation, it is, thrfor, dsirabl that sllrs find it optimal to sttl down to a stady-stat bhavior rathr than to oscillat. Scond, according to our modl, buyrs mak purchas dcisions basd on knowldg of prics and stimatd qualitis. If it wr possibl for sllrs to sttl down into a stady-stat stratgy that would consistntly dciv buyrs into stimating q >, thn this would allow sllrs to arn additional profits q r at th xpns of buyrs. In th prsnc of comptitiv marktplacs, buyrs would thn vntually lav th marktplac in favor of othr markts with bttr information. On th othr hand, if, undr all possibl stady-stat sllr stratgis th ffct of th rputation mchanism was such, so that buyrs stimatd q <, thn th opposit ffct would tak plac: buyrs would raliz xtra surplus at th xpns of q r sllrs. Onc again, w would thn xpct that sllrs would dsrt th marktplac in favor of othr, mor transparnt markts. Th only fair stady-stat stratgy, thrfor, is on whr q =. 4. Can binary rputation mchanisms b wll functioning? q r This sction will dmonstrat that, givn a rating function, which has th gnral form givn by (), whthr an Bay-lik binary rputation systm satisfis proprty WF dpnds on th rlationship btwn () and th quality stimation function q = f (, R). Furthrmor, w will show that, if buyrs ar lnint q a nough whn thy rat and corrspondingly strict whn thy judg sllr profils, sllrs will find it optimal to sttl down to stady-stat tru and advrtisd quality lvls if such an quilibrium xists undr prfct information. 4. Estimatd vs. ral qualitis in stady stat Lt us first focus our attntion on th circumstancs undr which a binary rputation mchanism satisfis condition WF. W ar assuming that WF holds. Thrfor, thr xists at last on stady-stat stratgy q r, q ) for ach sllr 4. A stady-stat stratgy is a stratgy that optimizs a sllr s payoff function, whil ( a at th sam tim rsulting in an stimatd quality q = f (, R), which is stabl ovr tim. Dnot q a q = q r ξ, whr ξ is th dcption factor, that is, th distortion btwn stimatd and ral quality at stady stat. If ξ > thn buyrs ovrstimat a sllr s tru quality, whras if ξ < thn buyrs undrstimat tru quality. Lt N b th total numbr of sals transactions of a givn sllr in th most rcnt tim window. It is asy to s that N Σ Σ Σ no rating. Assuming that buyrs rat according to = (), for larg N at stady stat th following will hold: Σ Σ = N Pr ob[ S > ] = N Φ[( q = N Pr ob[ S λ] = N Φ[( q q q whr Φ(.) is th standard normal CDF. r ) / σ ] = N Φ[ ξ / σ ] r ) / σ λ /( θ σ )] = N Φ[ ξ / σ λ /( θ σ )] (3) 4 Sction 4. will xplor th conditions undr which sllrs will indd find it optimal to sttl down to a stady stat stratgy.
Givn that q = f (, R), satisfaction of condition WF dpnds on th quality assssmnt function f. q a Mor spcifically, f must b chosn so that, for all stady-stat stratgis ( q r, q ) th quation: a q = q ξ = f ( q, R( ξ )) (4) r has a uniqu solution at ξ =. a Bay dos not spcify, or vn rcommnd, a spcific quality assssmnt function f. It simply publishs th quantitis Σ and Σ for ach sllr and allows buyrs to us any assssmnt rul thy s fit. It is important to not at this point that Bay dos not currntly publish th quantity Σ no rating (and thrfor for a sllr. As w will show blow, knowldg of N is ssntial for constructing rliabl quality assssmnt functions. Th rsults of this papr, thrfor, mak a strong argumnt that th numbr of transactions that hav rcivd no rating should b addd to th profil information publishd by Bay and similar systms. In this papr, w will xplor on gnral family of quality assssmnt functions which, whn implmntd corrctly and usd in conjunction with rating rul (), satisfy WF. W will furthr xplor diffrnt ways in which usrs of a rputation mchanism can us Σ, and N in ordr to corrctly implmnt thos functions. Σ Th gnral form of our quality assssmnt functions is givn by: q if ˆ( ξ R) q = f ( q, R) = a (5) a if ˆ( ξ R) > In othr words, buyrs assss th quality of an itm to b qual to that advrtisd by th sllr, if, basd on th sllr s profil, thy conclud that th sllr dos not ovr-advrtis. Othrwis, buyrs assum that th sllr lis and assss minimum quality. Function (5) thrfor uss th information providd by th rputation mchanism in ordr to driv a (binary) assssmnt of truthfulnss in advrtising. Assuming that sllrs hav a way of rliably infrring th sign of ξ from fdback profil information, sllrs who ovr-advrtis thir quality will quickly s thir stimatd quality fall to zro. Thrfor, if f is givn by (5), quation (4) has no solution for ξ >. Not that function (5) dos not prvnt sllrs from undr-advrtising thir quality bcaus for q a q ξ, all ξ ar also solutions of quation (4). Howvr, givn that w hav assumd that π / q, w would not xpct any profit-maximizing sllr to undr-advrtis. Thrfor, th only stady-stat sllr stratgy for sllrs would b to truthfully advrtis thir ral quality. In that cas, buyrs would stimat q = q =, a dsirabl outcom, which satisfis WF. q a r a = r N) Lt us now xplor thr diffrnt ways in which buyrs can us of ξ. Σ, Σ and N in ordr to stimat th sign Assssmnt basd on th numbr of positivs On way to stimat sllr honsty is to rquir that th fraction of positiv ratings of good sllrs xcd a thrshold. From (3) w can s that ˆ η Σ / N can b intrprtd as a point stimator of Φ [ ξ / σ ]. Givn
that Φ[ ξ / σ ] <. 5 for allξ >, assssmnt of th sign of ξ rducs to tsting th statistical hypothsis : η.5 givn ηˆ. Th corrsponding quality assssmnt function thn bcoms: H q a q = whr H if H accptd if H rjctd : η.5 givn ˆ η Σ /N (6) Hypothsis H can b tstd using on of th known tchniqus for computing confidnc intrvals of proportions following binomial distributions (.g. Blyth and Still 983). Function (6) is an appaling mthod for assssing sllr quality bcaus of its rlativ simplicity. Not that its computation dos not rquir knowldg of th modl paramtrs λ, θ and σ. Howvr, (6) is difficult to comput rliably without knowldg of N, th total numbr of ratd plus unratd transactions of a sllr. As was mntiond, Bay dos not mak N known to its mmbrs. Taking ˆ η Σ /( Σ ) would rsult Σ - Σ no rating in larg ovrstimation of Φ[ ξ / σ ], spcially bcaus, du to rating lnincy, is xpctd to b quit significant (in th data st of Figur Σ / N = no rating 48. 3% ). For that rason, on would infr that quality assssmnt basd on th numbr of positiv ratings is not (and should not b) widly usd on Bay. This hypothsis is consistnt with mpirical obsrvations (Dwan and Hsu ). Sction 4. will discuss anothr disadvantag of function (6), which is that it maks it asir for sllrs to oscillat btwn priods whr thy milk thir good rputation by ovrstating thir quality and dciving buyrs and priods whr thy rstor thir rputation by offring bttr quality than what buyrs xpct. Assssmnt basd on th numbr of ngativs In an analogous mannr, w xpct good sllrs to hav fw ngativ ratings. Thrfor, anothr way to stimat sllr honsty is to rquir that th fraction of ngativ ratings of good sllrs stay blow a thrshold. From (3) w can s that ˆ ζ Σ / N can b intrprtd as a point stimator of Φ [ ξ / σ λ /( θ σ )]. Givn that Φ[ ξ / σ λ /( θ σ )] > Φ[ λ /(θ σ )] for allξ >, assssmnt of th sign of ξ rducs to tsting th statistical hypothsis H : ζ Φ [ λ /( θ )] givn ζˆ. Th corrsponding quality assssmnt function thn bcoms: σ q a if H accptd q = if H rjctd whr H : ζ k Φ[ λ /( θ σ )] givn ˆ ζ Σ - / N (7) Lt us call k Φ[ λ /( θ σ )] th optimum trustworthinss thrshold. k is a monotonically dcrasing function of th lnincy factor λ. Thrfor, th mor lnint buyrs ar whn thy rat, th lowr th thrshold of ngativ ratings to transactions abov which thy should not trust sllrs, and vic vrsa. This is a rsult that corrsponds wll to documntd mpirical findings: most Bay buyrs wigh ngativ ratings much mor havily than positiv ratings whn assssing th trustworthinss of a prospctiv sllr (Dwan and Hsu ). Givn that thy sm to b rathr lnint whn thy rat thos sllrs, according to (7), w would xpct thm to b strict whn assssing th quality of sllrs, and thrfor to b rlativly intolrant of ngativ ratings. Th big qustion, howvr, is whthr buyrs us th right thrshold whn thy judg sllrs (in othr words, ar buyrs capabl of making th right judgmnt of just how many ngativ ratings ar too many?).
From quation (7) w can also s that an optimum k can b drivd for vry λ. On way of intrprting this rsult is that satisfaction of WF is always possibl no mattr how lnint (or strict) buyrs ar whn thy rat, providd that thy strik th right balanc btwn rating lnincy and quality assssmnt strictnss. In th nxt sction, w shall prov that, mor lnint rating (and corrspondingly strict assssmnt) incrass th liklihood that sllrs will find it optimal to sttl down to a stady-stat bhavior. Som dgr of lnincy, thrfor, can b bnficial to th stability of th marktplac. It is also important to point out that, unlss buyrs us th right thrshold whn valuating th numbr of ngativ ratings of a sllr, WF will not b satisfid. If buyrs us a thrshold k > k thn thr will b somξ > for which H will b satisfid and sllrs will b abl to consistntly dciv buyrs by ovr- advrtising thir quality. In contrast, if k < k, thr will b such that H will b rjctd for all ξ > ξ. In th lattr cas, to prvnt thir stimatd quality from dropping to zro, sllrs will b forcd to undr-advrtis and, thrfor, b consistntly undr-apprciatd by. k ξ < ξ W s, thrfor, that th choic of th right k is crucial to th wll functioning of th rputation mchanism, and of th marktplac in gnral. It is important to ask whthr buyrs can b rasonably xpctd to b abl to corrctly driv it. From quation (7), calculation of k rquirs knowldg of th modl paramtrs λ, θ and σ. It is unlikly that buyrs would hav accurat undrstanding and knowldg of thos paramtrs (spcially σ, which partly rflcts proprtis of th sllr). Nvrthlss, vn if th modl paramtrs ar not known, it is possibl to stimat th valu of Φ [ λ /( θ σ )] from Σ, and N. From (3): Σ ξ / σ = Φ ( Σ / N) k [ /( )] [ ( / N) ( = Φ λ θ σ = Φ Φ Σ Φ Σ λ /( θ σ ) ξ / σ = Φ ( Σ / N) / N)] (8) If N is small thn a confidnc intrval should b constructd for k. Evn with th hlp of quation (8), buyrs still nd to know N in ordr to proprly comput function (7). Ovrall, function (7) dfins a rathr fragil rul for assssing sllr quality fficintly. Givn that a lot of Bay buyrs ar havily basing thir sllr quality assssmnts on th numbr of ngativ ratings on th sllrs fdback profil, it is vry intrsting to ask what mthods thy us to comput thir trustworthinss thrsholds and, vn mor important, whthr thir trustworthinss thrsholds do indd com clos to satisfying WF. Clarly, ths ar important qustions, which invit furthr mpirical and xprimntal rsults to complmnt th rsults of this work. Assssmnt basd on th ratio btwn ngativs and positivs In both prvious cass, corrct implmntation of th quality assssmnt function rquird knowldg of N. On might think that, by basing quality assssmnt on th ratio btwn ngativ and positiv on may b abl to driv an optimal assssmnt function from Σ and Σ only. W will show that this is not possibl. From (3) w gt: Σ ρ( ξ ) Σ ( ξ ) Φ[ ξ / σ λ /( θ σ )] = ( ξ ) Φ[ ξ / σ ] (9) Function ρ(ξ ) is non-ngativ and monotonically incrasing in ξ. Furthrmor ρ( ) = Φ[ λ /( θ σ )]. Sinc ρ ( ξ ) > ρ() for all ξ >, assssmnt of th sign of ξ rducs to tsting th statistical hypothsis
H : ρ Φ[ λ /( θ )] givn σ bcoms: ˆρ Σ / Σ. Th corrsponding quality assssmnt function thn q if H accptd a q = if H rjctd whr H : ρ Φ[ λ /( θ σ )] givn ˆ ρ Σ / - Σ () Unlss buyrs hav knowldg of th modl paramtrs λ, θ and σ, calculation of Φ[ λ /( θ σ )] from (8) rquirs knowldg of N. Thrfor, using th ratio of ngativs to positivs is vry similar to using th fraction of ngativs and is qually tricky to gt right without knowldg of N. 4. Existnc of stady-stat bhavior Th analysis of Sction 4. has bn basd on th assumption that sllrs sttl down to stady-stat ral and advrtisd quality lvls. This sction will invstigat th conditions undr which sllrs will indd find it optimal to do so. Th altrnativ is to oscillat btwn building a good rputation and thn milking it by ovr-advrtising ral quality. As w argud in Sction 3, rputation-mdiatd marktplacs should b dsignd in ordr to induc sllrs to sttl down to stady stat bhavior (othrwis information about past bhavior will not b vry hlpful as a way of prdicting th futur). Th principal rsult of this sction is that whn quality assssmnt is basd on functions (7) or (), which involv ngativ ratings, thn, if th rating lnincy factor λ is larg nough, sllrs will find it optimal to sttl down to stady stat bhavior. In contrast, thr is no such guarant whn quality assssmnt is basd on function (6), which only involvs positiv ratings. This rsult shows that mor lnint rating (coupld with mor strict quality assssmnt) supports stability in th systm. For th sam rason, although mor fragil and difficult to gt right, functions (7) and (), i.. functions which bas sllr quality assssmnt on th numbr of ngativ ratings, ar prfrrd to function (6), which only looks at th sllr s positiv ratings. In ordr to driv our rsult, lt us considr ways in which sllrs may attmpt to raliz additional profits through oscillating bhavior. Assum that a sllr is abl to prform N transactions bfor ratings of thos transactions ar postd to hr fdback profil. This numbr dpnds on th frquncy of transactions and th dlay btwn transactions and th posting of ratings by buyrs (on Bay, this dlay is typically -3 wks). Lt us considr a sllr who, at th nd of priod, has compltd N transactions in th currnt tim window and has accumulatd a good rputation, by producing and advrtising itms of quality q, th quality that optimizs profits assuming stady-stat bhavior. Lt us furthr assum that buyrs assss quality basd on function (7). At th nd of priod : Σ Σ = ( ξ = ) = N priod N Φ[λ θ σ )] = () /( k At th bginning of priod th sllr dcids to milk hr rputation by choosing a ral quality q and thn ovr-advrtising hr quality by ξ so that hr profit is maximizd rlativ to th stady stat cas. Givn th sllr s good past rputation, initially buyrs will b dcivd. Howvr, aftr thy purchas th sllr s itms, thy will raliz thir infrior quality and will post proportionally mor ngativ ratings. Thrfor, at th nd of priod (aftr N dciving transactions):
N [ λ /( θ σ )] N [ ξ / σ λ /( θ σ )] Σ Φ Φ = > N priod N N k () and th sllr s subsqunt stimatd quality will fall to zro. Assuming that som buyrs ar willing to buy from sombody with zro quality if th pric is low nough, our sllr will stay in businss. In ordr to incras hr rputation onc again, sh nds to rduc th ratio Σ / N to blow th thrshold k. Th only way sh can achiv this is to go through a priod whr sh producs highr quality itms but rcivs lowr prics, surpassing buyrs xpctations (who now xpct = ) by ξ. Lt us assum that q it would tak N rdming transactions bfor Σ / N k. At th nd of priod : - Σ N priod N Φ[ λ /( θ σ )] N Φ[ ξ / σ λ /( θ σ )] N Φ[ ξ / σ λ /( θ σ )] = = k N N N = Φ[ λ /( θ σ )] (3) A profit-maximizing sllr will choos to oscillat if th profit from th dciving transactions rlativ to th stady-stat profit xcds th loss from th rdming transactions rlativ to th stady-stat profit. If ths two quantitis hav a finit ratio, thn, providd that th numbr N of rdming transactions that ar ncssary in ordr to undo th rputation ffcts of dciving transactions is high nough, sllrs will not find it profitabl to oscillat and will sttl down to stady-stat ral and advrtisd quality lvls. From (3) aftr som algbraic manipulation, w gt: N N N Φ[ ξ / σ λ /( θ σ )] Φ[ λ /( θ σ )] = = g( λ, ξ, ξ ) (4) Φ[ λ /( θ σ )] Φ[ ξ / σ λ /( θ σ )] Aftr som manipulation w gt g / λ > and g/ λ >. In fact g(.) grows xponntially with λ 5. Figur plots g(λ) for = σ = θ and som rprsntativ valus of ξ = ξ = ξ. Minimum ratio N/N 8 6 4 8 6 4.5.5.5 Lnincy factor (lambda) ksi= ksi= ksi=3 ksi=4 ksi=5 Figur : Minimum ratio of rdming to dciving transactions ndd in ordr to rstor on s good rputation following a priod of quality ovr-rporting. 5 Furthrmor, for a givn λ, g(.) grows rapidly withξ and dcrass vry slowly with ξ. This mans that th minimum ncssary ratio of rdming to dciving transactions grows with th amount of initial dcption ( ξ ) and cannot b significantly brought down by incrasing th amount of rdmption ( ξ ).
From Figur it is vidnt that in marktplacs whr buyrs rat lnintly (and assss quality strictly), sllrs nd many mor rdming transactions in ordr to rstor thir good rputation following a fw dciving transactions. Th rlativ numbr of rdming transactions incrass xponntially with th lnincy factor. Othrwis said, th largr th λ, th mor difficult it is for sllrs to rstor thir rputation onc thy los it. Consquntly, if λ is sufficintly larg, sllrs will find it optimal to sttl down to stady-stat ral and advrtisd quality lvls. Q.E.D. A similar rsult can b drivd if buyrs bas quality assssmnt on th ratio bas quality assssmnt on function (7), our analysis givs: Σ / Σ. In contrast, if buyrs N N Φ[ ξ / σ ] = Φ[ ξ / σ ] (5) Equation (5) givs N = N for ξ = and N slightly lss than N for ξ ξ < ξ. Othrwis said, following a st of dciving transactions, it taks th sam numbr of (or fwr) rdming transactions in ordr to rstor on s good rputation. In such a stting, it is mor likly that som sllrs will hav profit functions for which it will b optimal to oscillat. Thrfor, on xpcts that in rputation-mdiatd marktplacs whr buyrs us (6) to assss sllr quality, thr will b lss stability than in marktplacs whr sllrs us (7) or (). Th rsults of this sction provid som intrsting argumnts for both rating lnincy as wll as for basing th quality assssmnt of sllrs on thir ngativ, rathr than thir positiv ratings. 5. Rality chcks and som rcommndations Th rsults of th prvious sctions hav bn drivd by making a numbr of simplifying assumptions about buyr bhavior. Mor spcifically, w hav assumd that all buyrs hav th sam quality snsitivity θ and lnincy factor λ. Furthrmor, w hav assumd that buyrs always submit ratings whnvr thir satisfaction riss abov zro or falls blow λ. Both assumptions ar not likly to hold in a ral marktplac. Buyrs hav diffrnt prsonalitis, and thrfor, ar xpctd to hav diffrnt quality snsitivitis, as wll as lnincy paramtrs. Furthrmor, ratings do incur a cost (tim to log on and submit thm) and som buyrs do not bothr rating, vn whn transactions turn out rally good or vry bad. In this sction, w will injct a bit of rality to our modl and will xplor how our rsults chang if w tak into account th abov considrations. Rality Chck #: Som buyrs nvr rat W nd to modify our rating function r(s) in (), so that whn S >, r( S) = " " with probability β and r(s) = no rating with probability ( β ). Similarly, whn S λ, r ( S) = " " with probability γ and r(s) = no rating with probability ( γ ). Undr this nw rating function, th statistical hypothsis in (6) bcoms H : η β.5, whil th hypothsis in (7) bcoms H : γ Φ[ λ /( θ σ )]. W s that our nw assumption introducs two additional paramtrs to our modl. Th paramtrs nd to b rliably stimatd in ordr for proprty WF to b satisfid. Rality Chck #: Buyrs diffr in quality snsitivity and lnincy Lt s dfin ω λ / θ and lt s call p (ω ) th probability distribution of ω among buyrs. Thn (3) must b modifid as: ζ Σ Σ = N Pr ob[ S > ] = N Φ[ ξ / σ ] = N Pr ob[ S λ] = N Φ[( ξ ω) / σ ] p( ω) dω (6)
If quality assssmnt is basd on th fraction of positiv ratings using (5), thn rality chck # dos not introduc additional complications. Howvr, if quality assssmnt is basd on th fraction of ngativ ratings, which, in th prsnc of lnint ratings is th rul most likly to rsult in stabl sllr bhavior, thn things do bcom considrably mor complicatd. Mor spcifically, it is asy to s that th statistical hypothsis to b tstd in (6) must bcom H : ζ k Φ[ ω / σ ] p( ω) dω. In ordr to calculat th right k, on nds knowldg of p (ω ). Things bcom vn mor complicatd if w combin rality chcks # and #, which would b th situation that most closly corrsponds to actual rality. Of cours, on can bgin to think of ways in which individual buyrs might b abl to stimat, mayb with som dgr of rror, th additional modl paramtrs β, γ and p( ω) from Σ, and N. Σ Howvr, instad of mbarking in this dirction, at this stag w bliv that w ar providd nough argumnts to mak on of th main points of this papr: Binary rputation mchanisms can in thory b wll functioning undr th assumption of simpl rating and assssmnt ruls, but only if buyrs us th right thrsholds whn judging sllr trustworthinss. Calculating th right thrshold from Σ, alon, th only information currntly providd by Bay, is vry difficult. Calculating th right thrshold from Σ, Σ and N is possibl undr th simplifying assumptions of Sction but bcoms mor and mor difficult as our modls approach rality. In ralistic cass, th corrct assssmnt rul dpnds not only on th fdback profil of a sllr but also on proprtis of th ratr population. Givn that th fficincy of th marktplac crucially dpnds on th slction of corrct assssmnt thrsholds on th part of th buyr, th most snsibl cours of rsarch thrfor should b to think of additional information that th rputation mchanism can provid to ratrs, in ordr to mak this calculation asir. On ida is for th oprator of th marktplac, or som trustd third party, to introduc a small numbr of honst sllrs into th markt. Th bhavior of thos sllrs must b compltly undr th control of th marktplac oprator but thir idntitis should b unknown to buyrs (so that buyrs ar not biasd whn thy rat thos sllrs). Givn that th marktplac knows that for thos sllrs ξ =, it can us thir fdback profils in ordr to driv stimats of β, γ, p( ω) and k Thos stimats, or suitably chosn drivativs, can thn b communicatd to th buyrs for th purpos of facilitating thir sllr assssmnt procss. 6. Conclusions Th objctiv of this papr was to xplor to what xtnt binary rputation mchanisms, such as th on usd at Bay, ar capabl of inducing fficint markt outcoms in marktplacs whr (a) tru quality information is unknown to buyrs, (b) advrtisd quality is compltly undr th control of th sllr and (c) th only information availabl to buyrs is an itm s advrtisd quality plus th sllr s fdback profil. Th first contribution of th papr is th dfinition of a st of conditions for valuating th wll functioning of a rputation mchanism is such sttings. W considr a rputation mchanism to b wll-functioning if it (a) inducs sllrs to sttl down to a stady-stat bhavior assuming it is optimal for thm to do so undr prfct quality information and (b) at stady-stat, sllr quality as stimatd by buyrs bfor transactions tak plac is qual to thir tru quality. Th scond contribution of th papr is an analysis of whthr binary rputation mchanisms can b wllfunctioning undr th assumptions that (a) ratings ar basd on th diffrnc btwn buyrs tru utility following a transaction and thir xpctations bfor th transaction and (b) buyrs ar rlativly lnint whn thy rat and corrspondingly strict whn thy assss a sllr s fdback profil. Our first conclusion is that if binary fdback profils ar usd to dcid whthr a sllr advrtiss truthfully (in which cas buyrs assss quality qual to th advrtisd quality) or not (in which cas buyrs Σ
assss quality qual to th minimum quality), thn, in thory, binary rputation systms can b wll functioning, providd that buyrs strik th right balanc btwn rating lnincy and quality assssmnt strictnss. Furthrmor, assuming that buyrs bas thir judgmnt on th ratio of ngativ ratings rcivd by a sllr, if buyrs ar lnint nough whn thy rat and corrspondingly strict whn thy judg sllr profils, w hav shown that sllrs will find it optimal to sttl down to stady-stat quality lvls if such an quilibrium xists undr prfct information. This is an intrsting way in which (a) judging sllr trustworthinss basd on thir ngativ ratings is prfrabl to basing it on thir positiv ratings and (b) som dgr of rating lnincy hlps bring stability to th systm. Our scond conclusion is that, unlss buyrs us th right thrshold paramtrs whn thy judg sllr profils, binary rputation mchanisms will not function wll and th rsulting markt outcom will b unfair for ithr th buyrs or th sllrs. In that sns, although binary rputation mchanism can b wll functioning in thory, thy ar xpctd to b quit fragil in practic. Th crucial qustion thrfor bcoms whthr binary fdback profils provid sllrs (sp. rlativly unsophisticatd ons) with nough information to driv th right sllr judgmnt ruls. W hav found that th right judgmnt rul (.g. what is th right numbr of ngativ ratings abov which a sllr should not b trustd?) is difficult to infr corrctly from knowldg of th sum of positiv and ngativ ratings alon, which is th only information currntly providd by Bay to its mmbrs. If knowldg of th sum of unratd transactions is addd to fdback profils, thn, undr a numbr of simplifying assumptions, it is possibl to driv non-obvious but rlativly simpl optimal judgmnt ruls which rsult in wll functioning rputation mchanisms. Howvr, if th simplifying assumptions ar droppd, calculation of th right judgmnt rul from Σ, and N onc again bcoms difficult, as it Σ rquirs knowldg not only of sllr ratings but of th ratr population as wll. Our findings lad to th rcommndation that mor information should b providd to assist ratrs of such marktplacs us fdback profils in th right way. On ida is for th oprator of th marktplac, or som trustd third party, to introduc a small numbr of honst sllrs undr its control into th markt. If on knows, a priori, that a sllr is honst, hr fdback profil can thn b usd by th marktplac to stimat and publish a numbr of additional markt-wid paramtrs which, togthr with Σ, and N, will hlp buyrs mor rliably assss th quality of othr sllrs in th systm. Th thortical rsults of this papr rais som intriguing qustions rlatd to th fficincy, fairnss and stability of Bay-lik lctronic marktplacs. Th author would wlcom xprimntal and mpirical vidnc that will shd mor light into th qustions raisd and would validat th conclusions drawn from his modls. Rfrncs Akrlof, G. (97) Th markt for lmons : Quality uncrtainty and th markt mchanism. Quartrly Journal of Economics 84, pp. 488-5. Blyth, C.R. and Still H.A. (983) Binomial Confidnc Intrvals. Journal of th Amrican Statistical Association 78, pp. 8-6. Brs, J.S., Hckrman, D., and Kadi, C. (998) Empirical Analysis of Prdictiv Algorithms for Collaborativ Filtring. In Procdings of th 4 th Confrnc on Uncrtainty in Artificial Intllignc (UAI-98), pp. 43-5, San Francisco, July 4-6, 998. Dwan, S. and Hsu, V. () Trust in Elctronic Markts: Pric Discovry in Gnralist Vrsus Spcialty Onlin Auctions. Working Papr. January 3,. Kollock, P. (999) Th Production of Trust in Onlin Markts. In Advancs in Group Procsss (Vol. 6), ds. E.J. Lawlr, M. Macy, S. Thyn, and H.A. Walkr, Grnwich, CT: JAI Prss. Σ
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