Popularity, Novelty and Attention

P opularit y , No v elt y and A tten tion F a ng W u and Ber nardo A. Hub erman HP Lab or ator ies P al o Alto, CA 9430 4 Octob er 29, 201 8 Abstract W e analyze the role that p opularit y and nov elt y p la y in attracting the atten tion of users to dyn amic websites. W e do so b y d etermin in g the p erformance of three differen t strategie s that can b e utilized to maximize atten tion. The fi rst one pr ioritizes n o v elty while th e sec- ond emp hasizes p opularity . A third strategy lo oks m yopicall y in to the fu tu re and prioritizes stories th at are exp ected to generate the most clic ks within the n ext few minutes. W e s ho w that the first t wo strategies should b e selected on the b asis of the rate of no v elt y d eca y , while the third strategy p erform s sub-optimally in most cases. W e also demonstrate that the relativ e p erforman ce of the firs t t wo strategies as a function of the rate of no velt y deca y c hanges abr uptly aroun d a critical v alue, resembling a p hase transition in th e physical world. 1 1 In tro ducti on As millions of p eople u se the web for their so cial, informational, and consumer needs, cont ent pro vid ers vie for their limited atten tion by resorting to a num b er of strategies aimed at maximizing the num b er of clic ks dev oted to their web sites [1]. These strategies range from data p ersonalization and short videos to the dynamic rearrangemen t of items in a give n page, to n ame a few [2, 3, 8 ]. I n all these cases th e ultimate goal is th e same: to draw the atten tion of the visitor to a w ebsite b efore she p ro ceeds to the next one [4]. Ob v ious ly , the more in teresting and relev an t the site the more v aluable it w ill b e to users. In addition, since users n eed to d ecide among the existing plethora of links and sites, their p opularities are a determinan t of their success, for p eople often clic k on giv en links for no other reason than the fact that many others do. If we add the f act that without n ov elt y attent ion tends to deca y in time, one has a first order list of the requirements for capturing p eople’s atte ntion. Within this con text, w e h av e recen tly sh o wn that there is a stron g in terplay b et we en no velt y and collectiv e atten tion, w hic h is un iv ersally manifested in a r ather swift initial gro wth of the num b er of p eople lo oking at a new it em within a sit e and its e ven tual slo wd o wn as in terest fades among th e p opulation [7]. This result su ggests that ordering the links of a giv en page by their n o ve lty can guarantee a high degree of atten tion. This is indeed the case in man y news w ebsites, notably digg. com . And y et, giv en the rol e that popu larit y pla ys i n attracting the atten tion of users, a natural question arises as to wh ether alte r nativ e orderings, like one giving priorit y to p opularit y o ver no ve lty , m igh t not do b etter at attracting viewers to a site. This pap er answe r s this question b y taking the dynamics of col- lectiv e atten tion to a finer lev el of d etail and examining the role that p opularity and no velt y play in determining the num b er of clic ks within a giv en p age. In particular, we study three different strateg ies that can b e d ep lo y ed in order to maximize atten tion. The fi rst strategy prioritizes no ve lty while the second emphasizes p opularit y . Th e third strategy looks m yopical ly into the fu ture and prioritizes stories that are exp ected to generate the m ost clic ks in the next few min utes. W e 2 sho w that the first t wo str ategies sh ould b e selected on the basis of the rate of no ve lty deca y , while the thir d strategy p erforms sub-optimally in m ost cases. Most interestingly , w e disco ver that the relativ e p erfor- mance of the fi rst t wo b enchmark strategi es as a fun ction of the rate of n o v elty d eca y switc hes so sharply around some critical v alue that it resem bles phase transitions observ ed in the real w orld. The w ork is organize d as follo ws. W e first study th e question of w hether or n ot the lo cation of a lin k in a page dete r mines the o v erall num b er of clic ks in a give n time in terv al. Ha ving answered this in the affirmative through an empirical study of digg.com , we then p ro ceed to introduce a set of indexes w hose v alues determine the optimal strategy to b e pursued in order to maximize atten tion to a page. Usin g m easured v alues of the rate of d eca y from digg.com w e bu ilt a realistic simulator to collect s tatistically significan t data to measure eac h of th e indices in tro duced. W e then stud y the p erf ormance of eac h of these ind ices as a fun c- tion of the deca y rate and sh o w which strategy optimizes viewing for giv en v alues of the deca y . Most imp ortan tly we compu te a full phase diagram that indicates at a gla n ce the optimal strategy to us e giv en the parameter v alues of the site. This phase d iagram exhibits a sharp b ound ary b et w een th e c hoice of prioritizing nov elty o ver p opu larit y , th us resembling a phase transition. Finally w e su mmarize our resu lts and d iscu ss th eir imp licatio n s f or the design of d y n amic websites. 2 Lo cation m atte rs In this section we study ho w the ord er in which links are placed within a webpage (e.g. the n ews stories of digg.com ) determines the n u mb er of clic ks within a certain time frame. Assume that time flows discretely as t = 0 , 1 , 2 . . . min utes. Let N t denote the num b er of clic ks, or digg numb er of a story in digg.co m , th at app eared on the we b site t minutes ago (in this case w e sa y that the story h as lifetime t ). As we sho wed earlier [7] the gro wth of N t satisfies the follo wing sto chastic equation: N t +1 = N t (1 + ar t X t ) , (1) 3 where r t is a novelty factor that deca ys with time and satisfies r 0 = 1, X t is a r andom v ariable with mean 1, and a is a p ositiv e constant. This equ ation tak es in to accoun t tw o imp ortant factors that to- gether determine the gro wth of collectiv e atten tion: p opularity and novelty . Th e p opu larit y effect is captured by the multiplica tive form of Eq. (1), and the n o v elty effect is describ ed b y r t . All other factors are contai n ed in the noise term X t . W e next take the analysis to a fin er lev el by co n sidering a third p osition factor . A news s tory display ed at a top p osition on the fron t page easily d ra ws more atten tion th an a similar story placed on later pages. Hence the growth deca y ar t should d ep end on the physical p osition at whic h the story is p osted. In the sp ecific case of digg. com , its fron t page is divided int o 15 slots, b eing able to display 15 stories at a time. The stories are alw a ys sorted c hronologically , w ith the latest story at the top. If w e lab el the p ositions from top to b ottom b y i = 1 , 2 , . . . , 15, w e can mo dify Eq. (1) to allo w for an explicit dep endency of a on i : N t +1 = N t (1 + a i r t X t ) , (2) where a i is a p osition factor that decreases w ith i . The assump tion that the n o ve lty effect and the p osition effect can b e separated into t w o factors r t and a i needs to b e tested empirically . T o this end we trac k ed the gro wth rate for eac h slot, rather than for eac h story . F or multiplica tive mo dels it is conv enient to define th e logarithmic gro wth rate s t = log N t +1 − log N t . (3) When a is small (wh ic h is alw ays true for short time p erio ds) we ha ve from Eq. (2) s i t ≈ a i r t X t (4) for a story placed at p osition i at time t . T aking exp ectation of b oth sides, w e ha ve E s i t ≈ a i r t , (5) since E X t = 1. The logarithmic gro wth r ate s i t can b e measured as follo ws. F or eac h fi xed p osition i , if a digg story app ears on that p osition at b oth 4 0 20 40 60 80 100 120 140 0.0 0.1 0.2 0.3 0.4 0.5 t s t 1 (a) 0 50 100 150 0.0 0.1 0.2 0.3 0.4 0.5 t s t 1 (b) Figure 1 – The logarithmic gro w th rate for the top tw o p ositions on the fron t p age of d igg.com . Time is m easured in min u tes. Data is collect ed ev ery 5 minutes, the rate at whic h th e fr ont p age is refr eshed. The solid curve in (a) is the r esult of a minimum mean square fi t to the data (see text for more details). It has the fu nctional form f ( t ) = 0 . 120 e − 0 . 4 t 0 . 4 . The curve in (b) has the functional f orm f ( t ) = 0 . 106 e − 0 . 4 t 0 . 4 . times t and t + 5 (the fr ont page is refr esh ed ev ery 5 minutes), th en the observ ed qu an tit y 1 5 (log N t +5 − log N t ) coun ts as one sample p oint of s i t . Fig. 1(a) plots 1,220 s amp le p oint s coll ected from the top p osition at v arious times. Fig. 1(b) is a similar p lot f or the second top p osition. By comparing (a) and (b) w e see that s 2 t indeed tends to f all b elo w s 1 t , whic h ind icates that the p osition effect is real. T o b etter illustrate the p osition effect, w e plot the exp ected gro w th rate for p osition 1, 3 and 5 in Fig. 2. As can b e seen th ere, the gro wth rate deca ys as the story mo v es to lo wer p ositions. F rom this data we can also d etermine the v alues of a i quan tita- tiv ely . W e already established that f or digg.com the precise functional form of the deca y factor is r t = e − 0 . 4 t 0 . 4 . Th us, for these particular 5 0 20 40 60 80 100 0.02 0.04 0.06 0.08 0.10 t Es t i=1 i=3 i=5 Figure 2 – The exp ected logarithmic growth rate for p osition 1, 3 and 5 on th e front page of digg.co m . T ime is measured in min utes. As can b e seen, the gro wth rate deca ys as the story mo ves to lo wer p ositions. v alues, the minim u m mean squ are estimat or ˆ a i minimizes min a i X j [ s i t j ( j ) − a i r t j ] 2 = min a i X j [ s i t j ( j ) − a i e − 0 . 4 t 0 . 4 j ] 2 , (6) where t j is the lifetime of the j ’th data p oint. The estimator for the 1,220 d ata p oin ts obtained from the top p osition is calculated to b e ˆ a 1 = 0 . 120. Th e fitted curve ˆ a 1 r t = 0 . 120 e − 0 . 4 t 0 . 4 j is sho wn as a solid curv e in Fig. 1(a). An estimator ˆ a 2 = 0 . 106 for the second top p osition is also calculated and plotted in Fig. 1(b). As can b e seen from those figures, the p osition effect ( a i ) and the no velt y effect ( r t ) can indeed b e separated. W e can then conclude that Eq. (2) fits the data v ery w ell. 6 3 Optimal ordering for maximal at- ten tio n W e no w consider th e ord er in w hic h n ews stories s hould b e displa yed on a web page so as to ge n erate the largest n um b er of clic ks within a certain time p erio d T . This time p erio d needs to b e fi nite b ecause the total num b er of clic ks div erges as T go es to in fi nit y . Equiv alently , in an infinite-horizon framewo r k, we could discount future clic ks with a d iscoun t parameter δ , so that one clic k at time t count s a s δ t clic k at time 0. The ob jectiv e then is to maximize P ∞ t =0 δ t N t , where N t is the total n umber of clic ks generated from the n ews page in p erio d t . In what follo ws we will consider the finite-horizon ob jectiv e. T o simplify th e problem w e confine ourselv es to a s u bset of ordering strategies called indexing str ate gies , which is defined as follo w s. Giv en a story’s state, w hic h in our mo del is just a t wo- vecto r ( N t , t ), one first calculate s an index O for eac h story using a predefined index func tion O ( N t , t ), and th en sorts the stories based on their indices. The story with the largest index is disp la y ed at the top, the story with the second largest index n ext, and so on [5, 6]. Rather than considering a general index f u nction w e w ill concen- trate on three simple s tr ategie s . While neither of them is p erfect, eac h can increase o v erall atten tion to the site. 1. O 1 ( t ) = − t . The stories are sorted by their no velt y , with the new est story at the top. This is what digg.com is d oing tod a y . 2. O 2 ( t ) = N t . The stories are sorted b y their p opu larit y , with the most p opular story at the top. This strateg y is b ased on the fact that atten tion grows in a m u ltiplicativ e fashion (p opular stories are more lik ely to b ecome ev en more p opu lar). 3. O 3 ( t ) = N t r t . Th is is the “one-step-greedy” strategy . Ignoring the p osition effect (assume a = 1), a story in state ( N t , t ) ge n - erates on a verag e N t r t more clic ks (or “diggs” if one considers digg.com ) in the next p erio d. This strategy thus places the m ost “replicated” story at the top. Notice that b ecause N t gro ws with time, the effect of sorting by O 1 is almost the opp osite of sorting according to O 2 . 7 In ord er to test these strategies, w e b uilt a simula tor that closely resem bles the f u nctioning of digg.co m in that it incorp orates the fol- lo wing rules: 1. Initially there are 15 stories, all in state ( N t , t ) = (1 , 0). In w ords , eac h story starts with 1 digg and lifetime 0. (Because our mo d el is pu rely multiplic ative , the initial digg num b er do es not matter. W e just set it to b e 1.) 2. Allocate the 15 stories to 15 p ositions, in d ecreasing order of their O ( N t , t ), for an y giv en in dex function O . 3. Time ev olv es on e s tep (5 min u tes) at a time. The n u mb er of diggs generated from a story at p osition i is giv en b y ∆ N t +5 = N t +5 − N t = 5 a i r t X t N t . (7) The total num b er of diggs generated in this time step is th e s um of 15 suc h n u m b ers. The v alues of a i w ere estimated from r eal data an d sh o wn in Fig. 3. r t = e − 0 . 4 t 0 . 4 . X t is rand omly d ra wn from a normal distribution with mean 1 and standard deviation 0.5 (obtained from the real data f rom digg.com ). 4. On a verage every 20 m in utes a new story arr iv es. Th us th e n u m b er of stories arriving in one time step (5 minutes) follo ws a P oisson distribution with m ean 0.2 5. When a n ew story enters the p o ol, the story w ith the lo west index is dropp ed, main taining 15 stories in total. (It is p ossible the a new story is d ropp ed immediately after its arr iv al if it happ ens to h a ve the low est index.) 5. Go back to Step 2 un til the loop h as b een rep eated for enough rounds. The p erf orm ance of all thr ee index fun ctions w ere tested in our sim- ulator. F or eac h ind ex f u nction, Steps 2 to 5 w ere rep eated 100,00 0 times (or equiv alen tly 500,000 minutes). Strategy O 1 (sort by nov- elt y) ac hiev ed a total n u m b er of 514 ,314.8 d iggs. Strategy O 2 (sort b y p opularity) only generated 354.6 diggs. Str ategy O 3 (one-step-greedy) generated 452,40 2.3 diggs. Thus for th ese parameter v alues O 1 turns 8 2 4 6 8 10 12 14 0.06 0.07 0.08 0.09 0.10 0.11 0.12 i a i Figure 3 – The p osition factor deca ys as th e p osition low er s . The v alues of a i are measured by trac king the 15 slots on digg.c om ’s front page. out to b e b est strategy , since it is 13 . 7% b etter than O 3 and tremen- dously b etter than O 2 . T his confirms that digg.com is u sing the r igh t strategy . The r eason for the p o or p er f ormance of the in dex O 2 is easy to understand . O 2 giv es higher priorit y to stories that ha ve b een dugg man y times. According to the ind exing ru le, after one p erio d new stories can n ev er find their w ay to the front page since all the old stories ha ve more than 1 digg! When nov elty deca ys fast, the old stories r emaining on the fron t page s o on lose their freshness and cease to generate any n ew diggs. Th e system thus gets frozen in an unf r uitful state. The fact th at O 1 outp erforms O 3 is a b it harder to understand. Some int u ition can b e gained by considerin g an extreme case. Sup p ose eac h story completely loses its no v elty after one second ( r 0 = 1, r t = 0 for all t > 0). Then only “new arriv als” should b e disp la y ed since they are the only on es that can generate n ew diggs. S orting stories b y their lifetime is a goo d idea when no velt y deca ys fast. On the other hand, if 9 no vel ty nev er deca ys ( r t ≡ 1), the lifetime fac tor b ecomes ir relev ant . Th u s in this case, strateg y O 3 , which prioritizes pop u lar stories, will win ov er O 1 . Hence, the fact that O 1 w orks b etter than O 3 in our sim ulations sh ows that no vel ty deca ys relativ ely fast for dig g.com . Should it deca y at a slo wer rate, O 3 w ould b e a b etter c h oice. W e p oint out that our simulat ion only sho we d that the ordering implied by O 1 w orks b etter than O 3 for a p articular choi ce of T . In general this ma y n ot b e tru e for other v alues of T . In fact, for a time in terv al of T = 5 min utes (one time step) O 3 is b y definition the b est strategy . Hence, comparin g the p erformance of t wo or m ore index functions only mak es sens e after one has sp ecified a time horizon (or ho w muc h the future should b e discount ed if an in finite horizon is assumed). In order to quan titativ ely test the limiting b eha vior of the three strategies, w e rep eated our simulatio n s for a range of different v alues of the deca y parameter r t . O ur previous w ork suggested that r t deca ys as a stretc hed exp onen tial function, whose general form can b e written as r t = e − αt β . F or digg.com it turns out α = β = 0 . 4. The p arameter β determines the deca y rate. F or fixed α , the larger β , the faster r t deca ys. W e rep eated our exp erimen t for α = 0 . 4 and β ∈ [0 . 30 , 0 . 45]. The result is shown in Fig. 4. The p erf ormance of eac h indexing strategy is measured b y the logarithm of the total num b er of d iggs generated in 10,000 roun ds. W e see that as β increases (faster deca y), the num b er of diggs decreases f or all three indexing strategies. When β > 0 . 34 , O 1 p erforms slight ly b etter than O 3 and muc h b etter than O 2 . When β < 0 . 33, ho we ver, O 3 and O 2 p erform significan tly b etter than O 1 . In other w ord s, on the t wo sides of the v alue of β = 0 . 335, the stories should b e display ed in completely rev ersed order! W e therefore sa y that a phas e tr ansition tak es place at the v alue of β = 0 . 33 5. Other p oin ts w orth mentio n ing are that in Fig. 4 O 3 asymptotically approac hes O 1 and O 2 b oth in the fast and slo w d eca y limits, and that in general O 3 is the b est index among the three s tr ategie s (although for the sp ecific parameters of digg.c om ( α = β = 0 . 4) and our particular time horizon O 1 is slight ly b etter). T his is b ecause O 3 trades off b et ween p opularity and nov elt y in s tead of b etting on only one factor. 10 T o see this, consider th e equiv alen t index function O ′ 3 ( N t , t ) = log O 3 ( N t , t ) = log N t + log r t . (8) Clearly , O ′ 3 linearly trades off b et wee n log N t and log r t , assigning iden tical w eight to the t wo effects. Th is is b y no means the b est tradeoff. F or example, the index function O 4 ( N t , t ) = 0 . 6 log N t + log r t (9) ac hiev es 556,444 .1 diggs after 100,000 rounds of sim ulation, whic h is 8.2% more than O 1 and 23.0% more than O 3 ! How ever arbitrary it ma y s eem to giv e the term log N t w eight 0.6 rather than 1 is b ey ond the scop e of this pap er, bu t it do es show the complexit y of our p roblem. These exp erimen ts demons trate that the no velt y deca y r ate n eeds to b e measured with great care, as a sligh t c h ange in the deca y rate may totally rev erse the optimal order needed to m aximize atten tion. It is usually hard to analytically compu te the p erformance of a general index f u nction. F or the tw o simple s trategies O 1 and O 2 , how- ev er, some rough estimate can b e ac h iev ed. F or the sak e of generalit y , assume that there are m p ositions on the fron t p age. New stories ar- riv e at a r ate λ > 0. No ve lty deca ys as r t = e − αt β , w here 0 < β ≤ 1. Let ¯ a = 1 m P a i b e th e av erage p osition f actor, whic h equals 0.08 for digg.com . Let ∆ t b e the r efresh time step, which is 5 minutes for digg.com . Consider strategy O 2 first. According to the in dex rule, new stories nev er app ear on the fron t page. All diggs are generated b y the initial m stories. After time T we hav e from Eq. (3) that log N T = X t =0 , ∆ t,...,T − ∆ t a i r t X t ∆ t. (10) Hence on av erage eac h s tory’s log-p erf ormance is E log N T = X t =0 , ∆ t,...,T − ∆ t ¯ ar t ∆ t ≈ ¯ a Z T 0 r t dt. (11) When T is large, w e ha ve E log N T ≈ E log N ∞ = ¯ a Z ∞ 0 r t dt. (12) 11 0.30 0.35 0.40 0.45 8 10 12 14 16 18 20 β log(total digg) O 1 O 2 O 3 Figure 4 – T he total num b er of d iggs generated using th ree ordering strategies O 1 , O 2 , and O 3 , for α = 0 . 4 and a range of β . The nov elt y factor deca ys as r t = e − αt β . Pe r formance is measur ed by the logarithm of the total n umb er of diggs generated in 10,000 time steps. As can b e seen, O 3 asymptotically approac h es O 1 and O 2 in the fast deca y (large β ) and slo w deca y (small β ) limit, resp ectiv ely . A p hase transition happ ens around β = 0 . 33 5. 12 Next consider O 1 , which ord ers the sto r ies b y their lifetime. On a v erage every s ≡ 1 /λ min utes a new story replaces an old story , and eac h old story mo v es do wn one p osition. Hence on a verage eac h story sta ys on the front p age for ms minutes, wh ere m is the num b er of p ositions. W e call ms one p age cycle . It is the av erage time it tak es to refresh the whole page. W e no w see th at, b efore a story disapp ears from the f ron t page, it generates N ms = exp   X t =0 , ∆ t,...,ms − ∆ t a i ( t ) r t X t ∆ t   (13) diggs, w here i ( t ) is the story’s p osition at time t . When an story get s replaced by a n ew story , they are coun ted as one story r estarting fr om the state N t = 1 and t = 0. The multiplica tive pro cess starts o ver, and another N ms diggs are generated in the next ms minutes, on av erage. Th u s, in a total time p erio d T the pro cess is rep eated T / ( ms ) times, and a total num b er of N ms T / ( ms ) diggs are generated p er story . The log-p erformance of O 1 is appro ximately log N ms + log  T ms  = X t =0 , ∆ t,...,ms − ∆ t ¯ ar t X t ∆ t + log  T ms  , (14) where we replaced a i ( t ) by ¯ a s in ce on av erage eac h s tory s ta ys in p osition 1 , . . . , m for equal times. T aking exp ectation on b oth sides, w e ha ve E log N ms + log  T ms  ≈ ¯ a Z ms 0 r t dt + log  T ms  . (15) The critical p oin t can b e determined b y equating Eq. (12) and (15): E log N T − E log N ms = log T − log ( ms ) , (16) or ¯ a Z ∞ ms r t dt = log  T ms  , (17) whic h holds for any functional form of r t . T he left sid e of Eq. (16) can b e int erp reted as the total nov elty left after a time ms , or th e total log- p erformance that can b e gained from one story after one page cycle. The right h and side of Eq. (16) is the total log-time left after on e page 13 cycle. Thus, Eq. (16) and (17) sa y that, after one page cycle, if there is more no velt y left th an the log-time remained, the stories should b e ordered b y decreasing p opularity rather than b y d ecreasing no v elty ( O 2 is b etter than O 1 ). Conv er s ely , if no velt y deca ys to o f ast (not enough no velt y left after one page cycle ), then the stories should b e ordered by decreasing n o v elty rather than decreasing p opularit y ( O 1 is b etter than O 2 ). When r t = e − αt β it holds that Z ∞ ms r t dt = α − 1 β β Γ  1 β , α ( ms ) β  , (18) where Γ( a, x ) = Z ∞ x t a − 1 e − t dt (19 ) is the i nc omplete Gamm a func tion . In this case the critical equation can also b e written as ¯ a α − 1 β β Γ  1 β , α ( ms ) β  = log  T ms  . (20) F or the p arameters of digg .com (¯ a = 0 . 08, m = 15, s = 20) and horizon T = 50 , 000 one can solv e for the critical cur v e ( α, β ) on whic h O 1 and O 2 ha ve th e same p erformance. The curve is sho w n in Fig. 5 as a phase diagram. When the parameters ( α, β ) lie ab o ve the critical curve, the stories shou ld b e sorted by O 1 . Otherwise they should b e sorted by O 2 . T o illustr ate ho w sharp the ph ase transition is, w e plot the r elativ e p erformance O 2 / ( O 1 + O 2 ) as a fun ction of β , for fi xed α = . 4, in Fig. 6. As can b e seen, the trans ition is indeed v ery sharp. 4 Conclus ion In this pap er w e ha v e sho wn that dep en ding on the rate of deca y of no vel ty , t wo differen t strategies can b e deplo yed in order to maximize atten tion. The first one prioritizes no v elt y while the seco n d empha- sizes p opu larit y . Most in terestingly , th e shift from one to the other as a fun ction of the rate of deca y is extremely sharp, resem blin g the phase transitions ob s erv ed in the physical world. 14 0.3 0.4 0.5 0.6 0.7 0.20 0.25 0.30 0.35 0.40 α β O 1 O 2 Figure 5 – The phase diagram. The critical cu rv e is calculated by solving Eq. (20) with ¯ a = 0 . 08, m = 15, s = 20 and T = 50 , 000. When ( α, β ) lies in th e upp er half of the phase d iagram O 1 w orks b etter than O 2 . Otherw ise O 2 w orks b etter. 0.25 0.3 0.35 0.4 0.45 0.5 Β 0.2 0.4 0.6 0.8 1 O 2      O 1 + O 2 Figure 6 – The relativ e p erformance O 2 / ( O 1 + O 2 ) as a fun ction of β , for fixed α = . 4. 15 These results were obta in ed by focus in g on the dynamics of col- lectiv e atten tion and examining the role that p opularit y and no velt y pla y in d etermining the num b er of clic ks w ithin a giv en page. In par- ticular, we analyzed thr ee different strategie s that can b e deploy ed in order to maximize atten tion. Th e firs t strategy prioritizes no vel ty while the s econd emph asizes p opularit y . The third strategy lo oks my- opically into the future and p rioritizes stories that are exp ected to generate th e most clic ks in the next f ew minutes. W e then sh o we d that th e first t w o strategi es should b e selected on the basis of the rate of no v elt y deca y , while the third strategy p er f orms sub-optimally in most cases. Most in terestingly , we discov ered that the relativ e p erfor- mance of the fi rst t wo b enchmark strategi es as a fun ction of the rate of n o v elty d eca y switc hes so sharply around some critical v alue that it resem bles phase transitions observ ed in the real w orld. Giv en the imp ortance of m aximizing page views for m ost con tent pro vid er s , this w ork suggests a prin cipled w ay of choosing wh at to prioritize when d esignin g dynamic w eb s ites. Kno wledge of th e rates with whic h nov elt y and p opularit y ev olve within the w eb s ite can then b e translated into decisions as to wh at to show first, second, etc. References [1] Josef F alkinger. Att ention economies. Journal of Ec onomic The- ory , v ol. 133, pp . 266–294 , 200 7. [2] J. Garofalakis, P . Kapp os and D. Mourlouk os. W eb site optimiza- tion u s ing page p opularit y . IE EE Internet Com puting , volume 3, issue 4, pp. 22– 29, 1999. [3] W eiyin Hong, James Y. L. Thong and Kar Y an T am. Does anima- tion attract online u sers attent ion? The effects of Flash on infor- mation search p erformance and p erceptions. Information Systems R ese ar ch , v ol. 15, no. 1, pp. 60–8 6, 2004. [4] Bernardo A. Hu b erman, Peter L . T. Pirolli, James E. Pitk o w , and Ra jan M. Luk ose. S trong regularities in W orld Wide W eb surfing. Scienc e , vol. 280, no. 5360, pp. 95–97 , 1998. 16 [5] Jos ´ e Ni ˜ no-Mora. S to chastic scheduling. E ncyclop e dia of O ptimiza- tion , C. A. Floudas and P . M. P ardalos, eds., v ol. V, pp . 367–372, 2001. [6] F ang W u and Bernardo A. Hub erman. Th e economics of attent ion: Maximizing user v alue in information-ric h environmen ts. The First International Workshop on Data Mining and Audienc e Intel ligenc e for A dvertising (A DKDD’07) , 200 7. [7] F ang W u and Bernardo A. Hu b erman. No v elty and collectiv e at- ten tion. Pr o c e e dings of National A c ademy of Scienc es , vo l. 104, no. 45, pp. 175 99–17601, 2007. [8] Ping Zhang. The effects of animation on information seeking p er- formance on the W orld Wide W eb: S ecur ing atten tion or int erf er- ing w ith primary tasks? Journal of the A IS , volume 1, issue 1, 2000. 17