Recommending and Targeting Gabrielle Demange Paris School of Economics July 9, 2015 Gabrielle Demange (PSE-EHESS) Recommending and targeting 1 / 48
What ? a single item, a set of items, an ordered set (PageRank) Who ? who recommends ? who is targeted ? who reviews ? Why ? attract consumers on a platform, attract attention on a product How ? search engines, ads, targeting Gabrielle Demange (PSE-EHESS) Recommending and targeting 1 / 48
In this talk I focus on two settings ranking by search engines, journals information based on the hyperlink structure or citations how to aggregate these citations? targeting in a social network (exploiting positive externalities) what are the optimal strategies? what is the value of information on the network? Gabrielle Demange (PSE-EHESS) Recommending and targeting 2 / 48
Important questions left aside Are recommendations biased ? single product - experimentation Che Horner [2013] Kremer, Mansour, Perry [2014] - distorted value (Google to YouTube) de Corniere and Taylor [2014] multi-products (Amazon, Netflix) ? motives for bias between products ? main issue: personal data What are the consequences of better recommendation on welfare ? on prices ? on product design ? Bar-Isaac, Caruana, Cu˜ nat [2012] Gabrielle Demange (PSE-EHESS) Recommending and targeting 3 / 48
Ranking Ranking What does a search engine’s ranking mean? Aggregation of preferences or aggregation of information? Various methods, produce different results. e.g. counting, invariant method (basis for PageRank of Google) How to choose a method? Can we define new interesting methods? Useful approach: Characterization of a method through its properties (axiomatization) Gabrielle Demange (PSE-EHESS) Recommending and targeting 4 / 48
Ranking Ranking 1 The setting Some methods Illustration: Ranking economic journals Graphs/Web Targeting 2 Various targeting problems Constant returns to exposure Diminishing returns to exposure Increasing returns to exposure Gabrielle Demange (PSE-EHESS) Recommending and targeting 5 / 48
Ranking The setting Ranking problems N = { 1 , ..., n } be a set of n ’items’ to rank M = { 1 , ..., m } be a set of m ’experts’ n × m matrix π = ( π i , j ) column j = j ’s statement on the items π i , j = valuation of j on i A ranking method assigns scores to each admissible π � r = ( r i ) r i ≥ 0 , r i = 1 i Gabrielle Demange (PSE-EHESS) Recommending and targeting 6 / 48
Ranking The setting Examples 1 Web : incidence matrix π i , j = 1 if j points to i and 0 otherwise treated as ’Approval voting’ 2 Journal : π i , j = average number of references of an article from j to articles in i . In both cases M = N ’peers’ method normalized statements [ π ] i , j = π i , j for each i , j . π + j → Intensity-Invariant method to avoid a form of manipulation Gabrielle Demange (PSE-EHESS) Recommending and targeting 7 / 48
Ranking Some methods The counting method The scores ( r i ) are proportional to the received valuation totals: � r i ∝ π i , j for each i j ∈ M used by the Science Citation Index for ranking journals, by reviewers’ systems treats experts equally whatever their statements Gabrielle Demange (PSE-EHESS) Recommending and targeting 8 / 48
Ranking Some methods Experts’ weights most methods assign not only scores to items, r , but also weights to experts: q = ( q j ) s.t. = � r i j [ π i , j ] q j for each i the ranking is a weighted average of the statements weights may vary with the statements. � = counting method: q j = 1 / m , whatever π Three methods, invariant, HITS, Handicap-Based Equilibrium relationship between scores r and weights q Gabrielle Demange (PSE-EHESS) Recommending and targeting 9 / 48
Ranking Some methods Eigenvector methods N = M (peer setting), π irreducible Recursive Impact factor or LP (Liebowitz-Palmer) method � r i = λ π i , j r j for each i j ∈ N r principal eigenvector of π , dominant eigenvalue λ Invariant method: LP applied to normalized statement [ π ] Pinski and Narin [1976] � r i = [ π i , j ] r j for each i . j ∈ N Expert’s Weight= Expert’s Score axiomatization Altman Tennenholtz [2005] Palacios-Huerta Volij [2004] Gabrielle Demange (PSE-EHESS) Recommending and targeting 10 / 48
Ranking Some methods Example 1 10 10 0 10 30 0 19 13 9 3 π = 27 0 9 [ π ] = 0 10 13 1 9 3 9 0 0 10 19 Counting (0.4545, 0.4091, 0.1364) LP=(0.3734, 0.4382, 0.1884) reverse order for 1 and 2; 1 cites 2 a lot and ’conveys’ power; Invariant = (0.3806, 0.3945, 0.2249) ’power’ given to 1 by 3 diminishes, power given to 3 by 2 increases Gabrielle Demange (PSE-EHESS) Recommending and targeting 11 / 48
Ranking Some methods The Hyperlink-Induced Topic Search HITS method assign to each i two indices that distinguish between i ’s ability as an item (authority) from that as an expert (hub): The HITS method (Kleinberg [1999]) � � r i = π i , j q j each i and q j = λ π i , j r i each j j i → r principal eigenvector of π � π and q principal eigenvector of � ππ Gabrielle Demange (PSE-EHESS) Recommending and targeting 12 / 48
Ranking Some methods Handicap-based method N and M can differ. There are unique r and q � � π i , j q j each i and 1 1 r i = = λ π i , j each j q j r j j i The Handicap-based method : assigns scores r . Demange [2014-b] axiomatizations: the counting method and HB satisfy a homogeneity property HB is intensity-invariant, the counting m. is not HB is appropriate to aggregate vectors of proportions Gabrielle Demange (PSE-EHESS) Recommending and targeting 13 / 48
Ranking Illustration: Ranking economic journals Ranking economic journals Rankings of 37 journals, same data as in Palacios-Huerta, Volij (04) r and q (handicap-based) per article Same top 6 handi inv q QJE 10.02 11.44 5.34 Eca 9.65 11.74 3.42 J Econ Lit 9.65 9.26 8.16 JpolE 7.22 7.56 4.15 AER (proper) 7.01 7.52 2.48 RES 5.99 7.42 5.59 average score = 100/37 ≈ 2.97 =average experts’ weights Gabrielle Demange (PSE-EHESS) Recommending and targeting 14 / 48
Ranking Illustration: Ranking economic journals handi inv q J. Economic Behavior Organization 0.8 0.59 1.75 Scandinavian J. of Econ 0.77 0.47 3.81 Oxford Bull. of Ecs.Stat. 0.69 0.314 2.84 Economics Letters 0.57 0.355 0.66 Weights are positively correlated with the scores, but moderately rankings of theory journals go down : they receive citations proportionately more from top journals journals that go up : Journal of financial economics, Rand, Oxford Econ statistics, Social of economic and welfare Gabrielle Demange (PSE-EHESS) Recommending and targeting 15 / 48
Ranking Illustration: Ranking economic journals Remark on Irrelevance of independent alternatives (IIA) IIA: ranking between i and j only depends on statements on or by them the counting method satisfies IIA ’almost’ the only relevant one Rubinstein [1980] Brink Gilles [2009] IIA is NOT met by other methods the score of an item depends on the statements over all items via the values taken by the experts’ weights. IIA is not appealing in many contexts Gabrielle Demange (PSE-EHESS) Recommending and targeting 16 / 48
Ranking Graphs/Web Graphs/Web On a graph, a ranking gives a measure of ’importance’ of a node Counting= in-degree if directed Invariant = random surfer interpretation along directed edges Irreducibility: a directed path joins every two nodes Web graph is not irreducible; Perturbation technic Gabrielle Demange (PSE-EHESS) Recommending and targeting 17 / 48
Ranking Graphs/Web PageRank/damping factor Brin and Page [1998] PageRank perturbs the incidence matrix with a ”damping factor” � r i = (1 − α ) + α [ π i , j ] r j for each i . n j ∈ N r = 1 − α ( I − α [ π ]) − 1 1 1 n I = n × n identity matrix, 1 1 = n -vector of ones centrality measure for measuring ’prestige’ in a network (Katz [1953] Bonacich [1987] variation: introduce a personalized perturbation Gabrielle Demange (PSE-EHESS) Recommending and targeting 18 / 48
Ranking Graphs/Web Example 0 1 2 4 5 6 7 8 9 3 Boldi, Santini and Vigna [2007] Perturbed invariant method. 1 − α = 10 − 3 assigns 0.0049 to 0, 0.4943 to 4 and 0.4939 to 5 HB assigns 0.9595, to 0 with weights 0.2385 for i = 6..., 9 damping factor Google ( α = 0 . 85) Gabrielle Demange (PSE-EHESS) Recommending and targeting 19 / 48
Ranking Graphs/Web Could we do better ? How to interpret the absence of a link/vote ? Can we distinguish between negative votes and the absence of awareness ? How to choose the set of ’experts’ M ? impact of changing M ? Gabrielle Demange (PSE-EHESS) Recommending and targeting 20 / 48
Ranking Graphs/Web Other questions allowing multiple rankings along different dimensions (in Ideas) but also on different sets of preferences, on different expert’s sets ? related to personalized recommendations value of forming close communities to make recommendations (under anonymity) Demange [2010], interaction between current ranking and next statements hence next ranking → dynamics Demange [2012] and [2014-a] Gabrielle Demange (PSE-EHESS) Recommending and targeting 21 / 48
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