engine for hotels, using a unique data set containing transac- utility after purchasing a product. This idea naturally gener- tions from Nov. 2008 to Jan 2009 for US hotels from a maj ates a ranking order: The products that generate the highest travel web site. Our extensive user studies, using more than consumer surplus should be ranked on top 15000 user judgments, demonstrate an overwhelming preference for the ranking generated by our techniques, compared to a 2.2 The BLP model The major contributions of our research are: (1)We present a characteristics and estimate the corresponding weights assign- arge number of existing strong baselines The key for our model is to identify the different produ causal model, based on economic theory, to capture the decision- by consumers towards the characteristics and the price of the king process of consumers, leading to a better understanding product. However, different consumers hold different evalu- of consumer preferences. The causal model relaxes the assump- ations towards the product characteristics and towards the tion of" consistent environment"across training and testing money. To capture the consumer heterogeneity, we use the data sets: we can now have changes in the environment and Random-Coefficient Logit Model 3(also known as BLP can predict what should happen under such changes. (2) We This model incorporates consumer heterogeneity by assuming infer personal preferences from aggregate data, in a privacy- that consumers have idiosyncratic tastes towards product char preserving manner. (3) We propose a ranking method using acteristics. In other words, the coefficients B and a in equation the notion of surplus, which is derived from a"generative"user 1 and 2 are different for each consumer. Based on this, we behavior model.(4)We present an extensive experimental define the utility surplus for consumer i to buy product Xj as study: using six hotel markets, and 15000 user evaluations sing blind tests, we demonstrate that the generated rankings S=Uh(x1)-{n()-Um(r-p)+e(3) are significantly better than existing approaches. ∑·+5 2. THEORY MODEL Utility of money Stochastic error Utility of product In this section, we first introduce the background of the ex Here, I is the income of consumer i, P, is the price of product pected utility theory, characteristics-based theory, and economic X, Um is the utility of money(parameterized by user specific surplus. Then we discuss how we leverage these concepts into weight scalar a ) and Uh is the utility of product purchased our setting and empirically estimate our model. (parameterized by user specific weight vector B). Note that 2.1Ba E is a product-specific disturbance scalar summarizing unob- served characteristics of product X,, whereas a; is a stochastic Our model is derived from from expected utility and ratione choice error term that is assumed to be i.i.d. across products hoice theories. A fundamental notion in utility theory is that and consumers in the selection process. The parameters to be each consumer is endowed with an associated utility function estimated are a' and Bi, which represent the weights that con which is"a measure of the satisfaction from consumption of sumer i assigns towards"money" and towards different observe various goods and services. The rationality assumption defines product characteristics, respectively that each person tries to maximize its own utility The technical details for the model estimation are in 7. To More formally, assume that the consumer has a choice across etter understand our model, let's consider an example products X1,..., Xn, and each product X, has a price Pj. Buy ing a product involves the exchange of money for a product ExAMPLE 1. Suppose that we have two cities, A and B and Therefore, to analyze the purchasing behavior we need to have two types of consumers: business trip travelers and family trip two components for the utility function: (1)Utility of Product: travelers. City A is a business destination (e.g, New york The utility that the consumer will get by buying the product City)with 80% of the travelers being business travelers and 20% nd(2)Utility of Money: The utility that the consumer families. City B is mainly a family destination(e g, Orlando ill lose by paying the price pi for product Xj with 10% business travelers and 90% family travelers. In city A On one hand, the decision to purchase product X, generates a we have two hotels: Hilton(A1) and Doubletree(A2). In city product utility U(X, ) According to Lancasters characteristics B, we have again tuo hotels: Hilton(B1) and Doubletree(B2) theory (6 and Rosen's hedonic price model(10), differentiated Hilton hotels(At and Bi) have a conference center but not a products are described by vectors of objectively measured char- pool, and Doubletree hotels(A2 and B2) have a pool but not acteristics. Let rk denote the kth observed characteristics of a conference center. To keep the example simple, we assune product X,. Thus, the utility of product can be defined as that preferences of consumers do not change when they travel the aggregation of weighted utilities of observed individual in different cities and that prices are the same haracteristics and an unobserved characteristic, E,, as follows By observing demand, we see that demand in city A(busi U(x)=U(x}…)=∑时x+51,(1)JorDoubere.hnctyBoamadestinaonthedemandas 540 bookings per day for Hilton and 460 bookings for Doubletree On the other hand. assume that the consumer has some Since the hotels are identical in the two cities, the changes in disposable income I that ge a money utility U(D). Paying demand must be the result of different traveler demographics typically assume that pi is relatively small compared to the from hotel A(conference center, no pool)is US(A1)=5A1+ disposable income I, and the marginal utility of money remains (Bcon/1+Bpool-0)+e, and for family travelers, the corresponding onstant in the interval I-p, to I[. In this case, utility surplus is US(A1)=641+(Bnr·1+Bpa:0)+∈ U(r)-U(I-pi)=al-a(I-pi)=api business travelers towards"conference center"and "pool" and With the assumption of rationality, a consumer purchases by B, we denote the respective deviations for family travelers. utility. Let consumer surplus denote the"increase" Similarly, we can write down the utilities for hotels A2, Bi and B2. Following the estimation steps, we discover that familyengine for hotels, using a unique data set containing transac￾tions from Nov. 2008 to Jan. 2009 for US hotels from a major travel web site. Our extensive user studies, using more than 15000 user judgments, demonstrate an overwhelming preference for the ranking generated by our techniques, compared to a large number of existing strong baselines. The major contributions of our research are: (1) We present a causal model, based on economic theory, to capture the decision￾making process of consumers, leading to a better understanding of consumer preferences. The causal model relaxes the assump￾tion of “consistent environment” across training and testing data sets: we can now have changes in the environment and can predict what should happen under such changes. (2) We infer personal preferences from aggregate data, in a privacy￾preserving manner. (3) We propose a ranking method using the notion of surplus, which is derived from a “generative” user behavior model. (4) We present an extensive experimental study: using six hotel markets, and 15000 user evaluations using blind tests, we demonstrate that the generated rankings are significantly better than existing approaches. 2. THEORY MODEL In this section, we first introduce the background of the ex￾pected utility theory, characteristics-based theory, and economic surplus. Then we discuss how we leverage these concepts into our setting and empirically estimate our model. 2.1 Background Our model is derived from from expected utility and rational choice theories. A fundamental notion in utility theory is that each consumer is endowed with an associated utility function U, which is “a measure of the satisfaction from consumption of various goods and services.” The rationality assumption defines that each person tries to maximize its own utility. More formally, assume that the consumer has a choice across products X1, . . . , Xn, and each product Xj has a price pj . Buy￾ing a product involves the exchange of money for a product. Therefore, to analyze the purchasing behavior we need to have two components for the utility function: (1) Utility of Product: The utility that the consumer will get by buying the product Xj , and (2) Utility of Money: The utility that the consumer will lose by paying the price pj for product Xj . On one hand, the decision to purchase product Xj generates a product utility U(Xj ). According to Lancaster’s characteristics theory [6] and Rosen’s hedonic price model [10], differentiated products are described by vectors of objectively measured char￾acteristics. Let x k j denote the kth observed characteristics of product Xj . Thus, the utility of product can be defined as the aggregation of weighted utilities of observed individual characteristics and an unobserved characteristic, ξj , as follows U(Xj ) = U(x 1 j , . . . , x k j ) = X k β k j · x k j + ξj . (1) On the other hand, assume that the consumer has some disposable income I that generates a money utility U(I). Paying the price pj decreases the money utility to U(I − pj ). We typically assume that pj is relatively small compared to the disposable income I, and the marginal utility of money remains constant in the interval I − pj to I [8]. In this case, U(I) − U(I − pj ) = αI − α(I − pj ) = αpj . (2) With the assumption of rationality, a consumer purchases product Xj if and only if it provides him with the highest in￾crease in utility. Let consumer surplus denote the “increase” in utility after purchasing a product. This idea naturally gener￾ates a ranking order: The products that generate the highest consumer surplus should be ranked on top. 2.2 The BLP Model The key for our model is to identify the different product characteristics and estimate the corresponding weights assigned by consumers towards the characteristics and the price of the product. However, different consumers hold different evalu￾ations towards the product characteristics and towards the money. To capture the consumer heterogeneity, we use the Random-Coefficient Logit Model [3] (also known as BLP). This model incorporates consumer heterogeneity by assuming that consumers have idiosyncratic tastes towards product char￾acteristics. In other words, the coefficients β and α in equation 1 and 2 are different for each consumer. Based on this, we define the utility surplus for consumer i to buy product Xj as USi j = Uh(Xj ) − [Um(I i ) − Um(I i − pj )] + ε i j (3) = X k β ik · x k j + ξj | {z } Utility of product − α i pj |{z} Utility of money + ε i j . |{z} Stochastic error Here, I i is the income of consumer i, pj is the price of product Xj , Um is the utility of money (parameterized by user specific weight scalar α i ), and Uh is the utility of product purchased (parameterized by user specific weight vector β i ). Note that ξ is a product-specific disturbance scalar summarizing unob￾served characteristics of product Xj , whereas ε i j is a stochastic choice error term that is assumed to be i.i.d. across products and consumers in the selection process. The parameters to be estimated are α i and β i , which represent the weights that con￾sumer i assigns towards “money” and towards different observed product characteristics, respectively. The technical details for the model estimation are in [7]. To better understand our model, let’s consider an example. Example 1. Suppose that we have two cities, A and B and two types of consumers: business trip travelers and family trip travelers. City A is a business destination (e.g., New York City) with 80% of the travelers being business travelers and 20% families. City B is mainly a family destination (e.g., Orlando) with 10% business travelers and 90% family travelers. In city A, we have two hotels: Hilton (A1) and Doubletree (A2). In city B, we have again two hotels: Hilton (B1) and Doubletree (B2). Hilton hotels (A1 and B1) have a conference center but not a pool, and Doubletree hotels (A2 and B2) have a pool but not a conference center. To keep the example simple, we assume that preferences of consumers do not change when they travel in different cities and that prices are the same. By observing demand, we see that demand in city A (business destination) is 820 bookings per day for Hilton and 120 bookings for Doubletree. In city B (family destination) the demand is 540 bookings per day for Hilton and 460 bookings for Doubletree. Since the hotels are identical in the two cities, the changes in demand must be the result of different traveler demographics. More specifically, for business traveler, the utility surplus from hotel A1 (conference center, no pool) is USB(A1) = δA1 + (β B conf ·1+β B pool ·0)+, and for family travelers, the corresponding utility surplus is USF (A1) = δA1 + (β F conf · 1 + β F pool · 0) + . By β B • we denote the deviations from the population mean for business travelers towards “conference center” and “pool” and by β F • we denote the respective deviations for family travelers. Similarly, we can write down the utilities for hotels A2, B1 and B2. Following the estimation steps, we discover that family