What you Pay for is What you Get

1. What you Pay for is What you Get Tang Ruiming, Shao Dongxu, Stephane Bressan, Patrick Valduriez

2. Motivation and existing works • Almost all pricing frameworks sell a data item if a consumer’s willingness-to-pay (WTP) is larger or equal to the price p of the data item. • E.g. [Koutris et al., 2012], [Kushal et al., 2012], [Birnbaum and Jae, 2007] • What if WTP< p? • In real markets, it is still possible for consumers to get the products, e.g. second-hand goods, goods close to expiry date.

3. Motivation and existing works • Li et al. propose a framework for privacy concern in [Li et al., 2012]: • They assign prices to noisy query answers, as a function of the query and a standard deviation which consumers are able to tolerate. • If a consumer cannot afford the current price, she can set a higher standard deviation. • However: • They consider linear queries. • Standard deviation is not a meanful measurement without knowing the exact value. • People have to find an acceptable price by trying different values. We focus on pricing data We use probability People propose price directly

4. Framework description data provider data consumer data market owner Propose a price A tuple t, with price data consumer gets t data consumer gets an approximate value of t, whose accuracy is commensurate with the discounted price

5. Framework description Generate a distribution X Sample a value from X Intuition 1: the higher the proposed price is, the closer X is to t. Intuition 2: the higher the proposed price is, the larger probability of getting t from X.

6. Data model • The tuple t=(id,v). The domain of v is discrete and there are m different possible values. • (HT090481Y, A) and domain is {A,B,C,D,F} • An X-tuple is a set of m mutually exclusive tuples with the same id value but different v values. Each tuple is associated with a probability. • X={<(HT090481Y,A),0.5>, <(HT090481Y,B),0.2>, <(HT090481Y,C),0.3>, <(HT090481Y,D),0>, <(HT090481Y,E),0>} • X=(0.5,0.2,0.3,0,0) We use Earth Mover’s Distance to measure the distance between X and ground distance

7. Distance function δ • is an invertible function, which takes a proposed price as input, returns a distance between X and • is a pricing function. • Contra-variance: larger distance implies lower price. • Invariance: same distance values imply the same price. • Threshold: distance value cannot be larger than and the price of this distance value is • [0, ]  [ ]

8. Probability function π • is an invertible function, which takes a proposed price as input and returns the probability of a tuple sampled from X being t. • is a pricing function • Co-variance: larger probability implies higher price. • Invariance: same probability values imply the same price. • Threshold: the probability value cannot be less than 1/m and the price of this value is • [1/m,1]  [ ]

9. Optimal acceptable distribution • A distribution X is -acceptable if • An acceptable distribution X is optimal if • Y is an arbitrary acceptable distribution. • An optimal acceptable distribution is generated among all acceptable distributions, to ensure fairness among consumers. • Otherwise, it is possible that a consumer c1 pays more than a consumer c2, but the distribution X1 for c1 is less expensive than X2 for c2.

10. Optimal acceptable distribution • Let X be an optimal acceptable distribution. • (Theorem) • where j is an index maximizing |j-k| • and • Based on the proof of this theorem, two algorithms running in linear time are devised to generate such optimal acceptable distributions.

11. Conclusion • We propose a framework in which a data consumer is able to propose any price for her requested data and data accuracy is traded for discounted price. • In our framework, the value is approximate if she offers to pay only a discounted price. • We defined ancillary pricing functions and the necessary algorithms under several principles for a healthy market.