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consensuses
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Definitions of consensuses in various dictionaries:
noun - agreement in the judgment or opinion reached by a group as a whole
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Possible Dictionary Clues |
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Plural form of consensus. |
a general agreement. |
A general agreement. |
Consensuses might refer to |
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Consensus estimate is a technique for designing truthful mechanisms in a prior-free mechanism design setting. The technique was introduced for digital goods auctions and later extended to more general settings.Suppose there is a digital good that we want to sell to a group of buyers with unknown valuations. We want to determine the price that will bring us maximum profit. Suppose we have a function that, given the valuations of the buyers, tells us the maximum profit that we can make. We can use it in the following way:* Ask the buyers to tell their valuations. * Calculate * * * * * R * * m * a * x * * * * * {\displaystyle R_{max}} * - the maximum profit possible given the valuations. * Calculate a price that guarantees that we get a profit of * * * * * R * * m * a * x * * * * * {\displaystyle R_{max}} * .Step 3 can be attained by a profit extraction mechanism, which is a truthful mechanism. However, in general the mechanism is not truthful, since the buyers can try to influence * * * * * R * * m * a * x * * * * * {\displaystyle R_{max}} * by bidding strategically. To solve this problem, we can replace the exact * * * * * R * * m * a * x * * * * * {\displaystyle R_{max}} * with an approximation - * * * * * R * * a * p * p * * * * * {\displaystyle R_{app}} * - that, with high probability, cannot be influenced by a single agent.As an example, suppose that we know that the valuation of each single agent is at most 0.1. As a first attempt of a consensus-estimate, let * * * * * * R * * a * p * p * * * = * ⌊ * * R * * m * a * x * * * ⌋ * * * {\displaystyle R_{app}=\lfloor R_{max}\rfloor } * = the value of * * * * * R * * m * a * x * * * * * {\displaystyle R_{max}} * rounded to the nearest integer below it. Intuitively, in "most cases", a single agent cannot influence the value of * * * * * R * * a * p * p * * * * * {\displaystyle R_{app}} * (e.g., if with true reports * * * * * R * * m * a * x * * * = * 56.7 * * * {\displaystyle R_{max}=56.7} * , then a single agent can only change it to between * * * * * R * * ... |