| CPC G06Q 30/0202 (2013.01) [G06Q 30/0201 (2013.01); G06Q 30/0203 (2013.01)] | 20 Claims |

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1. An audience measurement system comprising a processor and a memory, the audience measurement system configured to perform a set of operations comprising:
receiving, from a plurality of meters via a network, metering data for a plurality of media events;
storing the metering data in a datastore managed by an audience measurement entity;
obtaining, from one or more service providers, return path data for the plurality of media events;
identifying a first merged media event for which a first deduplicated reach value is to be determined, the first merged media event based on a union including a second merged media event;
determining whether the first merged media event satisfies a mutual exclusivity condition;
in response to the first merged media event satisfying the mutual exclusivity condition, estimating the first deduplicated reach value for the first merged media event based on at least a merge ratio and a second deduplicated reach value previously estimated for the second merged media event, wherein the estimating is carried out in a manner that satisfies logical constraints on the first deduplicated reach value, and wherein the logical constraints are derived from a union inequality; and
outputting the first deduplicated reach value.
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