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In the last few years, highly distributed, heterogeneous and dynamic environments have become usual contexts for scientific and business domains. In this work, we consider query scheduling over a grid-enabled distributed database, where the data may be partially or totally replicated into the component sites. Although there have been some previous proposals for query scheduling in distributed databases, they did not consider site reputation, which is important in autonomous and heterogeneous distributed systems. We propose a reputation-based election-inspired query scheduling strategy. Sites are autonomous concerning candidacy for answering queries, in which case they must report an expected response time commitment to those queries. A reputation system is used for ranking sites on their response time estimations. Commitment information and subsequent outcome allows the reputation-based election-inspired approach to improve the overall mean response time of the system. We compare it experimentally with other distributed schedulers to show that the use of reputation and elections improves performance in heterogeneous autonomous environments.