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The parties are free to agree on the number of arbitrators. The role of the arbitrator is so significant in the arbitration system that its success or failure may depend on the credibility of the arbitrator. The arbitrator is endowed with not only the power of presiding arbitral procedures and of rendering arbitral awards, but also the right to remuneration and expense. The composition of the arbitral tribunal will be examined in the light of general practice. The administration of the arbitration also implies a methodology aimed at ensuring the smooth-flow and impartiality of arbitral tribunal. The UNCITRAL Model Law on International Commercial Arbitration identified a certain number of basic obligations and rights of an arbitrator, whatever the legal context of the arbitration in the cases. The obligation to be and remain independent and impartial; to conduct the procedure equitrably; the obligation of confidentiality; the right to reasonable remuneration and the right to expect honest cooperation from the parties and appropriate assistance from the arbitration institution. In practice, the party-appointed-arbitators in international commercial arbitration very often feel enormous pressure that comes from the expectation of the parties that nominated them.