There is new book out on Arbitration prior to and after the Conquest in Quebec, by Michel Morin and two colleagues. For a long time, it has been assumed that after the Conquest of 1760 and the establishment of British Courts in Quebec, French Canadians used arbitration to boycott British Courts in family affairs (i.e., issues concerning inheritance and matrimonial property, etc.). This boycott theory has more recently been challenged by historians, This book attempts to provide a comprehensive view of the relationship between arbitrators and the courts in France, England, the British colonies, New France and the Province of Quebec. It concludes that arbitration was generally used to resolve factual issues such as the value of goods or the partitioning of land, often with the active support of judges after a lawsuit was initiated. This was true from 1764 to 1784 in Quebec, when arbitrators were often appointed by the court. There are important fluctuations in the number of arbitrations found in judicial archives and notarized documents, but there is no apparent correlation with the introduction of English Law by the Royal Proclamation of 1763 or its repeal by the Quebec Act of 1774.
For more information see: http://www.editionsthemis.com/livres/livre-4821-les-tribunaux-et-l-arbitrage-en-nouvelle-france-et-au-quebec-de-1740-a-1784.html