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The order of the rules is definitely material. When a pair of records in a cluster is compared, the first rule in order that it hits will be the one that forms the relationship (or discounts it if there is a NO MATCH decision on the rule).
The 'priority score' on each rule is intended for external use to provide a simple numerical value that can be used to present matches in priority order. It has no effect on the order in which match rules are applied, which is based on their order in the table.
There is plenty of documentation on matching in the online help. Start with the matching concept guide then read the section on match rules for the match processor.
Thanks for you quick and clear response. Very helpful!