Try this also...
With Member [Measures].[Thing Count YTD] As
AGGREGATE(YTD([Effective Date].[Year-Week].CurrentMember)
, [Measures].[Thing Count] )
SELECT
[Measures].[Thing Count YTD] ON 0,
[Effective Date].[Year-Week].[Week].[2013 Week 6] ON 1
FROM
[Cube]
This keeps whatever it is you are counting from being double counted.
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