Wanted to get some opinions on this situation: I have a new direct who leads a small team of ~9 folks. We're in the performance review cycle and I'm writing the reviews since the team reported to me directly for most of the year (so, he is the new 'middle manager').
Would it be appropriate to have the new manager sit in on the review? I have my own opinion but am interested in what others think.

Yes
Yes the new manager should definitely sit in on the reviews. They will be doing the review next year and it will be good for them to see an example as to how you expect the meetings to be conducted and they can also know exactly what was discussed, if it is referred back to during the coming year. For example if you have discussions with a report who needs to improve in a certain area, the new manager can know what improvements are expected and will know exactly what was said.
There should be no surprises at a performance review anyway, as performance and goals should be discussed weekly at O3s and feedback be given regularly as needed. Therefore no need to not involve the new manager and many good reasons to involve them!
I took on a new team last year and this was just after the performance reviews had been held. It;s been difficult to refer back to those reviews as I was not present and the meetings and now only have one side of the story. Perhaps not surprisingly all of the team disagreed with the areas of development that had been discussed in the review, but that I was not privy to. So I pretty much had to start again and develop my own assessment of each person. This was good to do anyway, but it definitely would have helped to sit in on those reviews!
Good luck,
Jane
Yes
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