Three departments each describe the same process differently and none of them will budge. What do you do?

Get the evidence in the room and map it together rather than separately. Run one session with all three, walk real cases end to end, and let the data show where the process genuinely diverges. Very often all three are right about their own part and nobody has ever seen the whole. If a real decision is needed, name it and take it to the process owner.

I stop collecting descriptions separately, because that is how you end up as a courier between three versions. I get them in one room with real cases, and we walk a handful of actual examples end to end, pulling the records up as we go. What usually happens is that all three are correct about their own segment and nobody has ever seen the whole thing, so the disagreement dissolves as soon as it is on one wall. On a fulfillment process the warehouse and the customer service team were describing the same step two days apart, and the gap was a batch job nobody outside IT knew about. Where a real difference remains, it is normally a legitimate variation for a customer type or a region, so I document it as a variant instead of forcing false consistency. If it is a genuine decision about which way it should work, I name it clearly and take it to the process owner rather than mediating it myself.