In games where each team keeps their own book, you are right - home is official.
However, just to prevent such a discrepancy, at each half inning, I ask the offensive book how many runs were scored. I then ask the defense book the same question. If I get a different answer (about 1 time every 10 games), I ask the two scorekeepers to get together. If they can't (only happened once), then I will declare "home" official and move one.
This isn't really "my job" but it is common practice around here (to the point that it is expected) and besides, I find it to be a good practice in game management.
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Tom
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