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When a compound possessive is formed with "and," I think the rule is that both terms become possessive when there are multiple separate objects that are owned, as in "John's and Dave's cars" (John's car and Dave's car). Only the last term becomes possessive when you're talking about a shared object, as in "John and Dave's house" (one house where John and Dave both live).

Is there a similar rule with "or"? Like is there a difference between saying "That house on the left is either John or Dave's house" versus saying "That house on the left is either John's or Dave's house"?

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The same rule would normally apply, except that the following doesn't make any sense:

  • ? That is John or Dave's house.

Because of the rule, that is expressing joint ownership of the house between the two people; however, you can't have any kind of joint ownership in that sentence—unless you interpret the or as being inclusive and only referring to the situation where both are true. But I've never seen or used in that way, and it would be identical to and anyway.

In order to use or, and have it make sense, you would need to use one of the following:

  • That is John's house or Dave's house.
  • That is John's or Dave's house.
  • That house belongs to John or Dave.

Or, if you want to include the possibility of an inclusive or, you could add that explicitly:

  • That is John's house, Dave's house, or John and Dave's house.
  • That is John's, Dave's, or John and Dave's house.
  • That house belongs to John, Dave, or John and Dave.

The use of either (or both) in various places in these sentences is also possible. They might provide clarity, but they aren't essential.

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  • That house on the left is either John's or Dave's house

is a deleted form and absolutely standard.

  • *That house on the left is either John or Dave's house

is of the same form as

  • That house on the left is either the manse or Dave's house

and is illogical in structure, and not a permitted deletion.

.............

There is a situation we can contrive where ownership of the house is known to be in question, where say John and Dave are arguing over ownership in court:

  • That house on the left is either John or Dave's house, or Sue's house

(we don't know if it's Sue's, or the one whose ownership is being disputed).

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