I don't find it in the least bit hard to imagine. Political colleagues often detest each other, and have good reason to do so, but it doesn't seem to stop them working together closely. Tony Blair and Gordon Brown are a classic example.

If the winning contender thinks that the defeated one will help him or her get elected, and if the defeated one thinks that taking that job will be in his or her best interests, that is what will happen.

The crucial thing isn't whether they like or dislike each other, or whether they have said harsh thing about each other, it is those two "ifs".
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When the USA was set up the initial idea was that the Vice President would be the runner up in the General Election. Perhaps they should have stuck to that system...