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1. Have you decided whether you will go to the party or not?

2. Have you decided whether you will go to the party?

What is the difference between the two? The second sentence is enough to ask the very question you would like to raise. However, I am well aware the existence of the first sentence too. Why do you need it?
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You don't need the tag, but it helps stress the alternative, which may be implicit: 'have you decided whether you will go to the party or stay home?'
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MrM, is there a more complete sentence to this?

Have you decided whether you will go to the party or you will stay home?
Do you mean an extended form of my example? (Your original sentence does not extend that far-- I was just suggesting a parallel.) If we expand 'Have you decided whether you will go to the party or stay home?', yes, I suppose it would be 'Have you decided whether you will go to the party or you will stay home?'. It is in no sense more 'complete' though; as far as language use is concerned, it is on the contrary rather artificial.