It sounds a little odd because here losing is related to the election, but the way you have expressed them tells that there is no relation between them. I would say it this way: After losing in his home constituency, he said he was going to resign. After having lost in his home constituency he said he was going to resign.
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AnonymousAfter the election, he had said that he was going to resign after having lost hisNeither because you don't need the word home.homeconstituency.After the election, he had said that he was going to resign after losing hishomeconstituency.Which one is correct and why?