I think that your best bet may be to show two results. One with the actual results and one with the outliers removed. Then explain why you removed the outliers. Readers can then choose to either agree with your reasons for removal or disagree.
If you run a method that has the side effect of significantly changing just this one method, the natural response would be that you should use a different method. The person can then show a couple of alternatives with the outlier much better represented. Then they are accusing you of bad behavior. Your only real defense would be that you had a good reason to view that as an attempt at cheating. Which then gets us back to showing both results with your reasons for removal.
If you're on the transparent path, I'd just stay on it. It makes you more credible when you claim that you know that someone was trying to vote multiple times.
Another option would be to evaluate the votes with a range voting variant. For each ballot choice, give it one point for each ballot choice it is ranked ahead of. So if you have a ballot that says, Sanders, Clinton, Trump, then Sanders gets 2 points, Clinton gets 1, and Trump gets 0. Now if you have another ballot that says only Trump, Trump gets 0. Sum these numbers across all the ballots. Whichever choice has the most points wins. The problem with this is that it squelches all the single vote ballots.
Or you could eliminate duplicate ballots. Then all the single vote ballots for the same choice will count only once. Of course, this also may squelch some votes by legitimately different people. This would only work if most ballots are distinct and only some combinations are represented. If there's only three choices and all twelve combinations are represented, this wouldn't work.
Regardless, I still think that you should show multiple results. Explain why you did the different systems. Let people reading make up their own mind as to how to handle it.