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In addition to what Mari-Lou said about punitive downvotes for dupicate questions, there is some added irony in this case:
1) The "offending" O.P. actually linked to the duplicate question which shows that they did their legwork, homework and research with due diligence – something hardly deserving of a downvote.
2) I'm not convinced the questions are ...
Voting is a network-wide thing rather than an ELU-specific thing, and I think this is answered by an Meta.SE question, What's the difference between Suffrage and Vox populi badge. It's not possible to mark this question as a duplicate of that one because it's on a different site, but please do refer to it.
Suffrage: used 30 votes per day
Vox populi: ...
No, if you hit the downvote from a positive vote (+1), it does not return to the previous state (0), but the answer loses a vote (-1).
If you want to cancel your vote, click on the same arrow you used in the first place.
I think this is not a bug, but something the users should know.
I don't understand why a user has to penalise an OP for posting a duplicate question. Very often newcomers are unaware or unable to search a related question. Which doesn't appear to be the case here.
For us "oldies" who keep seeing the same question time and time again, it can get irritating. But that's not the fault of the OP. And maybe a duplicate ...
I don't understand why you want (or need) more than one vote. As @Lego Stormtrooper stated, you can always raise awareness (significantly) by offering a bounty on a question you like.
If you think a question especially worthy, I've seen someone in chat (I don't go often, so I don't know how common this is) ask others to look at a good question and vote.
What I can say is, it's only comments possibly meant as a joke and not an actual case of voting fraud. And since people don't necessarily like being told what to do, I'm sure most people won't care to upvote others' answers that way.
And flag such comments as no longer needed. Enough flags will remove them without requiring a moderator's attention.
Doesn't sound particularly worrisome to me. The comments you saw were maybe not useful (probably why they were deleted), but it's not like posting a comment asking for upvotes on certain answers (if I'm understanding this correctly?) is anything like, say, using sock-puppets to upvote or downvote answers. Leaving a comment doesn't affect the score of an ...
The other situation that can result is unusual score changes is when an content that you've downvoted on gets deleted, or a user who has downvoted your content gets removed. As far as I can tell, there is no way to suss out the details of these actions, they just get rolled up into other score changes.