Unless there is a clear pattern of this user consistently posting two answers on a question in hopes of getting the Populist badge, I wouldn't be concerned about this as an issue. Here's why:
The Populist badge is extremely difficult to earn, IMHO. My highest Stack Overflow answer only has a score of 13, and the requirement for Populist is that it:
- Be the highest score.
- Be more than 10.
- Must outscore the accepted answer by more than 2x
This means the post would need to have at least 21 upvotes, and that the accepted answer would need at least 10.
In addition to these requirements, the poster must somehow be precognitive and know how people are going to vote, that one post is going to get 1/2 the votes the other will get, and the poster must also somehow know, or convince, the op to accept the answer he/she predicts will get 1/2 the votes.
Additionally, this person must know that it could take years for this investment to pay any dividends, since it can take years for a Stack Overflow post to accumulate enough such upvotes.
If this person earns the Populist badge on this question, then I'd say he/she earned it. Still, it's good to keep our eyes peeled for unwanted behaviors, such as people trying to game the system, but let's not shut someone down just because there's a possibility he/she might somehow be able to game the system. ;)
Does it make sense to be a Populist over yourself:
I don't think that's how the badge was intended, and there could be several arguments both for and against this. This seems like such a boundary case where I really don't think it would matter either way, and I'm not sure it's worth the development time to change it, whether it actually works or not. However, if people start trying to game it to the detriment of SE then it may need to be addressed, but here's a thought:
The focus of Stack Exchange has always been on content, not people. So if there are two separate answers, they should be treated as separate answers for all intents and purposes, even if posted by the same user. Why? Same reason as with voting. We vote content, not people.
However, you could also argue that we don't award reputation for users self-accepting their own answer. True, this is a valid argument, but a counter-argument to this is that the Populist badge hinges on so many other criteria that are just outside of the user's control to where I don't really think it matters that much.