How do I encourage an asker to pick an answer?
Or for that matter, how to encourage voting for useful answers that took a lot of work to produce.
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Generally, you don't. The system already prompts users to accept an answer at an appropriate time, but accepting an answer is a completely voluntary activity, and it is up to the user to decide when (and if) an answer should be accepted at all.
And please do not leave comments asking users to accept answers. It might seem like a harmless reminder of a feature a user may simply have forgotten, but as the sites start to fill with them, it starts to look somewhat harassing and becomes noisy and annoying to everyone else looking on.
By default, answers are sorted by votes. So you can upvote your preferred answer and downvote other answers (if they are wrong), in order to help raising it to the top.
This way it will have more visibility and will receive more upvotes and will have a higher chance of being accepted.
You can also add a comment to your preferred answer like "This answer works great because ...", or if you want to be less subtle, "This should be the accepted answer because ...". And adding comments like "This doesn't work in case ..." to other answers can prevent other users from upvoting them blindly.