As a disclaimer, I must admit this may benefit me (I haven't checked), but probably not as significantly as most others. This issue is also something that has prevented me from answering questions by users with 1 rep in the past, especially if they are poorly fashioned.
New users with a programming question find SO from various methods, such as google. They ask a question with haste, hoping for a quick answer -- which they usually receive. Many of these users have no interest in Stack Overflow itself, but are simply interested in getting the solution they require. As a result of this, they'll check the site regularly for the first day or two until a sufficient answer has been posted. Once they get what they need, they bail; without the required rep or understanding that they should up-vote and select a response as the answer.
A great many questions on SO are abandoned by users with no intention of ever coming back. The answer they require has been provided, but for one or more reasons they have neglected their duty of contributing back by way of awarding reputation.
(Since Jeff loves Datum)
Some queries on the data dump examine the reach of this 'problem'.
The query I used is based on extensions of the following base query;
SELECT p1.Id, p1.Score, p1.OwnerUserId, p2.OwnerUserId, p2.Score
FROM posts p1
INNER JOIN posts p2 ON (p1.Id=p2.ParentId)
LEFT JOIN users ON (p1.OwnerUserId=users.Id)
WHERE p2.Score >= 2
AND p2.Score = ( SELECT MAX(p3.Score) FROM posts p3 WHERE p3.ParentId=p1.Id )
AND users.Reputation < 15
AND p1.PostTypeId = 1
AND p1.AcceptedAnswerId = 0
Result: 3,288 Questions by users with under 15 rep which have answers with 2+ up votes that have no accepted answer.
AND (users.LastAccessDate-p1.LastActivityDate) < 604800 // 1 week
AND p1.CreationDate < 1249084800 // 1249084800 is 1 week before latest dump data
to the where clause further reveals that 877 questions that have answers with 2+ up votes have no accepted answer, and the owner of the question has not returned since the week the question was asked.
Modifying there where clause, and removing the left join:
AND p1.OwnerUserId = 0
Reveals a staggering 3,675 questions with answers of 2+ votes by deleted users. These are questions that were probably answered but the users who did the work can never be recognized.
Building off the previous and using an even more restrictive WHERE clause
WHERE p2.Score >=5
Still 1,178 posts that can never have an accepted answer. How many posts are there with over 5 up votes that don't provide the correct answer?
Modifying the where clause for Reputation to
AND users.Reputation = 1
Still reveals 388 questions by users with 1 rep have been abandoned.
Similar to how bounty questions work, if a user has abandons the site (not active since
x time after the question was asked) with a question that has answers with 2+ up votes, force the answer with the most up votes to be the selected answer. This will reduce the amount of questions that are unanswered, and also give users more of an incentive to answer questions by new users without extra hesitation.
Added more statistics for deleted users.
Please feel free to add/remove rules to make this a truly practical feature.