I've had some doozies.
By contentious, I mean the question with the most downvotes yet still positive overall.
Is there a straightforward way to find it?
Stole that from another sites queries.
Looks like this is a leading candidate: Why are most of the main characters White/English in Game Of Thrones?
Sorry, missed that you wanted positive overall rep: Why is it logical to live long and prosper?
Note: All the numbers and ratios given in this answer were accurate when the answer was first made. Their inclusion here seems to have triggered some voting, though, so they’re probably all wrong by the time you're reading this.
If you define contentious not so much by total number of votes cast (up or down), but rather by the difference between the number of up- and downvotes cast, the results are a bit different from JohnP’s query.
For instance, if a post has 35 upvotes and 26 downvotes, that would count as very contentious in John’s query, which goes by vote count; but if we’re talking differences between up- and downvotes, it’s not really that high: there’s a difference of 9 votes between the 35 upvotes and the 26 downvotes, which is equivalent to about 25% of the total number of upvotes. In other words, only about 75% as many people downvoted the question as upvoted it; one direction of voters is quite a bit larger than the other (downvoters = 75% of upvoters), and the contention is fairly skewed.
A question with 12 upvotes and 11 downvotes has fewer votes overall and would score lower in John’s query; but there is here only one vote’s difference between up- and downvotes, corresponding to just 8.33% of the total number of upvotes. The two groups of voters are thus, percent-wise, more equal than in the previous example (here downvoters = 91.66% of upvoters) and the question is ‘more contentious’. A percentile ratio is, then, a good way of figuring out whether the distribution of up- and downvotes is heavily skewed in one direction, or fairly equal. An added benefit is that questions that have received little attention will not clutter up the list, since even a single vote’s difference will represent a high percentage if there are only a few votes either way.
I’ve forked John’s query to create an overview of questions with the lowest differential ratio. The differential ratio given is the difference between up- and downvotes as a percentage of total upvotes; i.e., the 8.33% in the example above, not the 91.66%. (I’ve limited it to posts that have at least 7 upvotes, just to get completely rid of the ones that haven’t received much interest—too easy to be ‘contentious’ when only a few people have voted).
From that, it seems the most evenly divided votes belong to:
10 up, 9 down — ratio: 10%
9 up, 8 down — ratio: 11.1%
– and then from there on, there are six questions with 8 up, 7 down (12%), etc.
Note: there is one answer that has an even lower ratio, with 12 up and 11 down (8.33%): this answer to Who is the first minority superhero in mainstream US superhero comics?
Second note: As mentioned by ThePopMachine in the comments, if we include those questions which have a negative overall score (i.e., more downvotes than upvotes), there are several that have even lower ratios:
The ratios here are a little different from the ones in ThePopMachine’s comment, since his ratio was based only on selecting questions with more downvotes than upvotes and changing nothing else—that means it still calculated the ratio relative to the upvotes. My ratios here are based on reversing the query entirely, calculating the ratio relative to the downvotes, now that they are the larger group. That way, the ratios remain consistent in both cases.