Consider the following actual question on Mathematics.SE:
https://math.stackexchange.com/questions/382736/are-all-prime-numbers-finite
As of this writing, the non-deleted answers have the following scores, upvotes and downvotes:
| SE order | SE score | upvotes | downvotes | Wilson score (z=2, center) | Wilson order |
|---|---|---|---|---|---|
| 1 | 83 | 86 | 3 | 0.946 | 1 |
| 2 | 55 | 59 | 4 | 0.910 | 3 |
| 3 | 30 | 30 | 0 | 0.941 | 2 |
| 4 | 3 | 4 | 1 | 0.667 | 4 or 5 (tie) |
| 5 | 2 | 2 | 0 | 0.667 | 4 or 5 (tie) |
| 6 | 0 | 1 | 1 | 0.5 | 6 |
| 7 | -2 | 1 | 3 | 0.375 | 7 |
If we use the vote difference (the SE score) as tie breaker, then only the second and third answers are exchanged. That’s despite in the SE scoring, the second answer scores significantly higher than the third.
Another example:
| SE order | SE score | upvotes | downvotes | Wilson score (z=2, center) | Wilson order |
|---|---|---|---|---|---|
| 1 | 68 | 69 | 1 | 0.959 | 1 |
| 2 | 37 | 37 | 0 | 0.951 | 2 |
| 3 | 19 | 19 | 0 | 0.913 | 3 |
| 4 | 14 | 16 | 2 | 0.818 | 6 or 7 |
| 5 | 12 | 15 | 3 | 0.773 | 10 |
| 6 | 9 | 9 | 0 | 0.846 | 4 |
| 7 or 8 | 8 | 9 | 1 | 0.786 | 8 |
| 7 or 8 | 8 | 8 | 0 | 0.833 | 5 |
| 9 | 7 | 7 | 0 | 0.818 | 6 or 7 |
| 10 | 5 | 5 | 0 | 0.778 | 9 |
| 11 | 4 | 5 | 1 | 0.7 | 13 |
| 12 or 13 | 3 | 3 | 0 | 0.714 | 11 or 12 |
| 12 or 13 | 3 | 3 | 0 | 0.714 | 11 or 12 |
| 14 | 2 | 2 | 0 | 0.667 | 14 |
| 15 or 16 | 1 | 1 | 0 | 0.6 | 15 or 16 |
| 16 or 16 | 1 | 1 | 0 | 0.6 | 15 or 16 |
This example demonstrates quite nicely how the Wilson score favours uncontroversial answers over controversial ones. For example, the highly voted but controversial number with SE score 12, on place 5 on SE, falls back to place 10 in Wilson score, beaten even by an uncontroversial score 5 question.
Note also that for questions with many votes, an additional vote counts very little in the Wilson score. In the SE difference model, upvoting an answer with no votes yet has the same effect as upvoting an answer with 50 upvotes and 50 downvotes (the score goes from 0 to 1). In the Wilson score, the first upvote raises the score from 2/4=0.5 to 3/5=0.6, while in the 50/50 scenario, it only raises the score from 52/104=0.5 to 53/105≈0.505.