Majority Acceptable Score voting
Majority Acceptable Score voting works as described below. Technically speaking, it's the graded Bucklin method which uses 3 grade levels and breaks median ties using Score voting.
 Voters can give each candidate 0, 1, or 2 points.
 If there are any candidates given above 0 by a majority, then all who aren't (that is, those with a majority at 0) are eliminated.
 (Do the same for 1. This probably doesn't matter, because any majority2 candidate would probably win in the next step anyway. But this step is part of Bucklin voting, which was used in over a dozen US cities during the Progressive era, and thus it gives this method a stronger pedigree.)
 The remaining candidate with the highest points wins.
Blank votes are counted as 1 or 0 points in proportion to the fraction of all voters who gave the candidate a 2. For example, a candidate could not win with more than 71% blank votes, because even if the other 29% are all 2ratings, that would leave 71%*71%=50.41% 0votes, enough to eliminate.
Here's a google spreadsheet to calculate results: [1]. On page 1, it has some examples of how different combinations of ratings would come out, suggesting that it could work well in both chicken dilemma and center squeeze scenarios. On page 2, it has some hypothetical results for the Egypt 2012 election, showing that this system could have elected a reformer over Morsi, despite votesplitting among the various reformers. IRV could have elected Morsi.
An example
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.
The candidates for the capital are:
 Memphis on Wikipedia, the state's largest city, with 42% of the voters, but located far from the other cities
 Nashville on Wikipedia, with 26% of the voters, near the center of Tennessee
 Knoxville on Wikipedia, with 17% of the voters
 Chattanooga on Wikipedia, with 15% of the voters
The preferences of the voters would be divided like this:
42% of voters (close to Memphis) 
26% of voters (close to Nashville) 
15% of voters (close to Chattanooga) 
17% of voters (close to Knoxville) 





Assume voters in each city give their own city 2; any city within 100 miles, 1; any city that is over 200 miles away or is the farthest city, 0; and the rest (those between 100 and 200 miles), get 1 or blank with 50/50 chance. (These assumptions can be varied substantially without changing the result, but they seem reasonable to start with.)
City  2's  explicit 1's  explicit 0's  blanks  total 0's  score 

Memphis  42  0  58  0  58  (84) 
Nashville  26  37  0  37  27.4  98.6 
Chattanooga  15  30  21  42  49.9  65.1 
Knoxville  17  28  42  13  52.8  (64.2) 
Memphis and Knoxville are both given 0 by a majority, so they are eliminated. Of the remaining two, Nashville has a higher score and wins.
If Memphis voters tried to strategize by rating Nashville and Chattanooga at 0 in the above scenario, it would take a bit over half of them to successfully execute the strategy. Even if all the Memphis voters strategized, Chattanooga and Knoxville voters could protect Nashville against this strategy as long as under half of those who had given Nashville a blank above switched to giving it a 1 (or a 2). Note that the offensive strategy involves moving a natural 1 down to the extreme value of 0, but the defensive strategy only means changing a lazy blank to a natural 1 (not to the extreme value of 2).