[EM] ranking and rating versions of Bucklin

[Simmons, Forest]

Mike, you're right about the FBC. The same effect causes a monotonicity failure in regular ER Bucklin (without the special delayed counting rule that you proposed).  But with your rule, in effect, the equally ranked candidates serve as place holders to delay the compression, so that this cannot occur.
 
As I mentioned, ratings do not require this complication because moving a candidate up in the ratings doesn't automatically bring up the lower candidates to fill in his place.  So no special rule is required.
 
In ratings you can put as many candidates as you want in each slot, and still have the approval line advance downward one slot per Bucklin round without harming either monotonicity or the FBC.
 
Your rule doesn't give the rankings voter this much control.
 
To see the difference, imagine an extreme case:  50 candidates and only three slots or three ranks.
 
In the ratings version, there are only two Bucklin steps.  In the rankings version (with your rule) there could be more than forty Bucklin steps.
 
In summary, just as three slot Bucklin (a.k.a.MCA) is simpler than three rank ER Bucklin, so in general the ratings version of FBC compliant Bucklin is simpler than the rankings version.
 
Here's MCA:  Circle the names of the candidates that you like the most, and put a check next to the names of the other candidates that you find acceptable.  If some candidate's name is circled on more than half of the ballots, then the candidate with the most circles is the winner, otherwise the candidate indicated as acceptable (by circle or check mark) on the greatest number of ballots is elected.
 
Try doing three rank ER Bucklin that simply.
 
Forest

 
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