[EM] Democratic Fair Choice and the set P

[Simmons, Forest]

Both DFC and DMC make use of the set P of all alternatives that pairwise defeat the alternatives that have greater approval.
 
I would like to define another set which I will call BP consisting of all alternatives that have beat paths to every alternative with greater approval.
 
In other words, alternative A is in BP iff for each alternative X with greater approval than A, there is a beat path from A to X.
 
Of course P is a subset of BP, and BP will always include the entire Smith set, as well as the approval winner, and when the latter is a member of the Smith set, BP will be the Smith set itself.
 
I suggest picking the winning alternative by random ballot from BP, rather than from P when there is serious potential for something like the 
 
49 C
24 B     (sincere B>A)
27 A>B
 
scenario.
 
Forest
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