[EM] another lottery method

[Jobst Heitzig]

Dear Folks!

I like Forest's idea. Most probably, one has to alter it slightly in order to get monotonicity. For example like this:

Let the "approval sequence" of a set S of candidates be the sequence of approval values of the elements of S in increasing order and continued to infinity by appending infinity at the end. Let's say that a set T has "larger" approval than a set S when T's approval sequence is lexicographically larger than S's, that is, when the first position in which both sequences differ is larger in T's approval sequence than in S's. Elect the winner from the [majority] dense set whose approval is largest in this sense, using Random Ballot. This way the method should hopefully be monotonic and the used dense set is automatically minimal without requiring this explicitly. 

E.g., if S={A,B,C} and T={B,D} are the only dense sets, and A,B,C,D have approval scores 5,3,10, and 4, then the approval sequences of S and T would be (3,5,10,infinity,infinity,...) and (3,4,infinity,infinity,...), and hence T would have a "larger" approval sequence than S since they coincide in the smallest approval but T's 2nd smallest approval is larger than S's. So the winner would be chosen by Random Ballot from T.

Yours, Jobst

"Simmons, Forest" <simmonfo at up.edu> schrieb am 12.11.05 01:14:53:
> 
>  
> 
> Paul Kislanko asked ...
> 
> Why introduce "majority dense" and not use that?
>  
> Forest answers:
>  
> 1.  Because it wasn't necessary for the purpose of my message, which was to nudge readers out of their mental ruts.
> 
> 2.  Is the introducer the only one who can use an idea?
>  
> Paul went on to ask ...
> 
> How do you define "approval sum" in this context?
>  
> I answer:
>  
> It doesn't matter what I had in mind, since my purpose is to get the reader to innovate.
>  
> Forest
> 
> 
> 
> <hr>
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