[EM] Ranked Preferences

[Juho]

Hello All,

Here is a new voting method for you to check. This method was created  
as a result of a study on if Condorcet methods can be made more  
expressive without losing their best properties. This method seemed  
to me to be a quite natural path forward. I'm not quite sure if the  
benefits outweigh the added complexity in all settings but at least  
this study was an interesting one (on expressiveness but also on  
different defence strategies). There are many variants of this  
method. I picked one for you to comment. Please check and tell what  
you like/dislike.


- Ballots may have preferences of different strength (e.g. A>>B>C>D>>>E)

- Worst candidates will be eliminated gradually during the  
calculation process
- Eliminated candidates can not win any more but they are still  
included in the preference calculations just like the non-eliminated  
candidates

- The top strength of a ballot is the strength of the strongest  
preference relation that still has non-eliminated candidates at both  
sides of it
- Preference relations that are weaker than the top strength of the  
ballot have no influence (they are counted as if they were "=")
- ">" is stronger than "="

- The unranked candidates are seen as ranked equal after the ranked  
candidates (as usual)
- By default the strength of the preference relation between the  
ranked and unranked canidates is the same as the strongest preference  
in the original ballot (there are also other options)
- The voter may also indicate the strength herself (e.g. A>B>C>>)

- While there is more than one non-eliminated candidate left,  
calculate the pairwise comparison matrix and eliminate candidates as  
described below

For each ballot, when comparing x to y
- Add one point if x is ranked higher than y (top strength or higher)
- Add one point if x and y are ranked equal at top (including lower  
strengths)
- Subtract one point if x is ranked lower than y (top strength or  
higher)
- Subtract one point if x and y are ranked equal at bottom (including  
lower strengths)
(Note that definitions of terms higher, lower and equal are relative  
to the top strength of the ballot here.)

- Find out the worst comparison result of the non-eliminated  
candidates in the matrix
- Eliminate those non-eliminated candidates whose worst comparison  
result is equal to this
- Unless that would eliminate all remaining non-eliminated  
candidates, in which case only one of them will be eliminated in  
random (it could be also possible to randomly elect the winner here)


As I already noted there can be many variants of this method (and  
many opinions as well) on e.g. the use of IRV-like elimination (not  
perfect but simple), minmax, the existence and strength of the top  
and bottom tie rules (I think they now stretch the discussion space  
wide enough), margins, default ballot completion, comparison to the  
already eliminated candidates, random and group elimination.

Thanks to Chris Benham for comments.

Juho Laatu



	
	
		
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