Theoretical perfect multiwinner voting system
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parker friedland
Dec 26, 2017, 8:42:18 AM12/26/17
to The Center for Election Science
FRV (https://groups.google.com/forum/#!topic/electionscience/YZgI8Wj8UAg) demonstrates that it might be possible to construct an ideal proportional multi-winner voting system that passes some of the same mathematical criterions that make rated voting systems such as approval and score voting stand out (favorite betrayal, simi-honesty, independence of irrelevant alternatives, etc).
Such a theoretical voting system should guarantee that:
1. Each district can only elect a limited number of representatives per district (Because legislative bodies only have a finite amount of seats)
2. Each district must elect at-least a single individual to each district (Because all districts must be equally represented. Being equally represented doesn't mean that each district has to elect the same amount of winners because different winners can have fractional weights in the legislature, but this does mean that each district must elect at least a single winner)
3. The voting system passes the favorite betrayal criterion or some other important criterion that demonstrates how resilient it is to free riding and other forms of strategic voting
4. The voting system produces results that have some degree of proportionality
5. The voting system is deterministic and gives voters complete control over the election (it doesn't use a delegation system)
6. It has basic fundamental properties that all voting systems should have (every voter's ballot is treated equally by the voting system, infinite domain and range, etc.)
I want to know if any of these requirements result in a contradiction.
Such a theoretical voting system should guarantee that:
1. Each district can only elect a limited number of representatives per district (Because legislative bodies only have a finite amount of seats)
2. Each district must elect at-least a single individual to each district (Because all districts must be equally represented. Being equally represented doesn't mean that each district has to elect the same amount of winners because different winners can have fractional weights in the legislature, but this does mean that each district must elect at least a single winner)
3. The voting system passes the favorite betrayal criterion or some other important criterion that demonstrates how resilient it is to free riding and other forms of strategic voting
4. The voting system produces results that have some degree of proportionality
5. The voting system is deterministic and gives voters complete control over the election (it doesn't use a delegation system)
6. It has basic fundamental properties that all voting systems should have (every voter's ballot is treated equally by the voting system, infinite domain and range, etc.)
I want to know if any of these requirements result in a contradiction.
Toby Pereira
Jan 1, 2018, 3:46:56 PM1/1/18
to The Center for Election Science
A few people (including me) have been trying to come up with a "perfect" system that fulfils a set list of criteria. Well, there isn't just one set list, how important each criterion is might depend on who you ask, but Warren D. Smith calls such systems "Holy Grail" systems, and there is an overview here: http://scorevoting.net/NonlinQuality.html#holygrail
parker friedland
Jan 1, 2018, 4:26:12 PM1/1/18
to The Center for Election Science
However, Warren's conjecture that steps 4 and 8 are in conflict with one another may only be the case in voting systems where each winner receives the same weight in the legislature. Perhaps they will not be in conflict with one another in voting systems that allow candidates to have different voting weight in the legislature depending on the election results. Also, Warren has not added any strategy resistance criterions to his list (such as favorite betrayal, which would allow a voting system to be 100% immune to free riding), but that is because it is impossible for the kind of voting systems he his looking at (voting systems that elect multiple candidates, give every elected candidate in the legislature the same vote weight, and are proportional) to pass the favorite betrayal criterion. Unlike Warren, I am only focused on voting systems that are proportional, and I don't care if they don't give every winner the same vote weight in the legislature, and I don't care if the multi-winner voting system occasionally elects a single candidate that wields the vote weight of the entire district when such a candidate is popular enough. As a result, unlike the type of voting systems Warren is interested in, it could be possible for the type of voting systems I am looking at to be resistant to free riding or even pass the favorite betrayal criterion.
Toby Pereira
Jan 2, 2018, 4:22:39 AM1/2/18
to The Center for Election Science
If elected candidates having different weights in the legislature is something you want, then I think you could do a lot worse than what I have described here: http://election-methods.5485.n7.nabble.com/EM-Weighted-PR-question-tc32664.html#a33213
But it's not entirely without problems: https://groups.google.com/d/msg/electionscience/5skD8rTZ82k/d0iOUacwAwAJ
Toby Pereira
Jan 2, 2018, 3:52:23 PM1/2/18
to The Center for Election Science
I forgot to mention that as that is an approval system, it needs to be translated to score. But that can be done with the KP transformation. This is where a voter is effectively "split" into parts. If the score is out of 10, then the voter is split into 10 parts numbered 1 to 10. All parts approve a candidate with a score of 10, parts 1 to 9 approve candidates with a score of 9, and generally parts 1 to x approve candidates with a score of x.
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