[EM] Is Alabama Paradox needed in MultiGroup elections?

[Juho]

- Four groups: L=Left, R=Right, N=North, S=South
- Four candidates (or smaller groups): LN, RN, LS, RS
- LN belongs to L and N, and similarly RN, LS and RS and belong to  
corresponding L, R, N and S groups
- Votes: LN:30, RN:30, LS:30, RS:10

Case 1: One candidate elected
- L gets more votes than R
- N gets more votes than S
- It makes sense to elect candidate LN (or candidate from group LN)

Case 2: Two candidates elected
- Electing RN and LS seems to be the best outcome
- Electing LN and RN seems worse since N would get all the seats
- Electing LN and LS seems worse since L would get all the seats
- Electing LN and RS seems worse since RS got so few votes
- Therefore it may be better not to elect LN although LN was maybe  
the best choice in the case where only one candidate was elected

Pure serial (monotonic/serial) allocation of seats doesn't seem to  
work well in the described setting.

Does this mean that in MultiGroup style of elections where candidates  
may represent multiple groups that all should be proportionally  
represented the Alabama Paradox (http://en.wikipedia.org/wiki/ 
Alabama_paradox) should be considered a feature whose presence is not  
a problem but maybe even a requirement?

Juho



		
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