Baldwin's method: Difference between revisions

[[Baldwin's method]] can be run in polynomial time to obtain a single winner, however, at each stage, there might be several candidates with lowest Borda score. In fact, it is NP-complete to decide whether a given candidate is a Baldwin winner, i.e., whether there exists an elimination sequence that leaves a given candidate uneliminated.<ref>{{Cite journal|last=Mattei|first=Nicholas|last2=Narodytska|first2=Nina|last3=Walsh|first3=Toby|date=2014-01-01|title=How Hard is It to Control an Election by Breaking Ties?|journal=Proceedings of the Twenty-first European Conference on Artificial Intelligence|volume=263|issue=ECAI 2014|series=ECAI'14|location=Amsterdam, The Netherlands, The Netherlands|publisher=IOS Press|pages=1067–1068|doi=10.3233/978-1-61499-419-0-1067|isbn=9781614994183}}</ref>. This implies that this method is computationally more difficult to compute than Borda's method.<ref>{{Cite journal|last=Davies|first=Jessica|last2=Katsirelos|first2=George|last3=Narodytska|first3=Nina|last4=Walsh|first4=Toby|last5=Xia|first5=Lirong|date=2014-12-01|title=Complexity of and algorithms for the manipulation of Borda, Nanson's and Baldwin's voting rules|journal=Artificial Intelligence|volume=217|pages=20–42|doi=10.1016/j.artint.2014.07.005|issn=0004-3702}}</ref>

 

 

A [[Cardinal Voting]] variant of this system can be made by simply taking the scores initially rather than taking ranks and converting them with [[Borda count]]. In this context the motivation for the normalization at each round is derived by considering an affine transformation. When the lowest scored candidate is removed such a rescaling would then rescale so that each voter has some candidate at the MAX and some at the MIN score. This will always maximize effective vote power which is the issue attempted to be equalized by this method.

 

 

 

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