|
[[Baldwin's method]] does not satisfy the [[independence of irrelevant alternatives]] criterion, the [[monotonicity criterion]], the [[participation criterion]], the [[consistency criterion]] and the [[independence of clones criterion]]. [[Baldwin's method]] violates [[reversal symmetry]] (unlike [[Nanson's method]]).<ref>{{Cite web|url=https://www.mail-archive.com/election-methods@lists.electorama.com/msg00625.html|title=Re: [Election-Methods] Borda-elimination, a Condorcet method for public elections?|website=www.mail-archive.com|access-date=2019-06-19}}</ref>
[[Baldwin's method]] can be run in polynomial time to obtain a single winner, however,but at each stage, there mightmay be several candidates with the lowest Borda score. In fact, it is NP-complete to decide whether a given candidate is a potential 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>
In practice, the computational bottleneck can be resolved easily enough by adopting some tiebreaking method (like eliminating all tied candidates simultaneously). However, the high frequency of near-ties leaves these methods open to lawsuits (similarly to [[Instant-runoff voting|plurality-with-elimination]]) and can lead to chaotic results.
==Cardinal variant==
AUsing [[CardinalScore Votingvoting|scores]] variantinstead of this[[Borda systemcount|Borda cancounts]] begives madethe by'''Cardinal simplyBaldwin''' takingmethod; the scoreslowest-scored initiallycandidate ratheris than taking rankseliminated and converting them with [[Borda count]]. In this context the motivationballots forare therescaled normalization(normalized) atin 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 willmaximizes alwayseach maximizevoter's effective vote power whichat iseach thestep; issueeliminating attemptedminor tocandidates bein equalizedthis byway thisprevents methodthem from substantially affecting the results.
Assuming the scores are all scaled to fall in the range [0, 1], ballots are rescaled as follows:
More explicitly. Let MAX and MIN be the extreme available grades. Let <math>u_c</math> be a voters score for candidate c, let <math>u_{min}</math> and <math>u_{max}</math> be their score for her worst and best candidates in the considered election round. The rescaled utility is:
<math>v_c(u_c) = \text{MIN} + (\text{MAX} - \text{MIN}) \frac{u_c - u_{\min}}{u_\max - u_\min}</math>
For example, inwe awould transform [0.1, 10.3, .5] systemto the[0, translation.5, is1.0].
<math>v_c(u_c) = 10 \frac{u_c - u_{\min}}{u_{\max} - u_{\min}}</math>
It would transform [1, 3, 5] to [0, 5, 10].
===Related systems===
|