Baldwin's method: Difference between revisions
→Cardinal Variant
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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
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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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:
▲ v_c(u_c) = MIN + (MAX– MIN) \frac{(u_c – u_{min})}{(u_{max} – u_{min})}
For example, in a [0, 10] system the translation is
▲ v_c(u_c) = 10 \frac{(u_c – u_{min})}{(u_{max} – u_{min})}
It would transform [1, 3, 5] to [0, 5, 10].
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