Enrique.
I totally agree with you that this method sucks. 😀 (your assertions were more elegant).
You'll recall I argued strongly for having a separate NOTA option against every every candidate slot.
We will learn sooner or later why we should have done it that way. The current method is just screwy.
Milton L Mueller
Professor, School of Public Policy
Georgia Institute of Technology
> On Aug 24, 2016, at 15:29, Enrique Chaparro <[log in to unmask]> wrote:
>
> Milton,
> Please excuse me, but as I see it (YMMV) your math is wrong.
> I'm afraid my example is somewhat complicated, because I
> pulled the numbers from the thin air and feel sometimes crippled
> without a blackboard :)
> [BTW: your guess of the minimal set is pretty close, but see section
> B below for a smaller set of voters)
>
> ::A::
> The election rules say that each voter may cast any number 'n'
> of votes 0<=n<=3 (the ballot form reads "select at most three").
> To further complicate the things, NotA (N) has ambiguous value
> i.e. one mark in the N box may count as 1, 2 or 3 votes.
> Therefore, there are 15 possible combinations for ticking the
> four boxes.
> ABC
> ABN
> ACN
> BCN
> AB
> AC
> BC
> AN
> BN
> CN
> A
> B
> C
> N
> 0 (no box is ticked)
>
> The number of Ns counts as a threshold against any candidate. And the
> problem stems from here! ABN means an 'explicit' rejection of C, AN
> means an explicit rejection of B and C, while AB and A don't mean explicit
> rejections. Please notice also a somewhat contradictory effect: a voter
> considers A the optimal choice, and B, C not fit for the position. Then
> s/he votes AN... but that vote will rise A's threshold.
>
> :B:
> By "the most consensual" I tried to mean the candidate with the largest
> nonnegative opinions ('for'+'neutral'). In the following example, C has
> the lowest number of explicit rejections (all non-listed combinations have
> zero votes):
> ACN 104
> BCN 104
> AB 20
> A 111
> B 97
> N 2
> Tally:
> 436 voters.
> Threshold: 104+104+2 = 210
> A: 235 > 220 → pass (with 106 explicit rejections)
> B: 221 > 210 → pass (with 106 explicit rejections)
> C: 208 < 210 → fail (with 2 explicit rejections)
>
> :C:
> As a conclusion: this curious voting method may take us out of the
> impasse now, but has a lot of undersirable properties: is prone to tactical
> voting, has no monotonicity, does not satisfy the Condorcet ciriterion, etc.
> Once we get through the current election process, discussing an acceptable
> voting system seems to be a wise move.
>
> Regards from the Far South,
>
> Enrique
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