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