hi Enrique,

thank you for that analysis.  it fit my gut feeling that the compromise
annnouncement would produce that sort of problem, and as a result makes 
me sad, if the outcome does produce a rejection of one or more  of the 
nominated candidates.

thank you for doing the homework and setting the examples that demonstrate
the issue with this compromise (with the second message correcting).

-ron

On Wed, 24 Aug 2016, Enrique Chaparro 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
>