I think I'm tending more and more to agree, Enrique, that NOTA as used here is confusing and problematic.

I think the best way for us to continue exploring this is to follow your lead (and the lead of those who study this stuff professionally), and present some good examples and scenarios.

While it can be helpful to find extreme examples of how an electorate might vote, as we've seen recently, to explore the possibilty of obscure flaws in a voting method, I think it is more helpful to start with a realistic scenario of a group of candidates and how an electorate views them, then craft ballots to represent segments of the electorate, and then see how the method would tally the ballots.

Here is one scenario I just threw together along those lines.

Candidates: left to right scale (or dog-to-cat lovers, or pick your own)
  A is moderately left
  B is middle-of-the-road
  C is strongly right

Consider an electorate with 100 voters

Here are the number of ballots cast by each population

Population 1: like A and B, don't really have clear opinion about C 
  30 A, B
Population 2: like A and B, oppose C, would prefer leaving seat open or finding new candidate
  30 A, B, NOTA
Population 3: like C, B, lukewarm about A
  30 C, B
Population 4: love C, oppose A, lukewarm about B [no clear way to express this with current system, decide not to vote for B]
  10 C, NOTA

Totals:
100 ballots

60 A
90 B
40 C
40 NOTA

A B and C are all elected (C due to a tie with NOTA: "if None of the Above option gets more votes than the candidate, the candidate will be considered not elected."

In a proportional system, C would probably be elected, to represent the views of a significant population of voters.  I think that makes sense for this scenario.

If you add just a few more NOTA voters to the previous scenario, C would not be elected.  You might view that as the tyrrany of the majority.

So I think that last point is an argument for proportional representation, and a system like RRV or STV.

On the other hand, I fear that introducing rankings or ratings might make some candidates uncomfortable, and we don't exactly seem to have an abundance of volunteers trying to get elected here.

If folks have other realistic sets of candidate views, electorate views, and scenarios to offer, we can see how they would work also.

Cheers,

Neal McBurnett                 http://neal.mcburnett.org/

On Thu, Aug 25, 2016 at 09:43:09AM -0300, Enrique Chaparro wrote:
> The 'big issue' with the system here is that 'supercandidate'
> NotA behaves strangely. We can live with that for this election,
> but I strongly advise against keeping it for the future.
> 
> "For/against/neutral" systems are used in real life is some
> cases,[1] but always when there is just one subject to be
> decided upon. This is not the case: NotA has an interference
> effect so weird that when the voter expresses lack of trust
> in one candidate, that negative vote is being transferrec to
> all other subjects to be voted. I guess that the original attempt
> was to express something like
> 1. X | NotX
> 2. Y | NotY
> 3. Z | NotZ
> but the result of the tally will be:
> 1. X | NotX+NotY+NotZ
> 2. Y | NotX+NotY+NotZ
> 3. Z | NotX+NotY+NotZ
> If we take it with a little humour, we could congratulate ourselves
> for having designed a non-monotonic election system![2]
> 
> Regards,
> 
> Enrique
> 
> [1] E.g., many decisions in the Wikipedia comunity are taken
> by this procedure.
> 
> [2] A system where increasing (resp. decreasing) the number of
> votes for a candidate *does*not* increase the chances for that
> candidate to become a winner.