[EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Dear all,

Please let me return to an older discussion (see emails below).
The issue of the hybrid ballot A>B=C>D.
 Just an idea on this topic, which might be worth mentioning.
It could be a way to handle the problem of bullet voting.
Ant it could be a way to disband the dichotomy between different criterias
of winning in condorcet elections (margins, winning votes, quotas losing
votes).

1] IRV-based elections:
Basically in IRV-based STV, when arriving at an equal sign in the ballot,
the ballot could simply be split into the number of candidates with equal
preferences and re-weighted accordingly (i.e. for instance A=B=C would give
three ballots, A>B=C, B>A=C, C>A=B, each with weight 1/3 of the original
weight).

Example:

Say we have an STV election with 20 ballots on the form
A>B=C=D>E
A is elected, and we need to transfer, say 9 surplus votes.
Normally in STV (say scottish STV) with fractional transfers, each of the 20
votes would have the weight 9/20.

When allowing equal signs we will instead create three new ballots for each
ballot as seen below.
Thus the ballot B=C=D>E is split into the following three ballots
B>C=D>E
C>B=D>E
D>B=C>E
Each of the ballots above would have 1/3 of the weight of the original
ballot

Thus when transferring the surplus votes using weight 9/20 in the example
above.
We would use the weights 9/20/3=3/20 for each of the three created ballots
above.

 The idea is to give the first preference to each one of the equally ranked
candidates and leave the others with the equal sign as second preferences.
This method would work for STV elections, which only look at the first
preferences.

Might the method above be a good one to use when equal-ranking ballots, in
STV elections which only look at first preferences?
Has the method above been used yet in any implementations?

Condorcet-based elections:
In Condorcet elections (including STV) then A=B would simply mean 0.5 wins
for A>B and 0.5 wins for B>A.

Kevin Venzke wrote in his mail below (May 9th 2010):
35 A>B
25 B
40 C
A will win. This is only acceptable when you assume that the B and C
voters meant to say that A is just as good as the other candidate that
they didn't rank. I don't think this is likely to be what voters expect.
It seems misleading to even allow truncation as an option if it's treated
like this.
End of quote

Well I think think that as a voter I would indeed be pleased if A would win
and not C.
If the completion system above would be used (i.e. A=B would be counted as
0.5 win for A vs B and 0.5 win for B vs A), then there the winner would
always be the same disregarding which of the following winning criteria was
used: winning votes, losing votes, margins or quotas.

Let us analyse the example in your mail below. We apply the Schulze beatpath
with different criteria (biggest win, margins and ratios):
35 A>B>C
25 B>A=C
40 C>A=B

Pairwise wins -
X   A    B   C
A   X    55  47.5
B   45    X   60
C   52.5 40  X

Path strenghts - Method 1: Biggest win
A vs B: 55
A vs C: 55
B vs A: 52.5
B vs C: 60
C vs A: 52.5
C vs B: 52.5

Beat-paths:
A beats B
B beats C
A beats C

A wins
(I hope the calculation is correct)

  Path strenghts - Method 2: Margins
A vs B: 10
A vs C: 10
B vs A: 5
B vs C: 20
C vs A: 5
C vs B: 5

 Beat-paths
A beats B
B beats C
A beats C

A wins

Truncated ballots:
 Using this system, optionally, all candidates not ranked would get equal
rank.
I.e. in the election of candidates A, B, C, the ballot A would be counted as
A>B=C.
A blank ballot would be counted as A=B=C.
An abstention could theoretically also be counted as A=B=C.

Discussion:
What are the pros and cons of the approach above?
Prima facie it seems that the treatment of hybrid ballots above could solve
the problem of bullet voting, but I am far from sure.

Best regards
Peter Zborník


On Sun, May 9, 2010 at 7:14 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:

> Hi Peter,
>
> We consider rank ballots that allow equality of ranking and truncation all
> the time.
>
> For Condorcet methods the question of how to treat equality of ranking is
> what Juho and I usually talk about.
>
> If Markus prefers not to use the split vote treatment it is probably
> because it violates CDTT (it doesn't respect voted majorities) and
> the Plurality criterion:
>
> 35 A>B
> 25 B
> 40 C
>
> A will win. This is only acceptable when you assume that the B and C
> voters meant to say that A is just as good as the other candidate that
> they didn't rank. I don't think this is likely to be what voters expect.
> It seems misleading to even allow truncation as an option if it's treated
> like this.
>
> There's also a strategy issue. When truncation is counted as zero votes,
> then you have three options when you decide how to rank the worse of
> two frontrunners (who is really better than all the other unimportant
> candidates):
> 1. sincerely support the worse frontrunner
> 2. insincerely bury the worse frontrunner (which can steal the election
> if the other faction does #1, or else elect a completely terrible
> candidate if the other faction does #2 or #3)
> 3. truncate. That protects the better frontrunner and it is not trying
> to steal the election.
>
> When you can't meaningfully truncate, you don't have #3. So #2 is both
> your offensive and your defensive strategy. That seems like a problem to
> me.
>
> Kevin Venzke
>
>
>
>
> ----
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>
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