[EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Dear all,

an alternative way to count wins against equally ranked candidates,
would be to give both 0.5 wins per vote and not 0 as I did in my previous
mail.

Thus the current state: A>B gives 1:0. A=B gives ?:? (A=B is only allowed at
the end of the ballot)
The proposal above: A>B gives 2:0. A=B gives 1:1 (linear transformation from
A>B - 1:0 and A=B - 0.5:0.5).
The soccer proposal  A>B gives 3:0, A=B gives 1:1 (linear transformation
from A>B - 1:0 and A=B -1/3:1/3. This proposal would (as in soccer)
encourage voters to differenciate between candidates, and candidates to try
to gain more support than the other candidates. The soccer ranking is purely
speculative though.

In the case, where we give 0.5 wins to equally-ranked candidates and 1 win
to higher ranked candidates, then I guess the second example below would
become:

A B C
A 30.5 45
B 31.5 45
C 17 17

given
30 B>C=A
30 A>C=B
1 C (i.e. C>A=B)
1 C>B>A

Thus B wins, but C does better than in the example below.

The example above is not the best illustration of how equal rankings can
change election results,
since a voter can always vote B>C=A by simply bullet-voting B.
A better example would be on the form A=B>C or A>B=C>D, but I hope you get
the point.

The question is, what the benefits and draw-backs are, if equal ranking of
candidates is allowed and if equal ranking should be allowed, but
discouraged, as in the soccer proposal.
If there are no draw-backs, then this ballot-type could be of use.

This is just a question out of curiousity and is really not a question for
the green party council elections.
I hope I haven't spammed this you too much with these emails.

Best regards
Peter Zborník


On Sun, May 9, 2010 at 2:52 PM, Peter Zbornik <pzbornik at gmail.com> wrote:

> Dear all
>
> If we study Condorcet voting with the two types of ballots: ranked and
> hybrid, then the differences can be drastic:
>
> Normal ranked ballots:
> 30 B>C>A
> 30 A>C>B
> 1 C (i.e. C>A=B, when using Schulze, see
> http://en.wikipedia.org/wiki/Schulze_method#Ballot)
> 1 C>B>A
>
> Pairwise preferences
> A B C
> A 30 30
> B 31 30
> C 32 32
>
> Thus C wins
>
> Hybrid ranked ballots (replace two > with = in the example above):
> 30 B>C=A
> 30 A>C=B
> 1 C (i.e. C>A=B)
> 1 C>B>A
>
> A B C
> A 30 30
> B 31 30
> C 2 2
>
> Thus B wins.
>
> I hope I calculated correctly.
>
> As a voter, I would prefer the hybrid ballot, as it gives me more
> expressive power, unless this kind of ballot has some other weakness when
> used.
>
> Best regards
> Peter Zborník
>
> On Sun, May 9, 2010 at 2:26 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
>
>> Dear all,
>>
>> have the properties of hybrid or generalized ranking/approval ballots been
>> examined?
>> A hybrid/generalized ranking/approval ballot is a ballot, with where the
>> voter ranks the candidates by either > or = without any other restrictions.
>> Say we have seven candidates ABCDEFG.
>> Say the voter likes A the most, then BC the same, then DE the same and
>> last FG.
>> Then instead of having the ranking A>B>C>D>E>F>G, or some approval of ABC
>> for instance, the ballot would look like
>> A>B=C>D=E>F=G.
>> For this type of ballot, the approval and ranked ballot would be a special
>> case.
>> I speculate that, such a hybrid ballot might take the best of two worlds:
>> the expressiveness of the fully ranked ballot and the robustness of the
>> approval voting ballot.
>>
>> The voters (at least I) would most likely appreciate this liberation of
>> their preferences, since they might themselves decide to use a fully ranked
>> ballot, an approval ballot or something inbetween.
>>
>> It seems that for instance the Schulze single-winner method allows for a
>> simplified hybrid system, as it allows for not listing all candidates.
>>
>> Would be nice to know your thoughts on this.
>> Are hybrid ranked ballots a good idea?
>> Would your preferred methods be able to handle hybrid?
>>
>> Best regards
>> Peter Zborník
>>
>
>
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