[EM] Challenge - give an example where FBC is violated for Condorcet methods

[Peter Zbornik]

Kevin,

Just a minor correction: Symmetrical completion gives the winner A not
C as stated below, but that is irrelevant to the argument that
Generalized symmetrical completion gives different results to
symmetrical completion and the same results as standard treatment of
truncated ballots with winning votes.

Best regards
Peter Zborník


On Mon, Jun 6, 2011 at 9:02 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
> Kevin,
>
> I am pretty sure you did not give an example, where generalized
> symmetrical completion as defined (in the challenge) make the problem
> worse.
> You gave me an example where symmetrical completiion makes things
> worse when it comes to FBC, but symetric completion and generalized
> symmetric completion give different results.
>
> With generalized symmetrical completion plurality holds trivially, as
> margins and winning votes with give exactly the same results with
> equalities resolved as 0.5 vs 0.5.
>
> If you mean the example:
> 35:A>B
> 25:B
> 40:C
> then standard Schulze Winning Votes gives B as the winner.
> Generalized symmetrical completion gives also B as the winner.
> Symmetrical completion gives the winner C.
>
> Generalized symmetrical completion completes the election to
> 35:A>B>X>C
> 25:B>X>A=C
> 40:C>X>A=B
>
> The stanard treatment of truncated ballots is the following:
> (i) equal ranking of canditates explicitly not ranked,
> (ii) lower ranking of candidates explicitly not ranked than candidates
> explicitly ranked.
> (iii) ties resolved 0:0, i.e. winning votes
>
> Symmetric completion:
> (i) equalities between candidates on the ballot (A=B) are resolved as
> 0.5 votes for each candidate in the pairwise comparison - i.e. margins
> (ii) candidates not explicitly ranked on the ballot are ranked equally
> below the null candidate.
>
> Generalized symmetrical completion is defined as follows:
> (i) equalities between candidates on the ballot (A=B) are resolved as
> 0.5 votes for each candidate in the pairwise comparison.
> (ii) Ballots are completed with the null candidate ("none of the
> above" X), who is ranked strictly lower than all candidates explicitly
> ranked on the ballot,
> (iii) candidates not explicitly ranked on the ballot (i.e. truncated
> ballots, excluding the null candidate) are ranked equally below the
> null candidate.
> Example: election with candidates A, B C, the bullet-vote ballot A is
> completed as A>X>B=C, A>B>C is completed as A>B>C>X).
>
> Best regards
> Peter Zborník
>
> On Mon, Jun 6, 2011 at 8:18 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:
>> Hi Peter,
>>
>> --- En date de : Lun 6.6.11, Peter Zbornik <pzbornik at gmail.com> a écrit :
>>> Personally I think that Condorcet methods (take Schulze as
>>> reference)
>>> with symmetrical ballot completion might satisfy FBC, but I
>>> am not
>>> sure, so that's why I ask for some guidance here.
>>
>> Actually I'm pretty sure I explained to you recently why symmetrical
>> ballot completion makes the problem worse.
>>
>> Kevin Venzke
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
>>
>