[EM] Beatpath vs Ranked-Pairs

[Michael Ossipoff]

Forest--

But, with covering sometimes overruling wv, wouldn't that spoil the
various majority rule and CW guarantees of RP and River?

Michael Ossipoff

On Mon, Oct 28, 2013 at 6:50 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
> Giving coverings more defeat strength than non-coverings will make the
> winner uncovered in both River and RP, but I don't think it works for
> Beatpath.  Jobst showed that River is still monotonic with this measure of
> defeat strength.  I'm pretty sure that Beatpath(with covering trumping WV)
> is not monotonic, but I don't have a ready example.
>
> I was srong about ( the Haas diagram of) the covering relation being a tree,
> but it is an acyclic graph, so in RP you can lock in all coverings up front.
> You have to start worrying about creating cycles only at the stage of
> incorporating additional defeats (i.e. the non-covering defeats)..
>
>
> On Sat, Oct 26, 2013 at 6:59 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>>
>>  Hi Forrest--
>>
>> Do RP and Beatpath have that property too?
>>
>> Michael Ossipoff
>>
>> On Sat, Oct 26, 2013 at 5:26 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
>> >
>> >
>> >
>> >
>> >> From: Jobst Heitzig <heitzig-j at web.de>
>> >> To: Michael Ossipoff <email9648742 at gmail.com>,
>> >>         "election-methods at electorama.com"
>> >> <election-methods at electorama.com>
>> >> Subject: Re: [EM] Beatpath vs Ranked-Pairs
>> >> Message-ID: <526A4064.4090505 at web.de>
>> >> Content-Type: text/plain; charset=ISO-8859-1
>> >>
>> >> Dear Michael,
>> >> (...)
>> >
>> >
>> >>
>> >> Even further, when defeat strength is defined as the approval of the
>> >> defeating candidate, then River, Beatpath, and Ranked Pairs are all
>> >> equivalent to DMC:
>> >>
>> >>
>> >> http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015465.html.
>> >> See here for a nice example:
>> >>
>> >>
>> >> http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-May/015873.html.
>> >>
>> >> Also, don't forget that if defeats that are also coverings are
>> >> considered
>> >> before defeats that are not coverings, the River winner will be an
>> >> uncovered
>> >> candidate.  Since the covering relation is a tree, it becomes a
>> >> sub-tree of
>> >> the River tree when defeats are ranked this way.
>> >
>> >
>> > Forest
>> >
>> >
>> > ----
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>> >
>
>