[EM] Beatpath vs Ranked-Pairs

Michael Ossipoff email9648742 at gmail.com
Fri Oct 25 12:54:34 PDT 2013

 Hi Jobst--

I'll check out those postings and discussions that you linked to.

You, Steve, and Markus know more about the properties of those 3
methods than I do.  My evaluation of them is more like that of a

What I do know is that RP (in which I include MAM) and River are much
more briefly defined and motivationally-justified than CSSD/Beatpath
is.  Between River and RP, of course RP is marginally briefer, due to
having only one rejection-criterion instead of two. But that doesn't
make River significantly more complicated than RP.

...And  know that Steve found, via simulations, that RP chooses winner
that are preferred to Beatpath's winners vastly more often than
Beatpath' winners are preferred to RP's winners.

Of course ideally we'd honor every public pairwise decision (PPD),
every pairwise-defeat. Pragmatically, we can't always honor all PPDs,
because, with a top-cycle, we wouldn't be able to elect anyone. So
it's only with reluctance that we ignore a PPD.

Pragmatism doesn't require ignoring a PPD because it contradicts a PPD
that doesn't defeat anyone, and does't disqualify anyone from winning.
So, when RP drops a defeat that makes someone defeated, and has an
effect, because it contradicts a defeat that doesn't make anyone
defeated (because they already are defated), and doesn't have an
effect, that isn't justified by pragmatic need, and it's contrary to
the principle of honoring as many PPDs as possible. So River adheres
to that principle better than RP does.

...But then, CSSD/Beatpath seems to adhere to it better still, because
it only disregards the minimum number of defeats, only as many of the
weakest defeats as need to be dropped to produce a winner.

Therefore it surprises me that Beatpath did worse, in terms of
collective public wishes. But it did, and that's what matters.

River's compliane with Indepenence from Pareto-Dominated Alternatives
certainly counts for it. I'll have to read about Steve's criterion
about avoiding majority-complaints.

So I'm going to look at those postings and discussions that you linked to.

Michael Ossipoff

On Fri, Oct 25, 2013 at 5:56 AM, Jobst Heitzig <heitzig-j at web.de> wrote:
> Dear Michael,
> I'm happy you took the time to read that lengthy old post. I must admit
> it has been years since I thought about this type of method before
> focussing on democratic (as opposed to majoritarian) methods.
> You description of River is correct: It is Ranked Pairs without locking
> in defeats against already-defeated options.
> The main advantages in my current view are these:
> - When a defeat is rejected because it would create a cycle, the
> rejection is easier to justify if the other defeats on the cycle were
> influencing the result (because they defeated a not-yet-defeated option)
> when they were locked in.
> - River (but neither Beatpath nor Ranked Pairs) fulfils Steve's IPDA
> criterion: Adding a Pareto-dominated alternative doesn't change the result.
> - River also fulfils the stronger ISDA criterion (see that same post,
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012772.html)
> and the related IWDA criterion (see
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-November/014156.html).
> All three criteria are forms of strategy-proofness since they mean one
> cannot manipulate the result by adding irrelevant "bad" options as "noise".
> - River allows an easier graphical representation of the result and its
> justification since it produces a tree of defeats (instead of a more
> complex acyclic graph of defeats as Ranked Pairs does), which can
> readily be layed out in a diagram (together with some additional
> information, see River+ in the above post) and allows a nice
> metaphorical interpretation as a river system that flows towards the winner.
> - River can thus be applied more easily in an interactive way in small
> groups (see my April 10, 2004 post:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012701.html)
> or using pen and paper from a large defeat matrix (see
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014149.html).
> - River does however fail Steve's I2C criterion:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014130.html
> Regarding other strategy-related criteria I believe not much has been
> investigated, but this later summary post might shed some light on it:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-September/013971.html
> River can be made robust against compromising and burying by combining
> it with approval information, as discussed in my "attempt of a grand
> compromise":
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014071.html.
> 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.
> Regarding simulations I must admit that I don't remember the details and
> have probably deleted the data by now, so we have to go by what I wrote
> back then:
>> Example with 10 options, no uncertainty (that is, no truncated ballots),
>> and L=0.4 (that is, with some correlation between voters preferences):
>> In only about 1% of the cases, the River winner differed from both
>> Beatpath and MAM winner, and in only about 0.5% Beatpath and MAM were
>> the same but River was not. In contrast, in about 5% of the cases, River
>> and MAM were the same but Beatpath was not, and also in about 5% of the
>> cases, River and Beatpath were the same but MAM was not. There were only
>> about 11% of the cases where the Immune set was not a singleton. That
>> is, in almost *all* cases where there were more than one immune element,
>> MAM and Beatpath chose different winners. In other words, whenever they
>> are "immunologically allowed" to choose differently, it seems they
>> almost certainly do...
> From this I concluded that River is a good "compromis" between Beatpath
> and MAM aka Ranked Pairs since it agrees more often with each of them
> then they agree with each other.
> To see this in more detail, I listed all non-trivial four-option cases
> and compared the three methods here (using the name Tideman for Ranked
> Pairs):
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012838.html
> It shows that only in 0.7% of the situations, River chose differently
> than both other methods, while in 6% [7%] of the cases Ranked Pairs
> [Beatpath] chose differently than both other methods.
> Another interesting example where I discussed a lot of methods including
> those three is here:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014145.html
> This summarizes all I was able to remember about River :-)
> Best, Jobst
> Am 25.10.2013 02:43, schrieb Michael Ossipoff:
>> Hi Jobst--
>> I've just read your EM postings for April and May of 2004.
>> I couldn't find the simulation report. What did the simulations say
>> about River vs Ranked-Pairs?
>> Does this accurately describe the difference between River and Ranked-Pairs?:
>> When River is described in language like that in RP's definition, as I
>> understand it, River additionally rejects a defeat if the defeated
>> candidate already has an already-kept defeat that is stronger?
>> ...the justifictation being that if s/he is already defeated, then
>> there's no need for hir new defeat.
>> And, not having that unnnessary defeat can avoid the unnecessary
>> rejection of some subsequent new defeat(s).
>> If that's right, then I understand the justificaton of River, in
>> comparison to Ranked-Pairs.
>> What are the differences in strategy-properties or strategy-guarantees
>> or strategy vulnerabilitie, between River and  Ranked-Pairs.
>> Would it be right to say that River is Ranked-Pairs, with an
>> additional reason for rejecting a newly-considered defeat?
>> That would mean that River is almost as simple as RP. What are its
>> strategic advantages over RP?
>> Michael Ossipoff
>> (I call myself "Michael" now, instead of "Mike", because at least 2
>> people have told me that it sounds better.)
>> On Thu, Oct 24, 2013 at 5:15 PM, Jobst Heitzig <heitzig-j at web.de> wrote:
>>> Dear all,
>>> I'd be really happy if you cared to consider also the River method when
>>> comparing Ranked Pairs and Beatpath. As you cite Steve's simulations,
>>> you might want to look at my April 24, 2004, post
>>> (http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012772.html),
>>> where I discussed their relationship and performed similar simulations
>>> showing that indeed River is a very good compromise between Ranked Pairs
>>> and Beatpath in terms of criteria.
>>> Best,
>>> Jobst
>>> Am 24.10.2013 20:23, schrieb Michael Ossipoff:
>>>> When  say "Ranked-Pairs" or "RP", I'm referring to the practice of
>>>> considering the pairwise defeats in order of their strength, keeping a
>>>> considered defeat if it isn't contradicted by already-kept defeats
>>>> (directly,or by being in a cycle with them).
>>>> Additionally, I'm referring to versions of RP that allow equal
>>>> ranking, and allow trunction, and judge defeat-strength by
>>>> winning-votes.
>>>> I'm not concerned about how ties ae dealt with, because, publc
>>>> political elections are the important voting-system appication, and
>>>> ties will vanishingly-rare in such elections.
>>>> I've already said some of this, but I'm now adding a little.
>>>> In that comparison, Beatpath is easier to program, and somewhat faster
>>>> to compute (but computation-time is negligible wth today's computers,
>>>> for either method).
>>>> Those attributes make Beatpath appealing for organizations.
>>>> But Ranked-Pairs is incomparbly more briefly-defined, and makes a lot
>>>> more sense, and is more easily and obviously motivated and justsified,
>>>> when proposing it to people.
>>>> Additionally, Steve Eppley's simulations found that, when RP and
>>>> Beatpath choose different winnes, the public colletively prefer RP's
>>>> winner to Beatpath's winner, overwhelmingly more often than
>>>> vice-versa.
>>>> In other words, anyone advocating Beatpath over RP needs to explain
>>>> why we should want a less demcratic voting-system.
>>>> I emphasize that, due to their chicken-dilemma, I don't advocate
>>>> either RP or Beatpath for public political elections in the U.S.
>>>> Instead, for the Green scennrio, I advocate Benham and Woodall, though
>>>> IRV would be acceptable, even though it has disadvantages (previously
>>>> described by me), in comparison to Benham and Woodall.
>>>> Michael Ossipoff
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