[EM] Beatpath vs Ranked-Pairs

Jobst Heitzig heitzig-j at web.de
Fri Oct 25 02:56:52 PDT 2013

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,
and the related IWDA criterion (see
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:
or using pen and paper from a large defeat matrix (see

- River does however fail Steve's I2C criterion:

Regarding other strategy-related criteria I believe not much has been
investigated, but this later summary post might shed some light on it:

River can be made robust against compromising and burying by combining
it with approval information, as discussed in my "attempt of a grand
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:
See here for a nice example:

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
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:

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
>>> ----
>>> Election-Methods mailing list - see http://electorama.com/em for list info
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info

More information about the Election-Methods mailing list