## Re: [RangeVoting] Re: More on the reversal problem

Expand Messages
• 2013/4/1 Stephen Unger ... I have no idea what you understand to be the formal definition of Bucklin. You explain that it involves full
Message 1 of 50 , Apr 1, 2013
• 0 Attachment
2013/4/1 Stephen Unger <unger@...>

> **
>
>
> I used what I understand to be the formal definition of Bucklin, not
> some abbreviated version (altho I am sure that, in actual use, various
> abbreviated versions were employed). In that case, we operate with a full,
> standard ranking, with a single candidate for each rank. The reverse
> of a vote is simply the ranking written backwards, which is what a
> voter would do if the object was to order the candidates with the
> worst one first, etc. This is the most straightforward way of
> interpreting the various terms.
>
I have no idea what you understand to be the formal definition of Bucklin.
You explain that it involves full ranking, but you do not explain what
tiebreaker you use in the case where two candidates reach 50% at the same
rank. In my understanding, Bucklin is a class of systems, including various
tiebreakers, as well as various rules about ranking/rating (that is, ties,
skipped levels, total number of levels, and labeling for levels). That
class includes several members, including GMJ, which fully meet the
reversal criterion.

This is entirely analogous to the class of Condorcet systems, which
includes a number of matrix-based systems with different ways of breaking a
circular tie and different rules regarding equal ranking. Different
Condorcet systems meet or fail different criteria, and an example where one
system fails criterion X is not enough to say that "Condorcet fails X".

>
> No such failures occur with approval or score. In approval voting, for
> example, every candidate approved in the initial election is NOT
> approved in the reverse election, and vice versa. There is no "middle"
> group approved both ways.
>
> So Bucklin clearly fails the reversal test.
>
No. Whichever version of Bucklin you were implicitly using does. GMJ and
some other Bucklin systems do not.

> The fact that the "middle
> votes are the same in both cases" is inherent in Bucklin. It explains,
> but does not justify, the mechanism of the failure.
>
I agree with this, for the version of Bucklin which you were using. One can
make arguments about how important it is that system Y fails criterion X,
but you're right: that doesn't make the failure disappear.

Jameson

[Non-text portions of this message have been removed]
• ... That would certainly be true, does not contradict what I wrote, and the concept of repeated voting with lowered approval cutoff was extensively discussed
Message 50 of 50 , Apr 6, 2013
• 0 Attachment
At 08:12 AM 4/5/2013, Bruce Gilson wrote:
>On Fri, Apr 5, 2013 at 9:38 AM, Abd ul-Rahman Lomax
><abd@...>wrote:
>
> > Bucklin appeared, in many analyses, to not pass reversal because of
> > mindless ranking without regard for approval.
> >
> >
>In fact, when Steven Brams discusses Bucklin in his book, *Mathematics and
>Democracy*, mostly in conjunction with his nearly identical system called
>"Fallback Voting," he makes it clear that only approved candidates are
>ranked by the voter.
>
>So at least one person outside this group has noted this.

That would certainly be true, does not contradict what I wrote, and
the concept of repeated voting with lowered approval cutoff was
extensively discussed by students of approval voting.

However, reviewing Mathematics and Democracy, I'm struck by what
seems to be entirely missing from it: any consideration of repeated
ballot, seeking an explicit majority, whether absolutely (Robert's
Rules) or as a goal (i.e., runoff systems that terminate, usually on
the second ballt, with a plurality result if a majority is not found
-- or that *force* a majority by disallowing any other votes that for two).

It's a glaring omission. It's not just Brams. The characteristics of
runoff voting were widely ignored in voting systems discussions,
including Bayesian Regret calculations that assumed the same voting
electorate with the same preferences. I can think of no example of
someone proposing runoff voting using an advanced voting system,
until I started doing it, and that blind spot seems to have existed
in the past.

Strangely, the actual behavior of runoff voting and how it differed
from IRV was either ignored, or was *explained* by some deficiency in
turnout, or manipulability by monied interests, ignoring the actual
situations. Yet Robert's Rules of Order is totally aware of the
problem of *not* holding a real runoff, using IRV. Their concern is
not abstract, they are parliamentarians. They also criticize IRV for
center squeeze, and their own preferential voting process *still
seeks a true majority or the election must be repeated.*

Almost by accident, in Arizona (it wasn't an accident, we have a man
on the ground there, who did yeoman work), we may be getting
Approval/Runoff, with a mandatory top two runoff. Technically, of
course, this is Top Two RAnge, which outperforms Range in simulations
with realistic voting patterns. We can probably do better, but this
is very good to start! (I've suggested that Bucklin for the primary,
at least, is an obvious move.)

(Pure Range with *accurate and commensurable* utility expression is,
by definition, optimal for summed social utility. But there are few
ways to get that expression. Interestingly, an inconvenient runoff
election does push results toward absolute utility, because if the
choices are not greatly different in utility, the voter has less
motivation to vote, hence expressed votes will tend to have higher
preference strength behind them.)

Reading over Brams I see that PAV is essentially what I've proposed,
but I've suggested a true hybrid ballot that allows equal ranking.
He's suggested, essentially, a ranked ballot with an explicit
approval cutoff. I've simply suggested using a Range ballot with
midrange as explicit approval cutoff. That allows ranking within the
approved and disapproved sets, yet the "sincere" ballot is easy to
vote, except for the *intrinsic difficulty*, deciding how to
categorize the candidates, which gets tougher when there are three or
more. (And there are always, in fact, many, if write-ins are
allowed.) Runoff systems make the decision in the primary a bit
easier, approval becomes a binary decision: would I prefer the
election of this candidate to a runoff being held?)

Brams also mentions voting after a series of pre-election polls. If
we assume that the polls are accurate, this is essentially repeated
ballot, but based on a sample instead of the full electorate.
However, that assumption can be a problem!

If, instead of a poll, it's a real election, in a runoff system
primary, we can be reasonably confident that a majority result is
real! Multiple majorities are a problem, but the hybrid ballots I've
suggested can find ways of making that choice, if it's considered
excessively inconvenient to refer it to the voters in a runoff.

(Polls should not simply collect favorite information, that will
distort them. Range polls are much better, that's been obvious for
some time. A Range 2 poll -- +/-, default 0 -- showed what
vote-for-one polls could not show, true relative position of
candidates, and strength of support and opposition.)
Your message has been successfully submitted and would be delivered to recipients shortly.