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

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• I tried vote-reversing the Burlington IRV election considering only the top three candidates: #Voters Their Vote 1332 M K W 767 M W K 455 M 2043 K M W 371
Message 1 of 50 , Mar 24, 2013
I tried vote-reversing the Burlington IRV election considering only
the top three candidates:

#Voters Their Vote
1332 M>K>W
767 M>W>K
455 M
2043 K>M>W
371 K>W>M
568 K
1513 W>M>K
495 W>K>M
1289 W

In the real election, K (Kiss) was the IRV winner, but M (Montroll)
was the Condorcet winner.

(It's interesting to note that only 866 voters explicitly marked M
last, far fewer last-place votes than the other two candidates got.
in, M still has the fewest last-place votes. This is what we would
expect for a Condorcet winner, as contrasted with a widely disliked or
merely unknown candidate.)

In order to turn the truncated ballots into fully ranked ballots, I
assume that the lower preferences of the voters who truncated are in
proportion to the preferences of the voters who fully ranked and had
the same first choice as the truncating voters. For example, I assume
that of the 455 M-only voters, 288.7 of them would vote M>K.W and
166.3 would vote M>W>K if forced to fully rank. Thus we get:

1620.7 M>K>W
933.3 M>W>K
2523.7 K>M>W
458.3 K>W>M
2484.2 W>M>K
812.8 W>M>K

(K is still the IRV winner and W still comes in 2nd place with these
altered ballots.)

Now reverse the preferences shown on the ballots. First round we get:

3784.4 W
3417.5 K
1271.1 M

So M is the least-UNpopular candidate according to 1st-choice votes on
the reversed ballots. But M was the least-popular candidate according
to 1st-choice votes on the original ballots. Just shows how silly it
is to use 1st-choice votes, Plurality style, to estimate "popularity."

Anyway, redistributing M's votes, the second round totals are

4242.7 W
4230.3 K

Note the difference is fairly small - a difference of 12.4 votes. IRV
came _close_ to declaring K to being the least popular as well as the
most popular candidate!

At any rate, IRV fails full-finish-order-reversal for this set of ballots.

It would be interesting to see how this analysis would turn out using
the original ballots with all 5 candidates (perhaps ignoring ballots
containing write-ins).
• ... 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
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.)
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