- 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.

And if the tied-last-place votes from the truncated ballots are added

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). - At 08:12 AM 4/5/2013, Bruce Gilson wrote:
>On Fri, Apr 5, 2013 at 9:38 AM, Abd ul-Rahman Lomax

That would certainly be true, does not contradict what I wrote, and

><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.

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.)