Range Voting Redux

[kevin_standlee]

Y'all might want to go have another look at the discussion on Range Voting from a few weeks ago. Advocates have (somewhat belatedly by LJ standards) chimed in on the subject here and here.

Update, 23 Jan 2007, 00:30: And now many other places. Whew!

Comments

[mishalak.livejournal.com]

I'm surprised they even noticed belatedly. Must be using some sort of google alert based on keywords. Perhaps I should do a post slagging them in my own journal.

Google

[thebrokenladder.livejournal.com]

Google blog search.

Re: Google

[kevin-standlee.livejournal.com]

That's sensible of you. If you mention "Hugo Award," "Worldcon," or "World Science Fiction Convention" in your blog, expect me to see it as soon as Google spits it out. As Chairman of the Mark Protection Committee, I feel obliged to keep an eye out for misuses of the registered WSFS marks. (And I do find them from time to time.)

[bovil.livejournal.com]

FUD doesn't fly with me.

[thebrokenladder.livejournal.com]

Science does not equal FUD. Don't dismiss the science unless you've got some pretty powerful counter-evidence, which I don't believe you do.

[bovil.livejournal.com]

The best FUD has basis in fact, but it's FUD nonetheless.

Back in the late 19th century, George Westinghouse and Thomas Edison were duking it out over whether Westinghouse's alternating current or Edison's direct current would become the standard that powered American homes.

Westinghouse promoted the power-transmission advantages that alternating current provided over direct current.

Edison electrocuted dogs, cats and an elephant using alternating current, and secretly financed the development and construction of the State of New York's first electric chair.

So it's factually correct that alternating current can be deadly at lower voltages and current levels than direct current is. Still, the switch to alternating current made our power transmission infrastructure more efficient and safer.

It's also factually correct that IRV has flaws and there are situations that can "crash" an IRV counting process. Still, many of your arguments are irrelevant to our application, and our many years of anecdotal evidence that IRV works fine for us stands up to your anecdotal evidence that people are "happier" with range voting.

We've developed a culture and a process for modifying our organization. You can work within that process and perhaps obtain your goal, or you can continue electrocuting cats.

[thebrokenladder.livejournal.com]

> Edison electrocuted dogs, cats and an elephant using alternating current, and secretly financed the development and construction of the State of New York's first electric chair.

At the Center for Range Voting, we don't engage in such practices. I'm vegan as a matter of fact.

> Still, many of your arguments are irrelevant to our application

The utility argument is one that isn't irrevelant to your application, and that's the biggest argument for RV. The very *point* of a voting method (just as with an individual choice), is to produce the greatest utility. RV produces greater utility than IRV, and not by a little, but by quite a lot. Choosing to use IRV instead of RV would be comparable to choosing to draw a name out of a hat, instead of using IRV (not _quite_ that bad, but close). Given that severity, I propose this is something that you should seriously consider, and not write off just because it seems unintuitive and non-traditional.

> our many years of anecdotal evidence that IRV works fine for us stands up to your anecdotal evidence that people are "happier" with range voting.

Our social utility efficiency calculations were very extensive. It is not justified to call the results "anecdotal". Consider the number of simulations performed (hundreds of millions), and the number of different parameters varied within those simulations (720), and the extremely large typical difference in utility between IRV and Range Voting, this is powerful evidence. How does the fact that you have been happy with IRV discount the value of being substantially happier? It's like saying, "Oh, I'm plenty happy with making 60,000 dollars per year, I don't want an easier job that pays 100,000." It's not a life-or-death thing, but more of a, "Why the heck wouldn't you?" That's what baffles me.

> We've developed a culture and a process for modifying our organization. You can work within that process and perhaps obtain your goal, or you can continue electrocuting cats.

Well, you can work within that process and try to switch to Range Voting as well. I'm not part of your organization, so I have little vested interest in this, except for that I'm a perfectionist/idealist (which is why I use dvorak, and speak Esperanto, and lust for the metric system). But for you, this is significant. You're frequently picking the "wrong winner" because you are using a very flawed voting system. As my spreadsheet scenario demonstrates, Range Voting can also fail to elect the right winner. But it picks better winners more often than the other methods. If the effect were small, I wouldn't be here chatting with you now. The effect is huge, and all I'm asking, whether you adopt Range Voting or not, is for you to simply acknowledge that.

[kevin-standlee.livejournal.com]

...which is why I use dvorak, and speak Esperanto, and lust for the metric system.

Yep, you're a Fan, all right, even though you don't know it. You'd be right at home at most SF conventions I've attended. I bet that at most Worldcons, you'd be able to find a BOF (birds of a feather) gathering for the first two quirky interests.

(Although I do happen to share your desire for the USA to join the rest of the civilized world and use the metric system for real.)

The effect is huge, and all I'm asking... is for you to simply acknowledge that.

I don't think anyone doubts that, by standards of "social utility" that you have devised, you have developed the Best System EVAR.

New proof that Range Voting > IRV, Condorcet, etc.

[(Anonymous)]

We shall show a sense range voting is superior to any
pure-rank-ballot voting method.

Theorem:
These criteria, for a single-winner voting system based on
pure-rank-order-ballots, are incompatible:
1. AFB = avoids favorite betrayal
2. ICC = immune to candidate cloning
3. reduces to simple majority vote in 2-candidate case
4. symmetry under candidate renaming
5. tiebreaks (if any) are random equally likely.
6. adding a new candidate to the election whom all voters unanimously
rank unique-bottom,
does not change the winner.

Proof:
Consider these 3 votes:
A>B>C
C>A>B
B>C>A
by symmetry axiom 4 this is a perfect 3-way tie.
However we shall argue under axioms 1-3 that A must win, which is a
contradiction that establishes the proof.
If A does not win, then B or C does.

If B wins, then the C-voter would betray C to vote A>C>B getting
A>B>C
A>C>B
B>C>A
and then {B,C} is a clone set and hence by axioms 2 and 3 then A must win
and hence the betrayal worked and hence we get a contradiction with
axiom 1.
[The alternate dishonest vote, which is not a C-betrayal, C>B>A,
would not work since B still would win:
A>B>C
C>B>A
B>C>A
now {B,C} is a clone set, so by axioms 2 & 3 B or C must win;
but winner here must be B and not C (and not BC tie) because if it were C
or BC tie then the A-voter could betray: B>C>A causing
B>C>A
C>B>A
B>C>A
in which case B must win by axiom 6.]

If C wins, or if BC tie, then the A-voter can betray A to vote B>A>C
getting
B>A>C
C>A>B
B>C>A
whereupon {A,C} is a clone set and hence by axioms 2 and 3 then B must win
and hence the betrayal worked and hence we get a contradiction with
axiom 1.
[The alternate dishonest vote which is not an A-betrayal, A>C>B would
not work since
C still would win when
A>C>B
C>A>B
B>C>A
because {A,C} is a winning clone set
and if A wins (or AC tie) then B>C>A voter betrays: C>A>B to
make C win
A>C>B
C>A>B
C>A>B
by axiom 6.]
Q.E.D.

Remark 1.
I do not presently know if this theorem can be extended to permit
equalities in vote-rankings.

Remark 2.
Antiplurality voting obeys all 6 axioms except for #2.

Remark 3.
Schulze beatpaths voting obeys all 6 axioms except for #1.

Remark 4.
Range voting obeys all 6 axioms if all range votes are
"normalized" so voters (obeying the recommendations for voting on the
http://rangevoting.org front page) always gove the best candidate the top
score and the worst the bottom score in a 2-candidate election
[i.e. in practice with voters who are not idiots].
But with possible-idiot voters, range fails axiom #3.

So we have proven a sense in which range is superior to EVERY
pure-rank-ballot voting
method, and using two of the most important voting criteria AFB and ICC.

Remaining Open question: what happens if we permit rank order votes to
have EQUALITIES in them?