
Counting Votes Is Hard - jdwyah
http://blog.forcerank.it/counting-votes-is-hard
======
tunesmith
I've always thought that descriptions of Condorcet methods are harder than
they need to be. Even the wikipedia page describes them badly.

The Condorcet criteria itself is easy. If a candidate would beat every other
candidate in a one-on-one matchup, that candidate should be the winner. There,
that's it.

That's really how it should be described. And then as a next step, we can then
describe "tiebreakers". Instead, wikipedia (and others) describe Condorcet
only in terms of their tiebreakers, making Condorcet methods themselves appear
flawed[1].

You see, loops are possible. In a vote, it's possible that A would always beat
B, B would always beat C, and C would always beat A. And the various Condorcet
tiebreakers (like Schulz) are ways to resolve those situations.

But the point is, if that happens, the vote really is accurately uncovering an
indecisiveness that actually exists in the voting population. So it makes
sense that a "tiebreaker" would be non-ideal in some sense. And they all are
in some way. The problem is not with the tiebreaking methods. The problem is
with the voting population.

I've always thought a good voting system would be the following:

First, rank the votes. If a Condorcet winner exists, the election is over. If
not, restrict the candidate pool to the Schwartz set, and start a new round of
campaigning so the voting population can research more and better educate
themselves.

[1]. Yes, we can argue that the Condorcet criteria is "perfect" if a Condorcet
Winner exists, with one caveat: it implies the value that all votes have equal
value. If you have that value, it's a logical implication that the Condorcet
Winner (if it exists) should be the winner. But other values are possible,
such as a utilitarian mindset of wanting to meet greatest social utility, such
as some voters being far more passionate or educated than others. Following
those implications bring up other tricky problems, though.

~~~
chongli
Why not ditch the ordinal voting and go with a cardinal system? People have
seen and understood the system used in judging competitions such as figure
skating, diving and gymnastics for many years. Wouldn't it be completely
straightforward for them to see it on a ballot? Range voting is the name of
that system and, unlike Condorcet methods, it is not subject to Arrow's
impossibility theorem.

~~~
bradbeattie
Because range voting devolves to approval voting. Why rate a candidate 4/10 if
you don't want them to win? You insincerely rate them 0/10\. Why rate a
candidate 8/10 if you want them to win? You insincerely bump them to 10/10.

On top of that, you then have to consider the potentially lower popularity of
your favourite choice against that of the current lead contenders. Do you
reduce your vote for the better of two evils so that your sincere preference
has a better chance? Ugh.

I'm not trying to suggest tactical voting doesn't exist in other systems, but
to suggest that it doesn't in Range voting is either misinformed or
disingenuous.

~~~
DennisP
Now suppose there's a candidate I like pretty well, not as much as my
favorite, but better than several others. Do I vote 10/10 or 0/10? Which is
more tactical? It's a little hard to say.

With approval voting I have to make that decision, setting some kind of
threshold of approval. With range voting it might be easier to just vote
honestly.

At worst, everybody votes tactically and you get approval voting, which is
still a good system. But sometimes the tactical decision is difficult, in
which case range voting gives you the option of just voting honestly.

------
tokenadult
Neither the blog post kindly submitted here nor the comments (so far) nor the
Wikipedia article mentioned in one comment mention the impossibility theorem
proved by Kenneth Arrow,[1] which shows that we can't build a perfect voting
system to take into account preferences among three or more candidates. As a
voter in a state with as many as ten candidates on the ballot in a typical
presidential election, and some amazingly close three-way statewide
elections,[2] I'm surprised that the Arrow paradox (Arrow impossibility
theorem) isn't more widely known. I learned about it in an article in
Scientific American back in the 1970s. My state has three "major parties" that
have automatic ballot access for nominated candidates, and I expect that this
year we may add one more political party to the list of major parties by the
rules established in state law. If voters have more than two choices, odd
results can happen in elections.

AFTER EDIT: A comment posted while I was typing the first version of this
comment mentions "range voting" as a response to the Arrow paradox. A
commentary by an economist[3] and a problem set by a mathematician[4] may
suggest to thoughtful readers here some issues to ponder while discussing
whether or not range voting provides better trade-offs than our current voting
system, and whether it indeed escapes the theorem proved by Arrow.

[1]
[https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem](https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem)

[http://www.math.ucla.edu/~tao/arrow.pdf](http://www.math.ucla.edu/~tao/arrow.pdf)

[2]
[http://latimesblogs.latimes.com/washington/2008/11/franken-c...](http://latimesblogs.latimes.com/washington/2008/11/franken-
coleman.html)

[http://www.politico.com/news/stories/0609/24383.html](http://www.politico.com/news/stories/0609/24383.html)

[http://www.amazon.com/This-Is-Not-Florida-
Minnesota/dp/08166...](http://www.amazon.com/This-Is-Not-Florida-
Minnesota/dp/0816670382)

[3]
[http://marginalrevolution.com/marginalrevolution/2009/11/ran...](http://marginalrevolution.com/marginalrevolution/2009/11/range-
voting.html)

[4]
[http://www.math.cornell.edu/~mec/Summer2008/anema/approval.h...](http://www.math.cornell.edu/~mec/Summer2008/anema/approval.html)

~~~
dllthomas
Range voting still has its issues - every voting methodology has some issues -
but range voting pretty well dominates plurality voting IMO.

~~~
baddox
That depends on how much you value electing a candidate who is the _top_
choice of the most voters. The value proposition is completely subjective.

~~~
kybernetikos
I think this is insufficiently talked about in discussions of voting systems.
For some situations it's better to have a divisive winner with passionate
support and in other situations it's better to have a compromise winner that
nobody hates too much.

Different voting systems can give you different angles on picking the option
with the most direct support versus avoiding picking options that stir up a
lot of dislike in the voting body.

~~~
dllthomas
While that's true and important, plurality doesn't do as good a job as other
methods at either.

------
lowry
Funny how the website authors failed to do research on voting systems _before_
writing the website.

~~~
jdwyah
I totally did look into them, I just didn't think it would matter much for our
use case. As a general rule I find that time spent with fun complicated
algorithms is rarely connected to actually creating business value..

Just turned out I was wrong this time :)

~~~
tunesmith
As someone who spent time with the fun complicated algorithms, I quite like
the UI and usability of your ballots - it matches up rather exactly with how I
imagined doing it myself before I got distracted messing with more algorithms.
;-)

------
LarryMade2
Heh, it always sounds easier in a meeting, "Bill, set up some sort of simple
voting system, should be a cinch, by the end of the week should be plenty of
time."

------
amishforkfight
I don't do a lot of this kind of work, but as an interested party with sunday
spare time, I think the problem here is that you're scoring anything other
than the first picks.

If you just look at first picks, Newbie HBase wins 3 to 1. If for some reason
Newbie HBase was in a 2/2 split with Mapreduce and KIR (flip James's top 2
votes), you then take into account 2nd rankings, which in this case means
Newbie HBase wins again.

I don't believe you ever want to take into account someone's griefer vote, too
much potential to game the system with no benefit to the group as a whole.

~~~
rspeer
Griefer votes are hard to do in Condorcet.

You're proposing plurality voting (plus a weird tie-breaker), which is the
worst method on basically every criterion except for "simplicity" and
"familiarity to Americans". It leads to really obvious vote-splitting, and
people will vote strategically, because they know perfectly well what happens
to honest votes in plurality voting. They will also simply propose fewer
things.

If the computer is counting votes for you, simplicity shouldn't be the highest
priority.

There's a reason people have put years and years of research into voting
methods. The best method is unlikely to be the one you think of off the top of
your head and post in an HN comment.

~~~
amishforkfight
I don't believe there is anything 'weird' about the tie-breaker, it's a pretty
standard technique - local elections, tournament tie-breaking, movie night
voting. What's weird about using second and third choices to determine the
best when there's a tie for the first choice?

What I think is really weird is why would a system put much weight, if any at
all, on someone's 4+ choice? We might be coming up with a result that received
the most points, but are we actually coming up with a result that the most
people will be happy with, or is it the least boring thing that people will
put up with?

~~~
jdwyah
(this is Jeff from ForceRank)

The thing to note about our particular situation is that we're really only a
little interested in the #1 result. The app is primarily about helping groups
prioritize things, for instance "What features do we need to build next".

Rating systems are a no go, because the whole point is to force people to
choose and hence consider the tradeoffs (hence "ForceRank" :)

In this case, some of the voting system criteria such as "susceptibility to
burying" play out a bit different than in a regular election. eg If everyone
thing "Project C" is a great idea but Frank _hates_ Project C, we want to do
what we can to highlight that fact, not just continue on our merry way with
the majority vote.

------
jellicle
Every voting system incorporates certain preferences. They are built in, and
cannot be removed from the system. In this case, the voting system used
essentially incorporates the idea that relative ranking is important -
something that the voter ranked #2 is more preferable to the voter than
something the voter ranked #10.

So the idea that the algorithm ended up picking something ranked #2 by
everybody over something ranked #1 by some people and #10 by some people is
not actually crazy.

If you choose a system with ten gradations of voting, that's what you get -
choices that are #2 for everyone are preferred over choices that are #10 for
some people. If you don't like that result, don't choose that voting system.
That's what a ten-point voting system _is_.

By the way, the images are wrong - the text implies that Matt ranked Newbie
Hbase very low, but the image shows the opposite.

