Ron Conway doesn't understand IRV

[Clay Shentrup]

http://sfist.com/2015/10/26/ron_conway_instructed_the_ceos_of_e.php

[Kevin Baas]

he's not alone.

i analyzed the ballots here:

http://www.acgov.org/rov/rcv/results/226/

one can excuse the xxx's and even the xyy's.

but the xyx's and xxy's.... clearly they don't understand how it works.

should be clear language on the ballot.  something like:

"Rank each candidate at most once."

"If a candidate is given two different rankings (e.g. 1st and 2nd or 1st and 3rd), only the first ranking will be used."

or if you want to drive home the point on a thick audience:

"If a candidate is given two different rankings (e.g. 1st and 2nd or 1st and 3rd), the ballot will not be counted."

would be nice to also add:

"Ranking a 2nd or 3rd choice will not diminish the chances of your 1st choice."

"Your 2nd choice will only be used if either your 1st choice cannot get elected, or your 1st has more than enough votes to get elected. (In which case your 1st choice will be elected.)"

On Wednesday, June 29, 2016 at 3:50:09 PM UTC-5, Clay Shentrup wrote:

http://sfist.com/2015/10/26/ron_conway_instructed_the_ceos_of_e.php

[Kevin Baas]

Between 1st and 2nd sentence:

"Ranking a candidate more than once will not increase their chance of being elected."

[Warren D Smith]

How many of each kind of error did your analysis find?

>he's not alone.
>i analyzed the ballots here:
> http://www.acgov.org/rov/rcv/results/226/

It was interesting to see two people Clay is complaining about,
each with rather opposed notions. Perhaps they should meet
each other...


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Warren D. Smith
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[Kevin Baas]

Can you access this?

https://www.dropbox.com/m/browse?path=%2FCongressional+District+Study%2FPrelim+Data+Anal%2FBerkeley+Nov+4+2014++ranked+choice+ballots%2C+aggregated

If not, I can copy it to somewhere you can.

[Kevin Baas]

I think the general error is that people think it operates like multiple non-transferable votes.

A few simple sentences on the ballot would go a long way to mitigate that. Though voters should know what to expect of the ballot before getting in line.

I also think empirical measure of voter understanding are important for any ballot type and counting method.

I'm happy to post the sources, the source code I wrote to process them, and the output they generates.

And particularly the source code I wrote to process them.

Remind me if I forget.

[Brian Olson]

This wasn't a problem in the Bulington VT elections of 2007,2009. Maybe they had other ways of preventing or filtering out repeated-vote, but I don't recall seeing any in their data set, or at least it was few enough to ignore. There were plenty (a vast majority I would say) of votes that reasonably ranked different candidates.

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[Warren D Smith]

On 6/30/16, Kevin Baas <happy...@gmail.com> wrote:
> Can you access this?
>
> https://www.dropbox.com/m/browse?path=%2FCongressional+District+Study%2FPrelim+Data+Anal%2FBerkeley+Nov+4+2014++ranked+choice+ballots%2C+aggregated

--no.

[Kevin Baas]

posted here:

ftp://autoredistrict.org/pub/ballots/

along with the source code for the ballot image parser and counter.

totals are:

district 1:

1254: xxx

138: xxy

123: xyx

1233: xyy

3361: xyz

district 4:

1828: xxx

93: xxy

182: xyx

1549: xyy

0: xyz

district 7:

559: xxx

63: xxy

49: xyx

540: xyy

575: xyz

district 8:

684: xxx

70: xxy

79: xyx

482: xyy

3649: xyz

[Kevin Baas]

not bad, i suppose.  about 5% were xyx or xxy.  the rest were about evenly split between partial and complete ballots.

just wrong	797	0.048271
partial	8129	0.492338
correct	7585	0.459391

[Warren D Smith]

On 7/1/16, Kevin Baas <happy...@gmail.com> wrote:
>
> posted here:
>
> ftp://autoredistrict.org/pub/ballots/
>
> along with the source code for the ballot image parser and counter.
>
> totals are:
>
> district 1:
>
> 1254: xxx
> 138: xxy
> 123: xyx
> 1233: xyy
> 3361: xyz

--??!! wait, that is amazing.
You are claiming 3361 people voted correctly in style xyz,
but 1254+128+123+1233=2738
voted incorrectly or at least in an undesirable fashion.
Are you lumping the "x**"
where * here means "no choice given, i.e. blank"
"bullet style" voters in with your "xxx"?

I guess it would be more informative if you
split out the "*" so the cases would
be, I guess

xyz --desirable
x** --legal but undesirable
xy* --legal but undesirable
xyx --illegal
xxy --illegal
xx* --illegal
xyy --illegal

[Warren D Smith]

whoops, I forgot the
xxx --illegal

8th possible case.

[Kevin Baas]

all the ballots had exactly 3 ranks filled out.  there were no x**.

i'm guessing the ballots looked something like this:

http://www.sfbetterelections.com/uploads/9/2/2/7/9227685/8089097_orig.jpg

in any case all voters had exactly 3 ranks.

and in any case, yes, less than half did xyz, so the majority of them didn't fully utilize their vote.

[Warren D Smith]

district 4:

1828: xxx
93: xxy
182: xyx
1549: xyy
0: xyz

was the most amazing of all, ZERO voters voted
in the desired xyz style? Maybe there were only
2 candidates?

That ballot picture with all the arrows looks like a nightmare!
My god!

[Warren D Smith]

ok, http://www.acgov.org/rov/rcv/results/226/

district 1: 3 canddts

district 4: only 1 guy ran, the xyx
etc votes concerned write-ins.

district 7: only 2 ran.

district 8: 4 ran.

Those ballots were even more of a nightmare if
fewer than 3 were running, which I'm sure
has a lot to do with your crazy vote-total findings.

I think the problem here was the horribly
badly designed IRV ballots they used, worst
I ever saw.

[Kevin Baas]

yep - only 2 candidates in district 4.

ftp://autoredistrict.org/pub/ballots/district4.txt

http://www.acgov.org/rov/rcv/results/226/rcvresults_8080.htm

...doesn't look right.  maybe my parser alignment is off.   checking.

[Kevin Baas]

i counted "0" as a candidate, which, from reading over the key, i see meant no valid vote.

so, with "-" representing no valid vote:

district 1

1051: xy-
88: xxy
11: -x-
716: xxx
538: ---
29: x-y
10: x-x
48: xx-
1166: x--
2273: xyz
63: xyy
102: xyx
8: -xy
4: -xx
2: --x

district 4

68: xx-
651: xxx
139: -x-
1539: x--
10: -xx
43: x-x
1177: ---
25: --x

district 7

539: xy-
36: xxy
3: -x-
278: xxx
281: ---
30: x-y
4: x-x
25: xx-
515: x--
25: xyy
42: xyx
6: -xy
2: --x

district 8

721: xy-
50: xxy
10: -x-
248: xxx
436: ---
19: x-y
6: x-x
15: xx-
449: x--
2898: xyz
31: xyy
63: xyx
11: -xy
2: -xx
5: --x

[Kevin Baas]

that wasn't their ballots as far as i know.  i don't know what their ballots look like. i was just saying that based on the data it probably gave them exactly 3 ranks regardless of the # of candidates.

in any case, after changing a zero to invalid (-), the results are no more encouraging.

[Kevin Baas]

so let's see...

district 1, 82% voted correctly, and 37% completely

district 8, 90% voted correctly, and 58% completely

district 7, 74% voted correctly, and 30% completely

district 4, 100% thought the ballot was a tic-tac-toe board

[Clay Shentrup]

On Friday, July 1, 2016 at 11:36:49 AM UTC-7, Kevin Baas wrote:

i counted "0" as a candidate

I assumed that's what you had done. Nice to see you corrected that bug.

[Neal McBurnett]

So did a single vote, for just the one candidate running, get turned into an "xxx" ballot somewhere along the line? So that slew of xxx ballots is not actually evidence that people don't get it?

Neal McBurnett http://neal.mcburnett.org/

[Brian Olson]

District 8

4964		ballots
436	8.8%	completely invalid ballot
3290	66.3%	not at all invalid ballot
1674	33.7%	completely or partially invalid ballot
1238	24.9%	partially invalid ballot

no comment on whether a not-at-all-invalid ballot was a full ranking of 3 choices.

Still, the population of Berkeley, CA gets a 66% C grade on correctly filling out a "1,2,3" optical scan ballot.

--

[Brian Olson]

Okay, District 8 from the 2014 Berkeley City Council vote is interesting!

http://bolson.org/~bolson/2016/berkeley_cc_d8_2014.html

IRV: Lori Droste

Raw Rating Summation: Lori Droste

Condorcet: George Beier

Instant Runoff Normalized Ratings: Lori Droste

--

[Kevin Baas]

"So did a single vote, for just the one candidate running, get turned into an "xxx" ballot somewhere along the line?  So that slew of xxx ballots is not actually evidence that people don't get it? "

no.  after i fixed ,my bug (counting invalid as candidate 0), a single vote would be "x--"

prior to my fixing the bug, it would have shown up as "xyy", and a ballot where no choices were filled out would have been "xxx" (where now it's ("---"))

any "xxx"'s after my bug fix are the voter actually filling out 1st, 2nd, and 3rd choice the same.  which is invalid, but still countable.

[Clay Shentrup]

On Tuesday, July 5, 2016 at 5:22:53 AM UTC-7, Brian Olson wrote:

Okay, District 8 from the 2014 Berkeley City Council vote is interesting!

http://bolson.org/~bolson/2016/berkeley_cc_d8_2014.html

IRV: Lori Droste

Raw Rating Summation: Lori Droste

Condorcet: George Beier

Instant Runoff Normalized Ratings: Lori Droste

I could swear I looked into this and Droste was the Condorcet winner. In any case, it was convenient for me that she won, because she worked with me on the RRV initiative here in Berkeley. 

[Drew Spencer]

Droste was the Condorcet winner. She beat Beier in the final round, head-to-head. Brian's page shows that down at the bottom, but for some reason the numbers in his "virtual round robin" are different, apparently moving 14 votes from Droste to Beier.

In fact, there have been over 100 RCV elections in the Bay Area with full ballot data available, many of them hotly contested, and the Condorcet winner has won every time. That includes several races where the ultimate winner did not lead in the first round.

It's true that the RCV ballots used there are not the best examples of ballot design. Nonetheless, more than 80% have two or more valid rankings count in the contested mayoral races, and more than 70% used all three of their allowed rankings. Of the 18 offices elected by RCV in Oakland, 16 won with more votes than the winners in the prior non-RCV elections.

Also, ballot error rates don't seem to be all that influenced by the use of RCV or the ballot design, but mostly by the number of candidates running. The preliminary "Top Two" election for US Senate in California in 2012 had higher ballot error rates than RCV elections (looking at ballots from the Bay Area cities that have RCV elections). With the number of candidates in this year's Senate race, I'm sure that will be true this year as well.

Drew.

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Andrew Spencer

[Toby Pereira]

I think this is quite interesting - the claim that in over 100 elections the Condorcet winner has won every time. I wonder if Warren or Clay have some of their own statistics on the likelihood of IRV electing the Condorcet winner, and how often it would fail criteria like monotonicity in practice.

Obviously there are arguments against using any ranked-ballot method (versus e.g. score, approval) but does this make any difference to the argument of how good/bad IRV is for a ranked-ballot method?

[Warren D Smith]

if in an IRV election, every voter employs the dishonest-strategic
voting style A s t u v w B
where the capital letters are from the 2 major parties,
then
(1) it is mathematically impossible for a third-party to win
(indeed, even if only 75% of voters employ this style - and
in Australia about 85% do)
(2) a "condorcet winner" will always exist and will always win.

However, (1) is a severe distortion of democracy which
has in fact massively damaged Australian IRV "democracy",
while (2) is a severe distortion of reality caused by
pro-IRV propagandists.

Another property will be
(3) The IRV winner will always be the same as the plain-plurality
winner (if all voters employ this strategy)

but the IRV propagandists do not mention this one very often.

In reality, IRV and condorcet winners have differed some
noticeable fraction of the time (e.g Burlington's final IRV
mayor election) but usually have agreed,
and IRV and plurality winners have differed
a noticeable fraction of time (Burlington again)
but usually have agreed.

[Clay Shentrup]

On Saturday, July 9, 2016 at 11:16:15 AM UTC-7, Toby Pereira wrote:

I think this is quite interesting - the claim that in over 100 elections the Condorcet winner has won every time.

Assuming the rankings were honest, which we don't know.

I wonder if Warren or Clay have some of their own statistics on the likelihood of IRV electing the Condorcet winner, and how often it would fail criteria like monotonicity in practice.

http://scorevoting.net/IrvParadoxProbabilities.html

[Drew Spencer]

The scenario Warren outlines assumes the use of partisan elections in which there are two major parties. This does not apply to the local, nonpartisan elections in the Bay Area, and there's no reason to think it even approximates what's going on there (only the top races are even polled). It is therefore a non-sequitur.

If your model suggests that the Condorcet candidate should lose in a significant number of RCV elections, then the Bay Area contradicts that. When a model does not match reality, the best thing to do is to discard (or modify) the model. What I am seeing here instead is special pleading: it is being claimed - without any evidence - that voters in the Bay Area must be voting dishonestly. Or, to be more charitable, I am seeing doubt-mongering about honest voting, such as Clay's comment that "we don't know" whether they are voting honestly or not. You may as well say that movie box office numbers only track popularity of movies if people are actually buying tickets to see the movies they want to see, rather than strategically trying to influence box office results - we don't know that they aren't! 

The fact is we have no empirical reason to think they are voting dishonestly. The most plausible explanation for the Bay Area results is that voters are using their rankings effectively and electing candidates who have a lot of support.

Note that this cynical attitude toward voters in the Bay Area is the exact opposite of the reactions I see to student elections using approval voting. There, candidates are winning with very little support, and we really have no empirical reason to think that the winning candidates are the Condorcet candidates. The student body president at Dartmouth was elected with 39% of the vote earlier this year, and Clay's reaction was to laud the vice-presidential election, in which the candidate won with majority approval (she was the daughter of Senator Rob Portman of Ohio and ran in a race with fewer candidates). Candidates regularly win those elections with less than 40% approval. When Dartmouth used RCV, the average number of votes for the winner in the final round was 1,073, with every RCV winner except one winning with more than 1,000 votes. Under approval, the highest number of approvals won by any candidate was 966, and the average is 808.

When approval is that low, we have no empirical reason to think that the winners are the Condorcet candidates, and good reason to doubt it.

As for Australia, there is again no evidence that favorite betrayal is actually occurring. David's thread about Australia amply made the point that there is no reason to think that voters would engage in favorite betrayal in the multi-seat Senate races, and the first-choice rankings for third parties in Australia is about the same in the single-seat House races as in the PR Senate races. That point was again dodged by saying "we don't know" whether voters are ranking their honest favorite first in the Senate races. This is special pleading. The most plausible explanation for why major parties dominate the House is because the House is elected in winner-take-all elections, and the major parties have the most support in each district.

Theory and models are useful starting points, but they are no substitute for empirical political science. As far as I can tell, the empirical evidence suggests that (1) the "IRV" algorithm overwhelmingly elects the Condorcet candidate; (2) to the extent that it doesn't, it nonetheless probably outperforms approval voting on that metric; and (3) there is no empirical reason to think that dishonest voting is undermining the case for the first two points.

Drew.

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Andrew Spencer

[Warren D Smith]

On 7/11/16, Drew Spencer <drew.s...@gmail.com> wrote:
> The scenario Warren outlines assumes the use of partisan elections in which
> there are two major parties. This does not apply to the local, nonpartisan
> elections in the Bay Area, and there's no reason to think it even
> approximates what's going on there (only the top races are even polled). It
> is therefore a non-sequitur.

--I was speaking about Australia, where it happens.

> If your model suggests that the Condorcet candidate should lose in a
> significant number of RCV elections, then the Bay Area contradicts that.

--maybe. How many cases were there in which there was a serious N-way
contest with N>=3? Obviously 2-candidate or 1-candidate contests
are of no import for deciding among voting systems. You forgot to even
mention that whole question, which as matters currently stand
makes it a little hard to take you seriously.

> When a model does not match reality, the best thing to do is to discard (or
> modify) the model. What I am seeing here instead is special pleading: it is
> being claimed - without any evidence - that voters in the Bay Area must be
> voting dishonestly.

--I did not make such a claim. Please find the exact words where you
say I made that claim.

--In the Dartmouth 2011 student president election, conducted with approval
voting, Max Yoeli won with 691 approvals. There were 1876 total approvals and
119 total candidates -- many of them "write ins" -- for 15.76
approvals per candidate average. I have a major problem seeing how
instant runoff - or for that matter any rank-order-ballot system at
all - could ask voters to rank-order 119 candidates. Frankly I doubt
even a single voter would have done so or even come close. Further,
if they had then many of their pairwise opinions expressed on their
ballots -- in fact the vast majority of them -- would have been
ignored by the IRV process.

One of the advantages of score voting is it allows voters to express
ignorance in an unbiased way. IRV does not allow that -- if you leave
somebody unranked that is
equivalent to ranking them co-equal last, which is the most-biased
possible way to misinterpret what voter said.
Obviously this Dartmouth race was about 98-99% ignorance-dominated.
Since IRV maximally-badly handles voters who want to express ignorance,
it was extremely dubious for use here.

--In the 2006 Dartmouth student president election, conducted with
instant runoff
voting, Timothy Andreadis won with 1269 in final (11th) round, out of
2435 total ballots. There were 176 candidates, many of them
(including the winner) were "write ins." It looks like about 40% of
voters "bullet voted" (i.e.ranked only 1 among
the 176), and that ballots ranking more than 3 candidates were rare.

Andreadis was a majority-winner (and hence Condorcet). Yoeli was not
a majority-winner
and may or may not have been Condorcet.

> As for Australia, there is again no evidence that favorite betrayal is
> actually occurring.

--in Australia, I repeat, about 85% of voters vote in A s t u v w B
style. This makes it mathematically impossible for third party to
win IRV seat. It also is plainly dishonest strategic behavior,
unless you really believe that the best two parties in Australia are
simultaneously the worst two parties in Australia. This is absolutely
massive strategic voting with IRV. It is hard to imagine how any
greater evidence could ever be produced.

Furthermore, this massive strategic voting behavior has caused massive
consequences, namely the inability
of third parties to win an IRV seat, for example 600 House races in a
row with zero third party winners. Again, it is hard to imagine how
the evidence could be any more massive.

So clearly IRV has been a failure in Australia. To confirm that,
we conduct nationwide polls of Australians. Three such polls all found
by large statistically-clear margins that Australia if given the
binary choice would drop IRV in favor of plain plurality voting.

So IRV has been a failure in Australia, even compared to plain
plurality voting, in the view
of Australians themselves. Australia has been by far the most
IRV-using country on the planet. Again, it is hard to imagine how the
evidence could possibly
be much more clear.

> David's thread about Australia amply made the point
> that there is no reason to think that voters would engage in favorite
> betrayal in the multi-seat Senate races, and the first-choice rankings for
> third parties in Australia is about the same in the single-seat House races
> as in the PR Senate races. That point was again dodged by saying "we don't
> know" whether voters are ranking their honest favorite first in the Senate
> races. This is special pleading. The most plausible explanation for why
> major parties dominate the House is because the House is elected in
> winner-take-all elections, and the major parties have the most support in
> each district.

--In fact, 85% of Australians again employ the same sort of A s t u v w B
voting behavior for the Senate as they do for the house. This makes
it completely undeniably obvious there is massive strategy going on
for the Senate also. However, the Senate uses a different voting
system which allows third parties to win seats. Probably not as many as they
should, but consistently more than zero.

> Theory and models are useful starting points, but they are no substitute
> for empirical political science.

--So, perhaps you should do some. See above. The Australian data
dwarfs anything from the Bay area, by the way.

> As far as I can tell, the empirical
> evidence suggests that (1) the "IRV" algorithm overwhelmingly elects the
> Condorcet candidate; (2) to the extent that it doesn't, it nonetheless
> probably outperforms approval voting on that metric; and (3) there is no
> empirical reason to think that dishonest voting is undermining the case for
> the first two points.
>
> Drew.

--the evidence from Australia I just mentioned means that the "Condorcet
winner" would always exist and always win with IRV (if 100% of voters
behaved this way)
but that would in no way whatever demonstrate the honest-votes Condorcet
winner won, because it is clear the votes are massively dishonest. Also, note
CWs do not exist 100% of the time, even though with that Australian
voter behavior (if 100%) they would "exist" 100% of the time. This
contradiction again demonstrates that
something is wrong, i.e. that your reasoning is simply not permissible.

If you know reasoning is impermissible, then I suggest not employing
that reasoning.
Or at the very least, qualify it with major asterisks.

Also, long as we are at it, it has been claimed (based on a
combination of actual votes
plus some evidence from polls) that every US president elected
(if using nationwide plurality popular vote) during the polling era,
was a Condorcet winner.
So I ask Drew: does he conclude from this that plurality is an
excellent voting system
that can be counted on to produce Condorcet winners, based on
"empirical evidence"?
And does he assert that all those plurality votes were honest?
Or, might some other conclusion be better?

[Warren D Smith]

And the original topic of this thread was simply the fact that a
rich CEO guy, Ron Conway, in a highly public way -- as well as many
other voters --
did not understand how the instant-runoff voting system they were using, worked.

IRV is a comparatively complex voting system which
evidently is capable of causing confusion. That is why it under equal conditions
has higher voter error rates and worse self-assessed
voter-understanding than any other major competitor. These are, as
Drew calls them, "empirical facts" -- not the result of "theoretical
models."

In the particular case of Berkeley, it looked to me like there were
complete idiots in charge of designing their ballot, which made it a
lot harder to understand than if they'd had a well-designed IRV
ballot... substantially worsening this inherent problem.

[Clay Shentrup]

this cynical attitude toward voters in the Bay Area is the exact opposite of the reactions I see to student elections using approval voting. There, candidates are winning with very little support

Saying they have "very little support" is a serious mathematical fallacy that I've already explained here.

http://clayshentrup.blogspot.com/2012/10/rob-richie-misleads-on-approval-voting.html

Are you arguing there was a candidate with more support that should have won but didn't? If not, then what is your point?

The student body president at Dartmouth was elected with 39% of the vote earlier this year,

The fact that you think something is wrong with that demonstrates lack of basic understanding of social choice theory. Again, my blog post explains your fallacy in simple clear terms.

When Dartmouth used RCV, the average number of votes for the winner in the final round was 1,073, with every RCV winner except one winning with more than 1,000 votes. Under approval, the highest number of approvals won by any candidate was 966, and the average is 808.

Wow. You just can't help yourself from making the same mathematical fallacy over and over again.

On Monday, July 11, 2016 at 7:28:46 AM UTC-7, Drew Spencer wrote:

I am seeing doubt-mongering about honest voting, such as Clay's comment that "we don't know" whether they are voting honestly or not.

You may as well say that movie box office numbers only track popularity of movies if people are actually buying tickets to see the movies they want to see, rather than strategically trying to influence box office results - we don't know that they aren't!

That's not a reasonable analogy, since we know people are motivated to see movies they enjoy, and not very motivated to skew box office results. Whereas in elections, people are motivated to get the best election outcome possible, as amply demonstrated by e.g. Nader supporters voting for Gore.

The fact is we have no empirical reason to think they are voting dishonestly.

I've lived in the Bay Area since 2004 (safe for a brief stint in the Pacific Northwest). Everyone I talk to about IRV (e.g. the ex-Google folks I work with) basically assumes it works like Borda. If that's their intuitive belief, then it seems perfectly reasonable to expect them to naively exaggerate the presumed frontrunners.

 

The most plausible explanation for the Bay Area results is that voters are using their rankings effectively and electing candidates who have a lot of support.

I'm not aware of any data to support this claim. A usability study conducted by Dana Chisnell, for instance, found exactly what I've experienced—that a significant number of voters think they're using Borda or something similar. They intuitively believe that exaggerating helps. I don't know with any certainty how significant a role this plays. I actually do think it's plausible that Bay Area politics is uniform in a way that skews the results, and gives you fewer Burlingtons. But I don't have good data on this and I don't think you do either.

and we really have no empirical reason to think that the winning candidates are the Condorcet candidates.

It's statistically plausible given reasonable models of voter strategy.

http://scorevoting.net/AppCW.html

Although I'm not arguing that the Condorcet winner is the best person to elect. You want the social utility maximizer, and the best Bayesian Regret figures we have say Approval Voting is massively better than IRV. If you disagree, you should do some BR calculations using preference distributions and other parameters you think are more realistic.

When approval is that low, we have no empirical reason to think that the winners are the Condorcet candidates, and good reason to doubt it.

What evidence do you have about the correlation between net approval and certainty of having elected the right winner?

it nonetheless probably outperforms approval voting on that metric

There's no evidence that IRV has lower Bayesian Regret.

[Clay Shentrup]

On Monday, July 11, 2016 at 7:28:46 AM UTC-7, Drew Spencer wrote:

When approval is that low, we have no empirical reason to think that the winners are the Condorcet candidates, and good reason to doubt it.

Another point here is that you're focusing on absolute instead of relative. Imagine two elections:

Election 1: Winner has 57% approval, runner-up has 51% approval

Election 2: Winner has 30% approval, runner-up has 12% approval

Which result would give us greater confidence that the right candidate won?

[Kevin Baas]

election 2, because 30/(30+12) > 57/(57+51);

[Dylan Hirsch-Shell]

Election 1, because 57 > 30

[Clay Shentrup]

On Wednesday, July 13, 2016 at 8:47:44 AM UTC-7, Dylan Hirsch-Shell wrote:

Election 1, because 57 > 30

2 was the right answer. I'm pretty sure.