Dartmouth professors Michael Herron, Jonathan Chipman and Jeffrey Lewis have put together a terrific study of the recount situation in Minnesota. They suggest that -- while many African-American voters in the Minneapolis area may have skipped the senate race intentionally -- the majority of unintentional undervotes that will be counted during the recount process are also liable to favor Franken.We show using a combination of precinct voting returns from the 2006 and 2008 General Elections that patterns in Senate race residual votes are consistent with, one, the presence of a large number of Democratic-leaning voters, in particular African-American voters, who appear to have deliberately skipped voting in the Coleman-Franken Senate contest and, two, the presence of a smaller number of Democratic-leaning voters who almost certainly intended to cast a vote in the Senate race but for some reason did not do so. Ultimately, the anticipated recount may clarify the relative proportions of intentional versus unintentional residual votes. At present, though, the data available suggest that the recount will uncover many of the former and that, of the latter, a majority will likely prove to be supportive of Franken.
The Darmouth guys don't offer a specific prediction about whether the number of recounted votes is likely to tip the balance of the race toward Franken, but their entire study (PDF) is worth a read.
(h/t Andrew Gelman)
11.14.2008
Dartmouth Study: Minnesota Undervotes Should Favor Franken
by Nate Silver @ 4:25 PM
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78 comments
zeroth! (undervote...)
Never mind that, which ballot design gets the most undervotes?
Senator Al Franken. What a fucking country.
That being said, if Coleman wins, the 360,000+ that voted for Obama but not Franken have some splaining to do.
I think someone should make an undergarment with a box on the front and X mark on the back - and call them "UNDERVOTES"
Nate,
I know this is grammar-Nazi stuff, but shouldn't it be:
"the majority of unintentional undervotes that will be counted during the recount process are also likely to favor Franken."
I've seen this quite a few times here before and I shudder a bit each time.
(This is a minor aggravation; thanks for everything all season!)
Paul, You can find which ballot design they used in Minnesota at: http://www.sos.state.mn.us/home/index.asp?page=227
It won't surprise. There should be prizes for the dopiest ballot design, least accurate optical scanners, etc.
Nate,
Where would you place the probability of 60 seats at this point? sounds like AK likely, MN even money or better, and GA a crapshoot?
Andy
Lets hope Franken wins just to see the outrage among the republicans. they will be screaming stolen election for years.
In my head, I figure each race to be:
90% in Alaska, 60% in Minnesota, 30% in Georgia...so 16% at all 3.
What's this I heard on Rush's program about finding a trunk load of ballots that some "democrat" was hiding...
Leitmotiv said...
What's this I heard on Rush's program about finding a trunk load of ballots that some "democrat" was hiding...
It was actually 32 ballots in his back seat which he forgot about. And I believe the guy's position is non-partisan... Rush was just exaggerating but what else is new?
@leitmotiv
Rush's smoke rings!
didn't happen...even repug says didn't happen...according to Olbermann
goAL!
In my head, I figure each race to be:
90% in Alaska, 60% in Minnesota, 30% in Georgia...so 16% at all 3.
Intrade has it at approximately 93% in Alaska, 49% in Minnesota, and 16% in Georgia.
Leitmotiv said...
What's this I heard on Rush's program about finding a trunk load of ballots that some "democrat" was hiding...
First, what per cent of the information that Lush Rimbaugh spouts is actually truth? Hint - negative numbers don't count.
Second, read this article about the fiction of the 'ballots riding around in the trunk of someone's car':
http://minnesotaindependent.com/17385/recount-hannity-pawlenty-car-ballot-lie
Terrific! Go Al Franken! He's not Paul Wellstone but Norm Coleman was a sorry, sorry replacement for the man.
A raging dangerous idiot threatens Barack Obama, his daughters, their classmates and his wife Michelle:
www.cuttingconfessionsfilm.blogspot.com
www.myspace.com/370392338
Hey all: would love for everyone who believes in equal rights to join me in signing this pledge against Proposition 8 in California.
http://www.couragecampaign.org/RepealProp8
They have over 150,000 "signatures" thus far. Will this do anything? Likely not. But it can't hurt to let the powers that be know how we feel about the U.S. Constitution being stomped on a 52%-48% vote.
Thanks for your time.
-- Joe
It was actually 32 ballots in his back seat which he forgot about. And I believe the guy's position is non-partisan... Rush was just exaggerating but what else is new?
Even less suspicious than that. Minnesota newspaper said it was 32 absentee ballots. They are all sent to one location in county to verify they're genuine and then driven to correct precinct to actually be counted. Apparently 32 ballots did not get delivered to correct precinct before polls closed so they were brought back. Both campaigns were told and ballots were always under control of election officials. It's just Republicans trying to work the officials.
My question:
Will ALL of the 3 Million plus votes be re-counted?
If so, what is the error rate on the optical scanner machines?
I'm sure this has been answered before but I'd like to know.
Thanks!
"That being said, if Coleman wins, the 360,000+ that voted for Obama but not Franken have some splaining to do."
I'm one of those 360,000+. I campaigned for Obama, too...I just wasn't convinced Franken is ready for the job and think Coleman has done a fine enough job that my conscience is clear should he win again (thanks to my vote for Barkley). I--and obviously many others--aren't going to vote for someone just because of the party they represent (particularly in a race as ugly as this one was). No splainin necessary, as far as I see.
================
RE:
I know this is grammar-Nazi stuff, but shouldn't it be:
"the majority of unintentional undervotes that will be counted during the recount process are also likely to favor Franken."
================
The original had said "...should favor Franken."
The answer is: only if you seriously believe Nate is issuing a moral imperative to inanimate objects (ballots). Or if you seriously believe a reader could see it that way.
I don't think a single one would.
I don't see much of a chance for Franken winning here but I guess it is possible.
Come see my new probably awful blog:
http://youngerpolitics.blogspot.com/
That being said, if Coleman wins, the 360,000+ that voted for Obama but not Franken have some splaining to do.
As a Minnesota voter, I see Franken as part of the same perversion of American politics that people like Rush Limbaugh and Michael Moore excel at. Much like I would scoff at voting for either of those two, I will not vote for someone as bad just because he happens to be a Democrat.
I cast my vote for Barkley with pride, and would do so again in a heartbeat even if Franken ends up losing by exactly one vote.
I would rather the state be subject to 6 more years of Coleman than sell my dignity in voting someone similar to Rush Limbaugh or Michal Moore into office simply because they were a member of a party that I share some viewpoints with.
I voted my beliefs and what I think is best for America and Minnesota; can people who voted for Franken say the same? Or can they only say they voted AGAINST Coleman?
There's a reason 15% of Minnesotans (and 20% of Minnesotan DLFers) voted anti-both parties. We don't have to explain to you or anyone else, and I refuse to have someone else question my vote simply because it doesn't conform to their view of what's 'right'.
Norm Coleman is a foul species of reactionary scumbag. It's amazing he passes for "moderate" in the Republican party, which only goes to show that the Party has drifted to the right of Attila the Hun.
Franken will make a fine Senator. He's quite intelligent and will be a solid Progressive. The attacks on him were scurrilous in the extreme -- who cares if he said some "politically incorrect" things as a comedian years ago.
Anyone who listened to him on Air America for years will tell you he's definitely the more intelligent one.
Ironic that Coleman's dragging the race into the mud won't work out for him and Republicans will scream "vote fraud!" for years -- by which they always mean "too many terrible NEGROS voted! IT's an outrage! Let's pretend that it's illegal!"
Oh ok, yeah I know Rushie is slanted, but I wanted to hear it from other lips. Thanks everyone.
RE, RE:
I know this is grammar-Nazi stuff, but shouldn't it be:
"the majority of unintentional undervotes that will be counted during the recount process are also likely to favor Franken."
The grammar mistake here (in the corrected version) really is that the subject and verb don't agree: "majority" (singular) and "are (plural)
It should read "the majority of unintentional unvotes...is likely..."
@ b. and alpha.dk, just curious and of course you can tell me none of my business, but why vote for Barley? I'm assuming you're pretty astute when it comes to handicapping the races and knew the polls showed Barley with no chance but Franken and Coleman essentially tied. If you cannot stand Franken because of his political commentaries and did not want him to win, then why not vote for Coleman?
<100th!!!! Yeah!
We're calling the Stevens/Begich for Begich.
we're thinking this one is a tossup with Coleman holding a slight edge because he has won the actual vote, but Franken (a very very smart guy with progressive values who will make CSPAN closer to fun) has an edge in the "pregnant and dimpled chad" category of votes.
And we're thinking that Georgia comes down to GOTV, with an edge to Sexy Chambliss because he actually won the election, just not by enough and they had a right wing stealing third party guy messing things up there, but OTOH, you have Obama's GOTV team moving into Georgia and working to get people out for the special election.
The math on Intrade suggests about an 7.5% chance of a 60-seat majority. I'd say it's probably closer to 20% (figure Begich is done, 50-50 on Franken and 4/10 for Jimbo Martin.
All this is, of course, good news for John McCain.
Chuck Schumer says the "hard-right" are trying to imtimidate Minnesota election officials.
Also, the scum just admitted they, and Katherine Harris, stole the 2000 election.
http://crooksandliars.com/john-amato/did-republicans-just-admit-katherine-ha
What's the latest count in Alaska for Begich?
Just wanted to thanks Alpha.dk and b. for explaining their position. I'm sure there are many like you, and it makes it much clearer why Franken ran behind Obama in MN.
This will sound counterintuitive, but the key number needed at this point to estimate the likely recount swing is the number of C voters who deliberately didn't vote for POTUS. That's because there are relatively few deliberate POTUS undervotes, so they are a much better measure of accidental undervotes than we can get from the Sen race, and we know the distribution of POTUS undercounts. It's almost exactly balanced between F and C, based on the precinct results. However, to estimate the accidental POTUS undervote, we need to make a small correction for the deliberate undervote. Almost certainly there were more C voters who skipped Mc/Pa than F voters who skipped Obama. Thus there were more unintentional POTUS undervotes from F voters than from C voters. That difference should translate directly (with statistical error bars of about 70)into more F votes found in the recount. How big? Anybody's guess, but I wouldn't be shocked if 500 people who liked the 'moderate' Coleman skipped Mc/Pa.
That would mean a win for F./mbw
Aw, come on. Norm Coleman would then be known as the only person in the history of the world to lose to both Jesse "The Body" Ventura and Al "People like me" Franken. At anything. Sure, people might lose at arm wrestling to Ventura or at chess to Franken, but can you imagine any competition where somebody could lose to both of them?
@Ryan...
From dictionary.com. Not my favorite linguistic source but OK.
"Usage Note: When majority refers to a particular number of votes, it takes a singular verb: Her majority was five votes. His majority has been growing by 5 percent every year. When it refers to a group of persons or things that are in the majority, it may take either a singular or plural verb, depending on whether the group is considered as a whole or as a set of people considered individually. So we say The majority elects (not elect) the candidate it wants (not they want), since the election is accomplished by the group as a whole; but The majority of the voters live (not lives) in the city, since living in the city is something that each voter does."
I think it's debatable but I would lean toward plural.
BTW, is Franken winning Real Joe's surprise?
Not so fast my friend.
From the Star Tribune:
http://www.startribune.com/politics/national/senate/34409514.html?page=2&c=y
Meanwhile, Franken scored a gain of one net vote in 196 randomly selected precincts where a hand count of votes was conducted in recent days to test the accuracy of voting machines, according to a Star Tribune calculation. The precinct-by-precinct results, which reduce Coleman's lead from 206 to 205 votes, were posted on the secretary of state's website Thursday night separately from the current unofficial tally. They will be included in the certified totals to be approved on Tuesday by the state Canvassing Board.
If the same rate of change were experienced statewide, the DFLer would gain 21 votes in all. The largest changes came in precincts in St. Louis and Ramsey counties. Most Hennepin County results are not yet in.
Minneapolis election director speaks: 'Ballots in my car' story false.
http://www.minnpost.com/davidbrauer/2008/11/12/4565/minneapolis_election_director_speaks_ballots_in_my_car_story_false
What's this I hear about 'Nate the Statistician' and his new book deal? As long as there are no plans for a country music record, more power to you!
http://skybarn.tumblr.com/
I wish you'd just say he doesn't have a prayer... next to president, this is the race I most wanted to see won by the Democrats. Franken has the chops and the attitude to be an amazing progressive senator. The fact that he didn't pull ahead after Hennepin came back with its final tally has me expecting the worst.
@ Another Mike...
I definitely knew, as you noted, that my vote for Barkley was essentially a null vote. But I honestly found him the most compelling candidate in terms of platform in comparison to the other two, and though I don't think Coleman is a BAD senator, I still wouldn't vote for him. My opinions on social policies are just a bit too different, but with an Obama administration/SCOTUS appointees, I'm not as concerned about Coleman continuing as senator.
And for another thing, he's got the worst veneers I've ever seen in my life. All I can think of is Mr. Ed whenever I see him.
Does anyone know when the OFFICIAL results come in for this election?
It might just be my imagination, but didn't 2004's official results come in A LOT faster than this?
Appreciate the response.
"b." wrote "And for another thing, he's got the worst veneers I've ever seen in my life. All I can think of is Mr. Ed whenever I see him."
That was a classic! Great image. It made me laugh out loud. Thanks!
Great appearance on Hardball, Nate.
Nate,
I know this is grammar-Nazi stuff, but shouldn't it be:
"the majority of unintentional undervotes that will be counted during the recount process are also likely to favor Franken."
I've seen this quite a few times here before and I shudder a bit each time.
(This is a minor aggravation; thanks for everything all season!)
I can't see any problem with that paragraph. Seems okay to me.
Senator Al Franken would be awesome. I'd like to see him take on Traitor Joe Lieberman eh'.
President Obama: Don't Do These!
When are today's Alaska votes going to be announced?
Does anyone know?
In the original figures from Minnesota, there was a difference between the number of votes cast in Hennepin County between the presidential and senate races of 4,985 votes. So just 4.2% of those would have to be unintentional undervotes for Franken to win, and that's just in that one county.
Official results in Minnesota come out on Tuesday. Once the official results are posted the recount can start.
If anyone is interested in seeing a good sample of what might happen during the recount, the Minnesota Secretary of State's Office has posted the results of the required "post-election review."
The post-election review is a check performed on the accuracy of the machines in each county. In each county, a hand count of the ballots are done in a random sample of precincts (the number of precincts depends on the size of the county). The result of the hand count is compared to the machine count to determine if the machines functioned properly.
As of earlier today, 194 of the 207 sample precincts had submitted results to the Secretary of State (6 of the missing 13 are from Minneapolis). From the 194 precincts, you had a total of 69 votes change. For Coleman, the changes included 15 votes gained and 10 votes lost (for a net of 5). For Franken, the changes included 30 votes gained and 14 votes lost (for a net of 16).
As there are 4130 precincts in Minnesota, if you extrapolate from these results (and there are problems with assuming that these precinct are sufficiently representative, so figure a good margin of error), it would translate into a statewide swing of 234 votes to Franken.
Begich's lead just expanded to 1,061 votes.
> but with an Obama administration/SCOTUS appointees, I'm not as concerned about Coleman continuing as senator.
b, you do realize that any SCOTUS appointments need to be approved by the Senate, right? You know, that chamber where the quaint filibuster rules make it possible for a Republican minority to block the majority. If Begich is in but Martin loses then that means the Obama administration needs three out of the Lieberman, Snowe, Collins, Specter cluster to get a nominee through.
The irony in all of this is that SCOTUS appointments are probably the one area where your choice is most likely to screw the Obama administration.
438 of 438 precincts reporting | Last update: 11/14/2008 3:15 pm ADT
Begich, Mark DEM 137,527 47%
Bird, Bob AI 11,933 4%
Gianoutsos, Ted NA 1,218 0%
Haase, Fredrick D. LIB 2,215 0%
Stevens, Ted REP 136,466
Nate-
Congrats on your two-book deal with Penguin. Looking forward to reading them.
Nate Silver Signs With Penguin In Two Book Deal Worth About $700,000
maybe Nate will have time to check his answers for the book, but his TV appearances are quite innaccurate for the most part. I am constantly seeing factual errors in his answers.
Are you only covering the people who think Franken will win this or is it really this clear? I haven't followed many elections due to my age, but I have trouble seeing somebody leading with a minimal amount of votes to be counted as an apparent underdog.
To all self-proclaimed grammar Nazis (and their detractors) here: as a university linguistics professor, I feel obliged to come to Nate's defense -- there is absolutely nothing wrong with his original formulation. CA Hawkeye's quote about collective plurals is accurate enough, and one of the main features of "likely" (and other so-called "raising" predicates) is that it places no restrictions whatsoever on its subject. Ergo "There is likely to have been much ado about nothing", "It is likely to rain", "The shit is likely to hit the fan," etc. Might I add that there are far more important (and legitimate) things to protest and worry about as 2008 draws to a close. And don't believe everything they told you in school.
You guys are idiots...
There are no such thing as undervotes.....
Under votes are no votes at all..
If you can't vote properly, you don't deserve to vote at all.....
Btw only property holders should be able to vote for property taxes...
The correct answer is still "Ballot A".
fibly - the opposite of truthy
@ Jim...
I do realize it, but appreciate the lecture and tinge of condescension nonetheless. I also realize that Bush was able to get Alito and Roberts through the Senate quite easily with at most the same number of Senators as the Democrats will have, and that the odds of Republicans filibustering every candidate for years so that no one is ever appointed is slim to none...so therefore you'll excuse me if I'm not all that concerned with the Senate's role in SCOTUS appointments as it currently stands.
In the future, of course it's something to consider. But for me, right now, I'm happy with how I voted--and that's what matters to me.
Aaaah, this is so cool. Herron is my stats prof. Dartmouth Students for Franken...
Jack-Be-Nimble-
Reasonable, because, renters don't pay property tax... Oh, wait. Yes we do. Maybe not directly, but my rent always seems to go up when property taxes do.
To polyticks et al. --
I believe Chris's quibble with the grammar was over the use of "liable to" instead of "likely to." The literal meaning of "liable" is "legally obligated." It is often used to mean "likely to," but generally in a negative sense. Thus I'd agree with Chris that "likely to" is better in this case.
tmess2,
It looks like all the precincts have reported in the audit.
By my count, I have Franken only picking up a net 2 votes. Franken gained 32 and lost 16. Coleman gained 28 and lost 14.
Not sure why those figures are so far off from yours which show a much smaller number of votes gained for Coleman.
These data do not bode well for Franken. Of the votes that were reclassified, he picked up 51.1% of them. But he is going to need about 55% of them if the number of reclassified votes statewide continue at the same pace.
One followup on the audit. Barkley gained at a higher rate than his raw vote totals. He picked up 17 votes while losing 5, a net of 12, compared to 16 for Franken and 14 for Coleman.
A lot of this was driven by one precint - St. Louis county #35. Barkley picked up 8, Coleman 11 and Franken 9 even though Franken easily won the precinct in the original vote (471-299-128). This precinct had a reclassified rate about 30 times greater than the average, accounting for 25% of the total reclassified vote.
In one other precinct, St Louis #500, Franken picked up 8, Coleman 3 and Barkley 0. Franken won the original vote 214-61-34. This too was a reclassified rate of about 30 times more than the average.
All other precincts had a vote or two here and there which added up to Coleman net 0 (14 added, 14 lost), Franken net -1 (15 added, 16 lost), Barkely net +4 (9 added, 5 lost).
Good job on Hardball, O Supreme Geek!
Jack-be-nimble,
You're wrong on both counts. By Minnesota law, any ballot marked in such a way that the "clear intention of the voter" is discernible is a valid ballot and must be counted for that candidate in the hand recount, even if it's marked in such a way that the optical scanner doesn't pick it up. So as a matter of law, there certainly IS such a thing as an "undervote." Your opinion to the contrary is just that, opinion--not law. That and $3 will get you a coffee at Starbucks.
As for property taxes: renters certainly do pay property taxes, and usually at a higher rate than homeowners. In most states rental property is classified as "commercial" and is taxed at a higher rate than "residential" single-family homes. Landlords pass property taxes (and all other expenses) through to tenants in the form of rent.
Sorry, but I'm not willing to give those who didn't vote for Franken but did vote for Obama a free pass. You folks must seriously enjoy the thought of shooting yourself in the foot to done something as BONEHEADED as that, especially if you knew anything about how the filibuster works before the election (if you didn't know anything about that, then you're an ill-informed bonehead).
Saying Franken is in the same boat as Rush and Moore is, frankly, one of the most laughable things I've heard this week. Basically, I think what it comes down to is you folks bought into the whole "he's from Hollywood, therefore he is bad" argument that was getting tossed around so much.
I'm sorry; I'm just really disgusted at this point.
That's your opinion, you're entitled to it. I'm not looking for a free pass, from you or anyone else--and think one of the lovely things about this country is that who YOU think I should vote for doesn't matter.
I do know how filibusters work, actually. I don't think Franken is a Hollywood type, actually. I studied this race closely, the candidates and their policies closely, and appear to just have a different opinion than you on how ready and capable Franken is. I don't think that makes me any less intelligent or less able to contribute to a meaningful discussion.
I do think it's too bad you are disgusted by people making independent, informed choices about who is best positioned to represent their state.
especially if you knew anything about how the filibuster works before the election (if you didn't know anything about that, then you're an ill-informed bonehead).
Look up Coleman's history on R filibusters and get back to me.
Oh, you were just repeating false dogmatic propaganda? My mistake, carry on.
And no, I didn't 'buy into' the whole 'he's from hollywood' argument. I was opposed to his running from the minute he announced his candidacy. I caucused against him in the primary; that obviously didn't work. I don't see why it 'disgusts' you that people are able to evaluate evidence and use rational thought to come to different conclusions than you; maybe, for example, I see a movement towards hate-based, divisive politics in the American political institution that, long term, will be much more dangerous to America than 6 more years of Coleman, and so I actively tried to stop it. Hence, voting for both Coleman and Franken was out of the question.
As for the rest, we'll have to agree to disagree. I sleep soundly at night, though; I hope you can do the same. 'Only' having a 58-seat majority is, after all, something to be ecstatic about, especially with Republicans like the two from Maine (and others, INCLUDING Coleman when it comes to filibusters) who will be likely to break party lines.
just lookin, I rechecked my numbers and looks like I dropped a digit on that large St. Louis County precinct (added a 1 to Coleman rather than a 10).
My final numbers come to Coleman (+27) (-14) and Franken (+32) (-16).
I would note that under the review rules, each county reviews at least 2 precincts (approximately 10% of the precincts in the small counties) and the largest counties review 3% of the precincts so there are a lot of small precincts in the review. The larger variations in the Duluth area can be atrributed in part to the larger size of the precints. When you are talking an error rate of less than 1% of the vote in all precincts, tiny differences appear larger.
In addition, statistics from multiple elections show a higher misread rate in lean Democratic precincts. It should be noted that misread does not mean that the ballot is marked incorrectly under state law just that it is not marked the way that the machine manufacturer desires.
meant 1 rather than 11.
Chris said:
I know this is grammar-Nazi stuff...
(This is a minor aggravation; thanks for everything all season!)
The irony, of course, is that Chris (likely;) felt irritation, not aggravation.
In the audited precincts, Coleman beat Franken 51.4% to 48.6% (disregarding other votes). If you weight teach precinct by the total number of reclassified votes, Franken bests Coleman 51.7% to 48.3% (which mirrors the proportion of reclassified vote that went for Franken), a difference of about 3%-points towards Franken.
Given a 50-50 split in all precincts, if Franken wins 53% of the reclassified votes in the full statewide recount, he is going to fall short by about 80 votes.
Kos is reporting that Franken picked up a net of 2 in the audit.
Out of 90 reclassified votes impacting Franken or Coleman, Franken won 46 of them (counting a lost Coleman vote as a Franken win), or 51.1%. As noted above, the audited precincts voted for Coleman 51.4%-48.6%. Franken would thus have a statewide win rate of 52.5% if these results repeat across the state.
The audit also suggests 2025 reclassified votes statewide. If Franken wins only 52.5% of them, he will pick up only 101 votes. The binomial distribution argues there is only about a 1% chance of him winning in this case.
On the other hand, maybe his true, underlying win rate is better than the sample seen in the audit. For example using the binomial distribution, the probability that Franken would have won 46 votes if his true audit win rate were 53.6% is 7.5%. That audit win rate would project to a statewide win rate of 55% and a 50-50 chance of him winning.
In comparison, the probability that Franken would have won 46 votes if his true audit win rate were 51.1% is 8.4%, not that much higher. Of course, there would also be a 7.5% chance of seeing 46/90 votes if Franken's audit win rate were 48.6%.
Using the methodology in the above examples, I computed the probability distribution of the true audit win rate, given you observed 46/90. I then computed the weighted chance that Franken wins as a function of the true audit win rate probability distribution. The result: franken has about a 30% chance of winning.
Jeff,
An excellent point. Though I don't think I'm completely incorrect here, as I have noticed this issue before and it is a reminder each time, so it is an aggravation of sorts. On the whole though, I'd probably cede the point to you.
Ryan,
Great catch.
Joe,
I'm not sure I understand what you're going for. I was simply trying to make a point about liable vs. likely. And let me say that all of us make grammatical and usage errors (like calling "liable" instead of "likely" a grammatical error) this is one I've seen quite a few times here.
Thanks to all those with interests in math (or at least politics) and language.
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