Yep. Following roadsigns is far more difficult. There’s much more information to process simultaneously than simply following the pointers on a static piece of paper.
Unclebeer
Befoer I waste my time, is there any particular statistical analysis of the Buchanan vote which you would consider effectivelty compelling that the ballot produced a bias? I know of more than one, varying in degrees of liklihood fro “one in a trillion” to a 62 Sigma deviation.
Of course, if your position is simply “it could have been a highly uinusual concentration of Buchanan suporters and no amount of statistical irregulariy can prove that it wasn’t”, well, all I will say is:
look at that bias.
Now, I disagree that any actions should be taken to correct that particular bias in this election, but that does not mean I bury my head in the sand and pretend that no bias existed.
I don’t believe I said that no bias exists. I merely said that RTF hasn’t provided anything I’d call reliable evidence of it yet. His evidence, much like my refutation of it, is a subjective opinion. Nor do I wish you to waste too much time on this. I’m perfectly willing to concede it’s possible for you, or RTF, to statistically show some kind of introduced bias. Since I’m merely an engineer and not a statistician, it’s unlikely I’d be capable of properly refuting a Sigma 62 deviation (especially since I’ve no idea what Sigma 62 is, or means). However, I do not believe you can find statistical evidence of intentional bias.
Spiritus, let’s not exaggerate, okay? 62 Sigmas? One in a Trillion?
I think it’s clear that voters screwed up in PBC. But I would put the probability of a real ‘spike’ in voters like that at more like 4 or 5 sigmas. Don’t you think it’s possible that, across America, there might be one or two districts in every 10,000 or so that might have a tight concentration of voters?
I am not exagerating. Personally, I think the 62 sigma analysis is definitely extreme. I also think that the chances that this represents a “population spike” so unlikely to be absurd. Is “one in a trillion” a high enough standard for you? If so, I will try to track down the analysis. (I have only seen a report of the result.)
My question was prompted because I have seen no, I mean zero, analysis that supports the idea that the PBC result accurately reflected the intentions of 3407 Buchanan supporters. Yet I repeatedly see supporters of the Bush campaign saying, “it could have happened . . .”
While this is true in the most strict sense (even for a 62 sigma result) it seems intellectually dishonest to me. What is wrong with simply saying, “yes, the ballots introduced a bias that resulted in mistaken votes going to Buchanan. It is unfortunate, and we hope the election officials in PBC take steps to ensure it neer happens again. Unfortunately, we have no recourse to override teh clear and valid ballot based upon our statistical realization that some, even most, of them were probably cast in error.”
- You missed the point entirely. Wanna try again?
The ‘evidence of our eyes’ to which I referred was not that most people wouldn’t get confused - it was that essentially no Bush voters would even have the opportunity for said confusion, given the ballot layout. Read the $%#@! post.
- Yeah, so people were repeating a UL, same day. Pretty impressive.
Look, one wouldn’t want to rely on anecdotal evidence by itself. But we routinely accept it as having at least some validity, in any number of contexts. In court, it’s called testimony, as it also is in contexts of a religious nature.
But again, you miss the point. It’s not just the confused people who tried to vote for Gore; it’s that, combined with the absence of any who voted for Bush.
- This one could, I suppose, be just evidence of an intense pocket of people who wanted to vote for Buchanan. But take a look at the graphs that dixiechiq linked to. Two other FL counties gave Buchanan substantially more support in the 1996 primaries than PB did; a bunch of others were pretty close behind PB. It was not far from the top of the pack, but it was definitely in the pack, statistically speaking.
Now look at the graph of the 2000 Buchanan vote. If ‘outlier’ had a picture next to it in the dictionary, this would be it. No other county in FL had more than 29% of the number of votes that PB supposedly gave Buchanan.
dixiechiq also links to a paper on this subject done by two professors at Carnegie-Mellon University and Chatham College. In 1996, the linear correlation between Buchanan primary votes and Dole primary votes was extremely high; you could use one to predict the other with a high degree of reliability. Excepting Palm Beach County, there’s a similarly high correlation between Bush and Buchanan general election votes: again, you can use one to predict the other pretty well.
But using the same model for Palm Beach that works for 66 other FL counties, we get a 1000-to-1 odds against Buchanan getting over 1000 votes in Palm Beach County, let alone 3.4 times that many. Statistically speaking, the burden of proof is on those who would argue that there really were 3000+ people in Palm Beach County who intended to vote for Buchanan. And by a country mile.
But that’s just the point, isn’t it? Many instances of bias (most?) are NOT in plain sight, are NOT obvious even to those involved. To carry your anology further, it’s very likely that there’s lots of counties where the voters would be very surprised to find out that they don’t on average weigh 168 pounds–the results said they averaged 168 pounds and they had no reason to believe otherwise. Nobody will be calling up Rush any time soon.
The fact that they are unaware (or that the bias might be small) doesn’t change the fact that this exists to some degree in virtually every election. To say that this particular instance is obvious misses the point. That’s the paradox, I think–by achieving more precision only in heavily Democratic Palm Beach County, you will have skewed the results and installed a bias for the entire election since a majority of the counties in the country will NOT be subject to a recount or the statistician’s analysis.
You can’t simultaneously say, I don’t think, that Palm Beach County demands this scrutiny in the name of mathematical precision, but screw the rest of the country, it’s their resonsibility to bitch loud enough, assuming they have a hint that there might be something awry in their own county. Statistical precision is not directly related to what is “obvious.” Your suggestion is contradictory and illogical, or I am missing something.
Since, I may be the person who came up with this 62 sigma number (I know I came up with something close to it)…although maybe it is another independent analysis that Spiritus refers to…I will try to (1) defend/explain it and (2) be clear on what its limitations are.
I do not want to claim that it represents the probability that this event occurred period, but rather that it occurred due to a statistical fluctuation in the specific sense of “Take a random sample of 431,000 people (the number who voted in Palm Beach county) from amongst a group of people who have a likelihood of 0.26% of voting for Pat Buchanan (which is the percent of voters across Florida, excluding PBC who voted for Buchanan). What is the probability that this random sample of such voters will produce 3400 or more votes for Buchanan?” The answer is that this result is 60-some standard deviations away from the mean which means its probability of occurrence is…well, you know, something along the lines of, “If you ran the simulation once every picosecond since the beginning of the universe, it would still be ridiculously unlikely to have it happen even once in all those trials.”
Of course, the rub is whether the people in “Palm Beach County” constitute a random sample of Floridians or not. Clearly, they don’t really…there can be concentrations of voters who lean one way or the other or there could be concentrated ad campaigns to a specific region or whatever. However, all the evidence from the 1996 Primary and General Elections suggest that they constitute a sample of people who tend to vote for Buchanan or for the Reform Party (in the personage of Perot) at a rate a bit below that of the rate of the state as a whole. And, Pat Buchanan says that in this election, he didn’t make any attempt to campaign there.
I’m not claiming this constitutes an argument for any sort of remedy, but I am claiming that, in light of any compelling explanation for this statistical aberration (and with the addition of anecdotal evidence, for whatever that is worth), I think that to argue that it may not have happened is wishful thinking to the extreme!!!
Whoops…just ran the numbers with the Poisson distribution, which is the more correct thing to use than the Gaussian, and assuming I calculated it correctly, I may have to back off on the picosecond part…You may be restricted to running it, say, every millisecond or microsecond in order to have it still be very unlikely to happen even once…I get the probability of occurrence in an given trial ito be something like 10^(-25). [Gotta be intellectually honest about this…you know! ;)]
jshore, can you show your math please, for someone who is genuinely interested? If it’s possible to squash it into a post somehow.
I am not in the crowd that dismisses the statistical significance of the Buchanan totals. But I’m not sure that Buchanan getting an extra 2000 votes in a 433,000 voting population (still less than 1%) is quite as improbable as you make it out to be. Again, sincerely interested in the math, if feasible.
- I read the $%#@! post. I didn’t miss the point. I know what you are saying. I understand it perfectly, I believe. You are saying, where confusion exists, it’s likely to cause the confused to vote for Al Gore. It ain’t that difficult to understand. But then, I can see why, since you think Republicans are stupid, you might believe that I am incapable of comprehending so simple a point. I assure you, it ain’t the case and I didn’t miss the point. I think your point is invalid.
My problem with your argument in favor of bias for the confused, is that I don’t see the opportunity for confusion, and certainly not on the scale you are alleging. The ballot is clear. And simple. Follow the damned arrows. I don’t see the difficulty in that.
BUSH --------> •
** • <-------- Buchanan**
GORE --------> •
Can you see it now?
- Urban Legend? I have no idea what you mean by this. If you are accusing me of posting something that could be called an urban legend in an attempt to back my argument, all I can say is you’re wrong. I saw a video clip of this man on one of the Sunday Morning Political Shows. The clip was introduced by George Will. It’s no legend. Just what do you mean?
Additionally, I’ve not seen anyone who has convinced me that they were so confused that they had voted for the wrong party and then had the presence of mind to be able to determine after the fact they had indeed cast an unintentional vote for the wrong party. If these people were so damned “confused” by the ballot, how in hell can they now say, with any conviction or veracity, for whom they voted? All we have are unconvincing anecdotes.
Testimony now, in a court of law, is subject to cross-examination. The words of the witness are not taken without critical examination. You appear to expect me to take your anecdotal evidence of bias at face value. And then a jury votes. The vote of the jury can reflect either their acceptance of the witness’s claims or their rejection of them. You have, in effect, cast your vote for their claims; mine is against. See? Subjectivity. You still have not proven bias.
3) 1996? What the hell? You are aware that Buchanan is a member of a completely different party now than he was in 1996, aren’t you? Maybe, just maybe, the Palm Beach vote reflects a pocket of people that chose to vote for the Reform Party. I haven’t been able to find county vote totals for the Reform Party in Florida in the '96 general election. I’m do not believe that your extrapolation is valid since party lines have changed.
But, I’m not sure I follow your argument on this point anyway. You appear to be saying, that because Buchanan received fewer votes in the general election in Palm Beach this year than he did in the1996 primary election in Palm Beach, that this is evidence of a bias allowing too many ballots to be recorded in his favor this year. It looks to me like the votes cast for him in the '96 primary totaled about. And the votes recorded in his favor in the '00 general election totaled 3400. Like I said though, I’m sure I’m misunderstanding you, but then I’m a stupid Republican. If not, this is specious, at best.
I disagree. I can see 3400 or so ballots that have been recorded with Buchanan votes. You have nothing but conjecture. Again, you’ve made a subjective conclusion and I do not believe you’ve proved bias, statistically, or otherwise.
Probability and statistics suggests that in any large enough sample, abberations will occur. For example, go out a billion decimal points or so in PI and you get this weird series of 8’s, like 27 in a row… Several times you also get the number 1-9 in sequence.
The chances of these specific things occuring are minute, but there they are. If it wasn’t those aberrations, it would be others.
What would be really weird would be if there were no aberrations. That would be suspicious.
Prob & Stat also says you do not tamper, examine, or recalculate these aberrations because you contaminate the result as the aberrations tend to cancel themselves out in a large sample.
Applying unusual scutiny to the PB sample of the vote only skews the results, and smells like intentional manipulation. No honest statistician would attempt such a thing.
A general election is the statistical problem of attempting to estimate an underlying true parameter from a set of data. We say that the true proportion of a country that wants candidate U is u. We must then estimate û, our best guess as to what u is. If the expected value of û is equal to u then we define the estimator û to be unbiased. If E(û) <> u then û is biased.
Generally speaking we need only count up all the ballots cast for U and divide by the total number of ballots. It can be shown (consult an elementary statistics textbook) that this is an unbiased estimator for a simple proportion. However in this case it has been submitted that this is not an unbiased estimator. This can be backed up as follows:
Suppose that the probability that a vote is cast in error for Buchanan rather than Gore is p. For simplicity say that no other votes can be cast in error (in this case this is actually equivalent to saying that all other errors are equally likely to be cast both ways). Then:
û = N_u/N (where N is the number of votes cast in total and N_u is the number cast for Gore)
E(û) = E(N_u/N) = E(N_u)/N = (uN - pN)/N < u
Therefore the ballot is biased.
I’m not offering any solutions here, Uncle Beer. Maybe everyone should just put it down to experience. But I am saying that as long as there is a positive chance that votes could be cast for Buchanan rather than Gore in error whilst Bush’s count is untouched (note that in this case E(ê) = e, where e is Bush’s underlying proportion), the result is biased.
regards
pan
A general election is the statistical problem of attempting to estimate an underlying true parameter from a set of data. We say that the true proportion of a country that wants candidate U is u. We must then estimate û, our best guess as to what u is. If the expected value of û is equal to u then we define the estimator û to be unbiased. If E(û) <> u then û is biased.
Generally speaking we need only count up all the ballots cast for U and divide by the total number of ballots. It can be shown (consult an elementary statistics textbook) that this is an unbiased estimator for a simple proportion. However in this case it has been submitted that this is not an unbiased estimator. This can be backed up as follows:
Suppose that the probability that a vote is cast in error for Buchanan rather than Gore is p. For simplicity say that no other votes can be cast in error (in this case this is actually equivalent to saying that all other errors are equally likely to be cast both ways). Then:
û = N_u/N (where N is the number of votes cast in total and N_u is the number cast for Gore)
E(û) = E(N_u/N) = E(N_u)/N = (uN - pN)/N < u
Therefore the ballot is biased.
I’m not offering any solutions here, Uncle Beer. Maybe everyone should just put it down to experience. But I am saying that as long as there is a positive chance that votes could be cast for Buchanan rather than Gore in error whilst Bush’s count is untouched (note that in this case E(ê) = e, where e is Bush’s underlying proportion), the result is biased.
regards
pan
Sorry for the doublepost - the board shut down on me. I thought I’d been clever by not reposting, but it seems to have decided to repost all by itself and get me anyway.
And now I’ve just wasted even more of your precious time with this apology. Ironic, eh?
pan
- OK, I get it now, Unc. You’re saying that there was no possible confusion here.
Let’s see - in the photo I saw, the arrow was pointing to the top of the hole. It was pointing closer to the dividing line between the holes than it was to the center of the hole. No confusion possible there.
There may have been instructions about which, and how many holes to punch, somewhere. But they weren’t present on that page. No confusion there.
A voter would never have tried to punch the hole opposite “Democratic Party”. No confusion there.
Seeing the arrow as pointing between the holes, no voters would have inferred that they were to punch one hole for each candidate (Pres. and veep). No confusion there.
No voter would have dreamed of glancing elsewhere for a millisecond while looking from left to right, and followed the dividing line instead. Nosirree, impossible. Couldn’t have happened.
OK, Unc, I yield to your higher wisdom. Humans aren’t fallible, and never make trivial, idiotic mistakes. Point well taken.
- Unc, you brought up the logic of ULs applying to this (“Up the butt, Bob”).
Does that never happen to you - when you do X when you should have done Y, don’t think anything of it at the time, then anywhere from five minutes to five days later, slap your head, go, “Aw, shit!” and run back to find what you left behind, fix what you’d done wrong, or whatever?
Happens to me with great regularity. And it happens overwhelmingly in situations where, by going back, I confirm the correctness of my sudden recollection.
For example, twenty minutes after I leave a restaurant, I’m driving down the road and all of a sudden, I realize I didn’t get my Mastercard back from the cashier when I paid. Sure enough, I check my wallet and it’s not there; I call the restaurant, and they’ve got it.
Given that this happens to me fairly often, and is exceedingly reliable when it happens, I have no reason not to believe the folks in Palm Beach when they say the same thing happened to them.
According to Time magazine, reports of this reached DNC or Gore headquarters (can’t remember which) pretty early last Tuesday morning. Other sources have documented that there were many instances of people telling others on Tuesday that they believed this happened to them. Not all these people could have decided they remembered something like this after hearing it on the news; there were too many reports of this before it made the airwaves.
You mention that testimony needs to be taken to court; good - let’s do so. That’s what I’m advocating.
Unc, the 1996 primaries have been brought in by those who say, “Look, Buchanan got 8500 votes in PB Co. in the 1996 primaries; why couldn’t he have gotten 3400 votes there now?”
The answer is, there was a strong correlation, in 1996, between Dole’s primary votes and Buchanan’s; the counties that gave high vote totals to Dole did the same for Buchanan. You can use one to guesstimate the other with a high degree of accuracy. Ditto Bush and Buchanan’s general election votes - except for PBC.
This isn’t such a hard idea - that the same tide of higher population and greater conservatism that would boost the GOP standard-bearer’s vote totals, in the center-right part of the spectrum, would also boost Buchanan’s vote count, out in the tail of the distribution. You’d expect a relationship. And there was such a relationship there, a very strong linear relationship, in 1996; and it’s there again now in 2000 - except in Palm Beach, which is not just a little bit out of line; it’s just plain out of sight.
And, to reiterate yet again, Buchanan’s 2000 PB total is out of line with his 1996 PB primary total in a more direct fashion - even though it’s below it. It should be obvious that voting for someone in a primary doesn’t necessarily imply that you’ll still vote for them if they lose and and run as an independent; most of the losing primary candidate’s voters will vote for the party’s standard-bearer in the general election.
So while Pat’s 8500 PB votes in '96 is more than double his 2000 total, this doesn’t mean anything until we have some idea of what the fall-off was for other counties. And the answer is: a great deal more. I don’t have county-by-county comparisons, but we know that in the 1996 primary, two counties gave about 12K and 11K votes to Pat; another five or six counties were in the 7-8K range; a couple more were around 6000, and a whole passel were in the 4000-5500 range. But only one of these counties gave as many as 1000 votes to Pat this time, and only three others gave Pat over 600 votes. We’re talking a drop-off of better than 90%, it seems. Except for Palm Beach.
Palm Beach’s 2000 Buchanan vote is miles out of line every which way you can think of. That’s not subjective; them’s the numbers.
- A question, not an argument: I haven’t mentioned the 19,000 double-punched ballots here, because we know nothing about them. (I figured we would by now, and I’m disappointed as hell about that.) How badly would the Buchanan-Gore double punches have to stand out from the rest of the possibilities for Bush defenders to admit that there might be a cause for that combination coming up more often, rather than its just being a fluke of the data?
My recommendation: there’s 45 ways to punch a ballot with 10 names on it exactly twice. If we find the mean and standard deviation of the number of disqualified ballots in each of the 44 categories other than Gore-Buchanan, one of them is likely to be outside a 95% confidence interval, so finding Gore-Buchanan there isn’t good enough. But if it’s outside a 99.9% confidence interval (on the high side, that is), we’re saying there’s a 1-in-2000 possibility that this could’ve happened by chance. Would that be good enough to impress the crowd? In this case, I’d settle for that standard as a fair test.
Mind you, this may be moot: we may never find out how those 19,120 ballots read. But if we do, can we agree among ourselves on a standard for judging the results ahead of time?
This is a response to Scylla as well.
There may indeed be other factors in voting mechanisms elsewhere that cause bias. We all agree that we don’t know what they are, or how they bias things. And then there’s this one, that we know about.
There’s nothing in probability theory that says it all balances out only if we leave Palm Beach the way it is. In fact, it’s exactly the opposite: a bias discovered in Palm Beach doesn’t affect in any way the likelihood of bias elsewhere. It’s more likely to be a bunch of random instances of bias that all cancel each other out excluding than including Palm Beach.
It’s like the old coin-flip problem: you flip 10 coins, which land in various places on the floor. The first 9 you pick up landed ‘heads’. What’s the likelihood of coin #10, which rolled under the bed, being heads? 1/2.
Like you say, Scylla, any large sample will produce clumps of apparently nonrandom data. So you don’t fix aberrations whose cause you don’t understand; they may be random. But here, I’m arguing, we have a cause. And (in the double-punched ballots, at least) we have a measurable (but as yet unmeasured) effect. When we have some outside force acting on the numbers whose effect we can measure, removing that effect makes the numbers more honest, rather than less. Any other bias, or any other just plain noise in the data, may or may not cancel out, but it’s more likely to do so once we’ve subtracted out the effects of any bias that can be accurately measured.
So the potential, even likely, existence of other unknown biases elsewhere is no argument for failing to deal with one we know about.
I cannot. I know of nobody who has even tried, since I know of nobody who advocates this position. So far, dispute on this issue seems to come downto 3 options:
-
People who say the statistical abberation is so significant that bias is demonstrated and want action taken to correct the results of this election.
-
People who say the statistical abberation is so significant that bias is demonstrated and want action taken to ensure such bias does not occur again, but so not feel there is any equitable way to correct the bias evident in this election.
-
People who deny any bias was present.
My own position is (2).
I understand the position of those who argue (3), though I have not heard any proposed solution that would not introduce more bias into the overall result (the national election) in attempting to correct the bias in the local result.
I do not understand how position (3) can be held except in ignorance of the statistics or lack of objectivity in the advocate.
[bart simpson]
I understand the position of those who argue (1)
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I understand the position of those who argue (1)
I understand the position of those who argue (1)
I understand the position of those who argue (1)
I understand the position of those who argue (1)
I understand the position of those who argue (1)
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[/bart simpson]
Okay RTF, let’s try this again with a little more reason and a little less emotion. Okay?
Again, I saw the ballot in question. In the sample I saw, the holes and arrows lined up pretty well; maybe we saw different examples. You’ve stated that on the sample you saw, the arrow pointed more directly to the top of the hole. You’ve also stated that the arrow lined up better with the demarcation line than the center of the hole. Now, which is it? It can’t be both.
Now you want instructions on every page? Do you require constant reminders for every little thing that you do? Do you honestly believe the voters are incapable of remembering a simple task for more time than it takes to turn a page? This is an absurd argument.
Do you really think that voters don’t know they get one vote for Pres/VP? Again though, even if there’s a significant number of voters that are not aware of that, I fail to see how this translates into a bias for any individual candidate/party. I also fail to see how ballot design would address this. Either you know you get one vote or you don’t. The ballot itself has nothing to do with your personal knowledge of the process.
Now, suppose I did glance away for just a millisecond and upon turning back I followed the dividing lane rather than the arrow. What, in your opinion, makes it more likely that a voter followed the line above the Gore/Lieberman slot than the line below it (in which case they’d have voted Socialist)? There’s no bias here. It’s equally likely that they’d follow either line, isn’t it?
It seems that for this concatenation of errors to take place, you’d need a voter going about the process rather cavalierly. And if this is the case, then I don’t think those who are now complaining about the unfairness of the ballot can really say how they punched the card with any accuracy.
At any rate, the party now bitching about the ballot did approve it prior to the election. Crying about it now and rationalizing seems like sour grapes. If they believe this was a biased ballot, then why would they approve it?
Yes, I guess I did bring up UL’s. But I did this to show that false memories do take place. And with alarming frequency. I had thought you were saying that the guy I saw complaining about punching the wrong hole was an Urban Legend. I stand corrected.
The remainder of your contention on this point fails though. If I believe I’ve left my MasterCard at the restaurant, all I need do is check my wallet. I have something concrete that I can check. This is not the case here, and in fact, your experience may be a form of vividness. You remember the times you thought this and did indeed leave your card behind because you then had to do something about it. There are probably times you felt this way and do not remember it. In those cases you don’t remember simply because you didn’t have to do anything about it; there’s no reinforcement of the memory and hence, it lacks vividness. This is a very well documented phenomenon. All we have in the FLA vote case are unconvincing, to me, anecdotes. If we take a quick look at the subjectivity of memory, you’ll see why I consider these anecdotes to be unconvincing. This is from the Skeptic’s Dictionary.
and
All this directly contradicts your claim that anecdotal evidence is evidence of bias.