jshore, thanks! If you are able to confirm the estimation of the probability of the 68 sigmas, that would be much appreciated as well. Again, thanks for your help.
RTFirefly, why would you look for evidence of a bias for the Buchanan votes in the disqualified ballots? As you’ve pointed out, evidence to the contrary, there’s no reason to assume the separate instances have any relationship to each other. If you’re stating that disqualified ballots do not signify bias just by virtue of their existence, why consider them at all, what suggests to you that they are related in any way to the Buchanan votes? And if I assume disqualified votes are not suggestive of bias, couldn’t I make the subset of disqualified voters in Palm Beach County part of your calculation for S? IOW, why wouldn’t I assume that E(S) is still zero (and ignore the PBC disqualified votes)?
But why wouldn’t the existence of a disproportionate number of disqualified votes only in particular counties (perhaps Duval County) suggest a bias? There may be reasons why this isn’t really bias, just as there may be reasons (unlikely though it may be) that the Buchanan votes in PBC aren’t examples of bias–we don’t know, and we’re being very choosy in where we obtain clarity, it seems to me.
Could it be that we’re simply going on a selective fishing expedition? Not trying to be contentious–it just seems that all roads lead only to an analysis of a particular county where the discovery of unreported votes will likely favor Gore.
Let me ask you flat out–don’t you agree that subjecting every county to the same rigors of analysis, auditing and counting will produce the most accurate overall conclusions? How could it be otherwise?
Scylla - it’s blatently obvious that you’ve never worked for an insurance firm analysing data for premium rating purposes. We routinely throw out and adjust vast quantities of data because it’s biased. Postal strikes mean that January’s data ought to be counted with December’s. A change in admin systems means that response delays in the old data must be adjusted to reflect the new delays. Very little data is not adjusted.
Your argument ultimately rests on the law of large numbers to even out the inequities. However if you have a bias then all this will do is ensure that the bias is noticed.
I’d be interested to know the qualifications of those arguing here. I’m a mathematician working in a very statistical field (actuarial science). It seems to me that jshore and RTFirefly are also statisticians in some form or another. We are all telling you that in real-world statistics (as opposed to high-school or elementary degree-level), biases are introduced and must be dealt with.
Furthermore we’re saying that regardless of opinions as to what should have been the case, analyses indicate that there was a significant bias.
Spiritus Mundi said it best (as usual). I can empathise with his positions (1) and (2). (3) however is borne in ignorance. Ignorance of statistics maybe, which is hardly a shameful thing, but ignorance nonetheless.
regards,
pan
kabbes:
No I’m not an actuary. State law, licensing concerns, and my companies preference prevent me from identifying my profession. sorry. I know it sounds like BS, but there it is.
UncleBeer wrote
and provided a diagram similar to this:
BUSH --------> • ------------------
-------------- • <-------- Buchanan
GORE --------> • ------------------
-------------- • <-------- Someone
(I modified UncleBeer’s diagram, adding blank lines above and below the Buchanan line, and adding the lines dividing the candidates, to make the following more clear.)
This is the view you see looking straight down at the ballot. This is also the view shown in the sample ballot. The holes are not in the plane of the ballot, however, they are somewhat beelow the ballot. Taking a cut through the plane of the holes, looking from the left, you’d have something which looks like this
W B G S
H H H H
where W is the arrow pointing at George W. Bush, B is for Buchanan, G is for Gore, S is for whoever was next, and H are the holes. Looking from in front and above, rather than directly above, you’d see something which looks like this:
BUSH --------> ------------------
•
-------------- <-------- Buchanan
•
GORE --------> ------------------
•
-------------- <-------- Someone
The Buchanan hole moves down, relative to the names. This is where the opportunity for confusion comes from. The actual apparent position of the holes would depend on how tall the voter was, and where they were standing, so the offset could vary from what I show.
In one shot I saw on TV, the photographer was showing someone demonstrating the ballot. He was off to the left, but the view showed essentially what I show in the bottom diagram.
BTW: I’m not arguing that there’s not a bias.
As you make use of statistical data, there’s probably not much interest in the people evaluating the data in manipulating the result. The adjustments that are made are in accordance with strict standards. The results that you produce do not tend to be either A or either B. You are looking at averages tendencies and trends.
If somebody wins by one vote in FL. That sways the whole thing. It’s a little different then calculating life expectancies where if the data is slightly off and everybody gets an extra day, it doesn’t make much difference.
Within an election, exacting precision is sought, and necessary. The bias that may come in adjusting the data after the fact far outweighs what bias may exist in a preapproved ballot beforehand, IMO.
Part of what makes an election fairly impartial is that while voting and tabulating, those doing so do not know what effect if any there actions will have in the larger picture. In PBC this is not the case. They know. There is a much greater potential for bias if it’s unwilling, to be introduced, especially if one side outnumbers the other 2 to 1.
For example, in Broward County according to CNBC. One double voted ballot got counted for Gore. It had “Homer Simpson” as a write in. The committee decided that the Gore vote was serious, and the Homer wasn’t, and counted it that way.
As close as this thing is, a very slight tendency to bias which would be acceptable in an actuarial environment can throw the whole thing.
Thank you, Kabbes. You flatter me, but it’s nice to know at least someone reads my posts, even if it is not, apparently, those to whom they are directed.
As to background, as a mathematician I am an amateur. I did complete the coursework for a BS in mathematics, but I chose other majors for my thesis work. Even as an undergrad, I was far more attracted to abstract algebras than probability theory.
[QUOTE]
*Originally posted by Spiritus Mundi *
**
Personally, I was more attracted to the female undergrads.
This statement is not reasonable.
While it is impossible to place an exact number on the number of Buchanan votes affected by bias, the magnitude of the difference from the expected mean is on the order of 2000 votes.
I have seen nothing in the results of the sample handcount from PBC that indicates a shift in votes that “far outweighs” a bias of that magnitude. In fact, the estimates I have seen place the expected vote shift at less than 1000.
Beyond that, though, balancing these particular actions against each other makes little sense. The handcount was not instituted to corrct the bias demonstrated in teh number of Buchanan votes. No action has been taken to balance that bias.
Yes it is.
I was referring to handcounts.
I had not heard this, but if it is true I find offensive. I see no way, assuming that both “votes” were obviously marked, to make such an assumption of intent. The voter could as easily have voted Gore, reconsidered, and placed a “protest” vote for Homer Simpson. (I mean, really–I can see confusing Bush for Smithers or Gore for principal Skinner, but Homer? )
The ballot should have been disqualified.
I know what you were referring to. In fact, I addressed the matter quite directly. Your statement is not reasonable because:
- Your assesment of the relative weight of bias, based upon observed Buchanan votes and extrapolated hand count adjustments in vote totals, is incorrect.
- The balance you set up is irrelevant to the actual situation, since the handcount is not being performed to balance out the bias evident in ballot construction.
Frankly, I am amazed that you could read my earlier post and miss those elements.
Good question, Bob - maybe I just kinda assumed that, since this had been talked to death since last Wednesday, everyone had noticed the key connection here. Anyhow, here’s the deal:
Regardless of which photo of the disputed ballot one looks at, you will see that the paper of the ballot is shifted up somewhat, relative to the holes on the spine. (Or the holes are lower, relative to the candidate names.) The result is that, if you’re looking at the box for any one party and its candidates, not only is the hole corresponding to that party between the lines marking the top and bottom of the box, but the hole corresponding to the next candidate up (on the other side, but up) has been nudged partway into that range. (Just how far seems to vary at least slightly.)
This presents an increased opportunity for an assortment of confusions involving the hole for the candidate above your own. (Which is why Dubya voters’ possibility for confusion was actually reduced by this shift - Bush/Cheney have the top line; there’s nobody above them, for them to be confused with.) This both lines up the Buchanan hole with the Democratic party name, and pulls the holes down far enough to have the thought creep into people’s minds that maybe they’re supposed to punch holes for both Pres. and veep.
Anyhow, it is the shift that seems to have bumped the possibility for confusion up to the level where we all now know about it, as well as having increased the level of bias involved. (If the shift had been in the other direction, then Bush voters would have been equally subject to the possibility of misreading the ballot, and nobody would have had grounds for griping, IMO. And Buchanan would have gotten Bush votes, and the Socialists would have gotten way more Gore votes than they did. Or that’s the theory.)
So it’s the shift that’s, in theory, causing both the Buchanan bump and Buchanan-Gore double-punches. The theory says they both ought to be improbably high. How you test theories is by their predictive powers. The one thing it can genuinely predict at this point (since we already know the Buchanan total) is that, of the 45 double-punch possibilities, Buchanan-Gore ought to stand out like a sore thumb.
If it does, that strongly suggests that the theory is valid, in the absence of any other theory to explain both effects. And that’s why I’d like to see inside the 19,120 ballots disqualified because of their being twice-punched in the presidential voting - we’ve got a specific theory here, and in that pile of ballots is the evidence that should say whether this theory is on target, or a bust.
So, for me at least, this is hardly a fishing expedition. Mind you, I’d see nothing wrong with subjecting all the results - in the state, or in the country - to the same scrutiny. And I’d be quite happy to just redo the entire election in two or three weeks’ time, in PBC, in FL, or from coast to coast. But I’m enough of a conservative, in the old-fashioned sense, to believe that the smallest solution is the best one, as long as it works.
RTFirefly wrote:
[q]quote:
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?
I’ve heard (but haven’t checked, myself) that there was an unusually high Socialist vote count in PBC as well. [/q]
Just for the record- the actual figures for McReynolds, the Socialist candidate, according to http://www.cbsnews.com , are: Statewide- 618
Palm Beach Co.- 302
The next highest county figures for McReynolds are Dade-35 and Broward- 34.
Thanks for the info, nebuli. That’s most enlightening.
It seems pretty unlikely, completely apart from all the other evidence, that Palm Beach County would provide Buchanan with 1/5 of his total FL support, and provide the Socialist candidate with 1/2 of his FL support.
Of course. It is well known that, in addition to being a hotbed of radical conservatism, PBC is the statewide capital of marxist activity. As a resident I can assure you we are a seething boil of radical politicians and raving followers that threatens any ay to erupt into full-scale warfare. Indeed, only the unbalancing element of anarcho-terrorist, whose constant shifts of allegiance prevent any side from consolidating an advantage, keep the undercurrent of rage from escalating into full revolt. Why, the streets of West Palm Beach remind me more and more of pre-Franco Barcelona. You haven’t known fear until you’ve innocently turned the corner from Footlocker into the food court and blundered into a stare-down between septagenarian Buchanan ravers and illiterate McReynolds maniacs. In the backgroud, someon sing Maria as the neo-Nazis click their walkers in eerie percussion. the socialists circle, their dance steps uncanniily precise thanks to orthopedic soles in their shoes. Someone scream, and I’m not ure if it’s me . . .
Or maybe it was a crappy ballot.
You may get your wish. I heard Alan Dershowitz (is this the right name (Yes, I know it’s spelled wrong), or am I confusing him with someone else? One of the lawyers challenging the ballot in one of the suits brought in PBC, anyway) say they would ask for this information in discovery.
This would be very important, since it would indicate the Gore supporters erred in both directions, although more substantially towards Buchanan. Presumably, the republicans would similarly tend to incorrectly vote for Buchanan, so some of Buchanan’s “extra” votes would have come from republicans. You could still sort it out, but not as cleanly.
That’s nice. Do I now win a concession off you? That would still make it 2-1 to you I believe.
No, no, no. No. The application of statistical methods to real-world bias are the same, whether the analysis and/or cleaning of data is for insurance premium rating or ballot counting.
However the thrust of this thread was not to talk about what should be done about the bias but whether the bias exists or not. Reread the OP - RTFirefly doesn’t once suggest any actions that may be taken as a result of the bias, merely what we might do to confirm it.
I’m glad to see that you agree that result was biased. I repeat - I’m not suggesting that cleaning the data is appropriate in this case (nor am I suggesting that it isn’t). I’m not American, I’m not an expert on your constitution and I don’t see it as my place to tell you what to do about your own mess. I’m just pointing out the mathematical facts of the matter. But we appear to be in agreement about the OP now, so unless UncleBeer still remains to be convinced, I’ll bow gracefully out.
[/quote]
Those with weak stomachs, please feel free to stop reading now.
Spiritus Mundi - it wasn’t unjustified flattery. Your posts invariably either add something to my worldview or successfully sum up a complex situation in fewer than 100 words with fewer than four syllables. This seems to be true regardless of whether the topic involves metaphysics, religion or maths (if those things aren’t all the same). Now you must excuse me - I’m not one given easily to such blatent vomit-inducing sycophantism. I feel I must go lie down.
regards
pan
I’ve meant to mention this in each of my last two major posts, but it’s somehow eluded me both times. Fortunately, nebuli, you jogged my mind one more time.
UncleBeer asked:
And, as nebuli noted, I answered that the Socialist vote in PBC was rumored to be up as well. (And thanks again, nebuli, for verifying that.) Still, that wasn’t the complete answer. After all, why an extra 2500 or so Buchanan votes in PBC, but only an extra, what, 275 votes for McReynolds, the Socialist candidate?
The answer is, there is a bias here: the shift that I discussed at length in my response to Bob Cos, in my second post before last. Again, the central thesis about ballot bias here is that, since the paper is higher than it should be, relative to the holes, one is more likely than otherwise to punch a hole above the hole one intends to punch - and, similarly, less likely to punch a hole below the intended hole. Downward errors are still possible, but my claim is they’re a hell of a lot less likely than upward errors. So people who aimed for Gore, and missed, should have been much more likely to unintentionally vote for Buchanan than for McReynolds.
Now if they’d thrown themselves at the ground, and missed, then you woulda had something. 
Don’t forget that to those not concentrating, since Gore was the second candidate named, people may have automatically punched the second hole down.
I know it’s already been mentioned, but it’s important not to lose sight of this extra* factor in all the kerfuffle about planes, sighting angles and following of arrows.
pan
*not alternative. There was more than one source of bias to this ballot paper.