Survey Response Error: Variance v. Bias (Another Election Thread)

kabbes:

I’d like to offer you a concession but the chad is not fully detached.

Spiritus:

It appears I’m havin a different argument than everybody else.

ZenBeam - I’d read, this morning, that Dershowitz was now in the case, representing the Palm Beach voters suing over the ballot. If he’s asking to see that info, that’s good news indeed. (Anyone on the pro-Bush side want to place any sig line bets over what it will turn up?)

Spiritus - my wife hails from central FL (Plant City, if you’re wondering), and when we’ve visited her folks, I’ve frequently suggested that we cruise down to Palm Beach. So far, she’s managed to dissuade me. Now I find that she was protecting me from geriatric factionalist rage! And I’d been expecting nothing but sleepy shuffleboarders. :wink:

RTF:
Have you ever taken a shufflebord disk across the ankle? Beware the geezer, my friend. It is a lesson the wise man learns only once.

scylla:
What did you think you were arguing? I will be happy to demolish your babble in any context you choose. :wink:

kabbes:
You have rendered me speechless.
[sub]who wins the pool?[/sub]

Scylla - you’re not completely off the subject, since nebuli raised the question, back at about the eighth post on this thread, of whether the machine count introduced a bias in counties where voting is done by the voter punching holes in the ballot. So discussing the question is certainly fair game; it’s just not the main thrust of the discussion.

So you may have to make it a little bit more clear just what claim of bias you’re rebutting, but don’t let us chase you away. Since we’re allowing sycophantic posts here, I want to mention that I’m always glad to see your name in a thread, even when we’re on opposite sides of an issue.

And while I’m on this sort of note, Spiritus, kabbes’ comment summed it up well for me, too. You manage to condense a great deal of understanding into wonderfully concise posts. People like me who simply throw words at the page, hoping to eventually bury their opponents, absolutely detest guys like you. :wink: On those rare instances when we’ve been on opposite sides of a debate, I’ve known I was in trouble.

OK, now I’ll shut up.

I’m arguing the same thing concerning handcounts that we were pretty much in agreement about in the other thread you ignorant dolt. :wink:

He’s not all that great you know. He just looks good compared to me.

Great. Now I need a new hat.

Quick, somebody open a PIT thread before I become insufferably smug. :smiley:

[sub]oops, too late.[/sub]

Here ya go.

http://boards.straightdope.com/sdmb/showthread.php?threadid=46696

RTFirefly, thanks for taking the time for your response; that helps clarify things. Do you agree that there is an automatic inter-county bias since some use paper ballots and some use electronic ballots? To the extent that each county has a different composition of registered voters, mustn’t this be the case?

And, Spiritus Mundi, um, I think you’re a swell guy too. (Sorry, the peer pressure was more than I could bear.)

One WAG- they were Nader voters who got confused. I can’t recall positively, but believe Nader was the next candidate below. If so, this would seem to support RTFirefly’s hypothesis that in cases of confused voters inadvertently punching the wrong hole the bias would be to punch the one above the intended ticket.

Bob,

Well, I checked, and while the 68sigma part was right, this 36-year-old brain failed to remember the formula for the Poisson distribution, which is P(n,mu) = exp(-mu)(mu^n)/n! where mu = 1120 in this case and n = 3400.

To compute the cumulative probability for this, we have to call on our good friend the “incomplete gamma function” (yeah…he ain’t no friend of mine either). What we are looking for is either gammainc(1120,3400) or gammainc(3400,1120), depending on how it’s defined (there doesn’t seem to be a very standardized convention on this). When I tried plugging it in to MATLAB (which uses the first convention), I got 0…Turns out it is so improbable that it underflows the double precision arithmetic! If you back off to gammainc(1120,2600), you get 10^(-310).

So, to make a short story long, the chance of >2600 votes due to statistical fluctuation is already 10^(-310), which is, needless to say, so ridiculously small that even these since-the-beginning-of-the-universe analogies can’t do it any justice. Hell, the chance of even >2000 votes is already 10^(-123). [I was sort of wondering why a 68*sigma event wasn’t more improbable than what I calculated last night…But I thought maybe it was just that the tail of the Poisson is much more forgiving than that of the Gaussian. Turns out this is true to some extent, but the main problem was just to calculate it right!]

I was comparing the votes cast in the fallible punchcard counties to the less fallible marksense counties and noticed that Gore dominates the fallible and Bush dominates the less fallible.

If there were a statewide manual (or machine - I’ll explain later) recount of the “undercounted” ballots, then the punchcard heavy candidate will gain more votes.

Each time a marksense ballot is read by machine thwere is the SAME statistical error possiblility. Each time a punchcard is read, the error rate actually DECREASES. It is known that the error rate on the punchcard ballots stabilizes after the fourth count. Why is this? Because a few of th chad falls off on every recount, and the likelyhood of getting the correct count goes up!

Does chad that has not been punched fall off? No. Only hanging chad will fall off on subsequent counts.

So I would propose MACHINE counting every county five or more times, and then looking at the results each time.

Why should we accept the second count in any county as being better than the first in any case? What ever happened to the intrinsic american right (just kidding) of “best two out of three”?

In any case if the second machine count is acceptable, why can we not demand a fourth or fifth machine recount? We know more hanging chad will be eliminated after each count, and the will of the people will be more clearly heard.

Who could this possibly hurt? Well if someone started to vote for one guy, but changed their mind and punched the other, but the first punch was “pregnant”, after 5 recounts this would end up as a double vote. So who does that hurt? Well… it shows the will of the person as being “undecided” and I say that’s OK.

jshore, thanks again.

Some blithering idiot posted this arrant nonsense

D’ohh! Today’s NY Times shows that not only is the guess wrong, but the premise is too. Browne, not Nader, was the Prez candidate following Gore (hey- geriatric Libertarians, wuz that Socialist McReynolds stealin’ your votes?). Probably not, if a comparison can be drawn with a sample of doublepunched ballots. The Times looked at the 144 doublepunched ballots found when 1% of the precincts in PBC were handcounted.

RTFirefly had said:

The most frequent combinations found were:

Buchanan/Gore- 80
Gore/McReynolds- 21
Bush/Buchanan- 11
Gore/Brown- 5
Bush/Gore- 3

That thumb look sore enough to you RT?

As sore as if someone had been trying to hammer a nail, and it their thumb instead! (And I know from experience just how sore that is…:eek:)

Thanks, nebuli! Say, you wouldn’t happen to have a link to the story, wouldja?

I saw the figures in the paper version of the Times (Nov. 16, section A, page 29).
However, it can also be found at

Free registration will probably be required to view that page.

The figures I mentioned are in a sidebar to the article “Gore Lawyers Focus on Palm Beach County
Ballot”. They are in a popup window- to reach them click on the link “Punching Two or More in Palm Beach
County”, and then click on the link “Click Here to See…”

Thanks again, nebuli - your link and instrucions got me there. I’d searched for any mentions of ‘Palm Beach’ on the nytimes website earlier, arranged by date, and I’d looked through the most likely ones dated 11/16. Damned if I know why that one didn’t turn up.

The quick statistical crunching on the TI-83, assuming the 144 ballots that the Times looked at are a random sample of the double-punches:

The 99.9% confidence interval for the proportion of the 19,120 ballots that are Gore-Buchanan:


lower bound:  8017
upper bound: 13227

The same interval, for Bush-Buchanan:


lower bound:   68
upper bound: 2853

In other words, assuming randomness, there’s a 1 in 4 million chance that Gore lost less than a net of 5164 (=8017 - 2853) votes to what were almost certainly unintentional double-votes. And that’s without considering the Gore-McReynolds double-punches, or the Buchanan votes themselves.

A more statistically centered estimate that includes all that, as opposed to a 4-million-to-1 worst case scenario that doesn’t, is that Gore lost a net of 12-13,000 votes to the Palm Beach ballot problems. But what of it? 5164 votes is 16 times as many as was needed; it’s even 3.5 times the margin of difference between the original count and the machine recount. And 5164 votes would still be enough to tip the election after the absentee ballot count is completed tomorrow night.

Of course, this ignores the disqualified votes in other counties (e.g., 26,000 in heavily Republican Duval) that, at least potentially, would more than offset this increment for Gore. I have done a study of my own that shows that 99% of these are for Bush, and my calculations indicate that this is as certain as tomorrow’s sunrise. Don’t ask me to show you the math because it would confound MIT professors (plus I don’t want to show up RTFirefly).

Bob Cos said:

See the NYTimes story at

This reports that c. 16,000 of the 26,000 were from heavily Democratic parts of the county however. In several Democratic precincts one third of the ballots were disqualified. The Dems have nobody to blame for this but themselves though- whoever said no fiction writer could have ever peddled a story like this election didn’t even begin to imagine how ridiculous things would become.

The Democrats’ get-out-the-vote volunteers stressed to their cliental how important it was to vote in every race, and “on every page”; overlooking the fact that this year in Duval Co. the presidential portion of the ballot was two pages long. Must be reassuring to those volunteers to learn that so many people will follow their guidance :slight_smile:

Thanks for not showing me up, Bob - I can use all the help I can get right now. I’m ready to let this thread sink peacefully into oblivion anytime it wants to go; I’m getting too old for all this intellectual counterpunching over here in GD. This geezer’s getting ready to ride off into the sunset, and peacefully retire to the Fathom board, or at least to MPSIMS and IMHO.

I saw a Washington Post online story to the effect of what nebuli posted, and linked to it in one of the other twenty gazillion election threads around here (“What Annoys Me Most About Florida,” IIRC; I’m too damned tired even to link to it right now). So I guess Duval is out as far as providing theoretical help for the GOP side. And as I said there too (I must be running out of original thoughts tonight ;)), we’ve scrutinized Florida so much at this point that any GOP counterarguments concerning vote totals would almost have to concern other states.

One last thing I should mention, though: the photo of the Palm Beach ballot that you see on the way to the NYTimes’ little chart with the double-punch counts has the arrows lined up quite well with the holes. Earlier in this thread, UncleBeer and I were going 'round a bit about whether the ballot was confusing; the answer may well be, it depended on whether the paper portion of the ballot went into the metal spine with the holes like it was supposed to, or whether it wound up riding too high (and if so, just how high).

I have no idea how it worked in practice: did each voter get handed the ballot, already assembled? Did they put the ballot in the spine themselves? Did the paper slide in, or was the spine hinged somehow? I’d love to hold one in my hands, and test it out, finding out how it worked, and in what ways it might fail to work as designed. But maybe not this week.

Actually, this is being investigated, because IIRC 18,000 of those rejected ballots came from heavily Democratic precincts. Most were double votes, and the Dems are interested in determining how many of these are Gore + someone else.