Please decipher for me - Florida recount

Factual Questions
1

I stupidly posted a message on a political board that was discussing the Florida recount. What I said was that because ‘every vote counts’ is a mantra that has been drummed into us, I believed that every vote should be counted and re-counted ad infinitum if that’s what it takes.

I received the following reply: “Since the degree of error (+ - 1%) is larger than the difference between the canditates + - .00001%) there is a 75% chance that Gore would come out on top in three different counts! His odds of winning based on pure error (either by machine or by hand)get better with every count. For instance, if there is a fourth count he has an 87.5% chance of winning!Anyway, this is why he wants more counts. Eventually he has to win and his chances get better every time. That is why it is a travesty to continue counting.”

My one any only Stat class was about 25 years ago so I don’t know if his logic is faulty or if I can’t remember how it all works. Gut reaction is that there’s something wrong here. Any help? Thanks!

2

I’m no statistics genious, but…

The margin of error swings both ways – not just in Gore’s favor. Also, the margin of error isn’t a given, just a possibility.

A major issue is the fact that each recount results in more votes for Gore–this raises some troubling issues.

3

Well, there’s been one statewide recount, which increased both candidates’ counts, Gore’s moreso. That can be attributed to chance. There’s been a countywide recount in Palm Beach, which also gave both candidates more votes. Since this county voted overwhelmingly in favor of Gore, it’s no surprise that he picked up several more votes than Bush. I don’t see anything troubling.

Basically, if the recounts swing by chance either way, and Gore presses for recounts until he is in the lead, it is likely that at some point he will get it. This is based on the assumption that Gore will have the votes recounted until he wins, and that the error in each count is based purely on chance. The real situation is rather more complex, but serves as a poor example to illustrate statisical principles.

4

Some of the recount, please note, arises from computer cards (remember computer cards?) that were not fully punched, or where the punched hole was not read by the machine.

Oldsters will recall that was a common problem with computer cards – if the card were slightly bent or if the little “tag” didn’t fall all the way out, or if the hole was too small (for whatever reason), it might not be read.

Thus, the recounts are turning up more votes for both candidates, no surprise, and since the areas being recounted are largely Democratic, the number of new votes tends to favor Gore.

My understanding is that Florida law requires the hand recount, and that a similar law was passed recently in Texas – that is, this is Florida law, and not something weird that the Democrats have forced on an unwitting electorate. Of course, the Republicans would prefer that the tally stays where it is, and hence are opposing the hand recount.

I personally think the hand recount is nowhere near as big an issue as the 19,000 “double punched” votes that arose because of crummy ballot design in a county where the vast majority of voters are senior citizens (hence, poor eyesight and not necessary adept at computer punch card stuff anyway.) However, I can understand that the Democrats would prefer a Gore majority through a straightforward recount, rather than a court challenge.

5

Agreed. What the person straykat23 quotes is really saying is: “The popular vote in Florida is basically tied. Since there is tabulation error when votes are counted, the ‘winner’ of each [re]count depends solely on the error, which is random. Gore will keep requesting recounts until he ‘wins’. The chance of Gore getting a ‘win’ after three counts is 75%, and after four is 87.5%.”

This logic basically likens the election count to flipping a coin, where heads = Bush wins, and tails = Gore wins. This logic is flawed, I would say, for the following reasons:

  1. If you’re talking about pure coin-flipping, you’ll get at least one tails (Gore win) in two flips 75% of the time (not three flips), and at least one tails in three flips 87.5% of the time.

  2. If you assume that the vote counting is equivalent to coin tossing, then realize that no flip influences subsequent flips. Therefore, the statement that “[Gore’s] chances get better every time” is misleading. His chances stay the same every time, he just has more chances. This might seem to be semantics, but since two counts (flips) have already happened, then the chance of getting a tails on the third flip only is just 50%, not 75% or 87.5%.

  3. The estimate of the degree of error (+/-1%) seems high to me. In particular, recounts are supposed to eliminate known sources of error, so I would say, at least, that subsequent recounts would have decreased error.

  4. The “actual difference between the candidates” (+/-0.00001%) is ridiculously low. This is one vote out of ten million (Florida had fewer than 6 million votes cast). Coupled with #3, I’d say that the assumption that the error far outweighs the true difference between the candidates is pretty suspect.

  5. Probably most importantly, the basic assumption that recounts are independent is invalid. Certainly large discrepancies from one count to the next would be looked at carefully.

Anyway, I suppose the basic premise that “the more recounts there are, the better chance Gore has of scoring at least one win” is true (obviously, as of now he has exactly zero wins), but the geometric progression of probabilities suggested in the OP is false, due in large part to the greater complexities of the real situation.

6

The problem is not so much with a hand recount - but the “interpretation” of what the voter meant. These ballots were meant to be read by machine, not by a human.The canvassers have said that they will try to determine the voters intention on ballots rejected by the machines. You do not have to vote for president, you can vote for just the local dog catcher if you wanted, and skip the president. Well, maybe they started to vote for Gore, pulled the sylus back and started to vote for Bush, or Nader, and said, aw, screw it skipped them all. Just assuming no President choice shown,(or two, as some people are reporting" and if they vote the straight democratic ticket, the canvassers can “determine” that they “intended” to vote for Gore. You now have low level party hacks determing how your vote should go. The machines at least were impersonal. I believe, but am not sure, that the original “handcount” idea was to make sure all ballots were processed through the machines, so that you had 33337 ballots cast, the machines should have shown 33337 counted, even if some are rejected. What they are doing now is basically changing the rules after the election, and applying a more generous interpretation to only strongly Democratic area. If you want to recount them, recount them all everywhere if Florida, by the same rules.

The hand recount law in Texas by the way, is slightly different - it refers to handwritten, marked paper ballots not the machine kind here.

7

The problem is with people who don’t know HOW to vote, not with poor ballot design.

The ballot had a list of names and big arrows pointing to the hole to punch. This is a normal ballot design. You always have lines on ballots, text [description of amendment, tax change, bond issue, etc.] The position of the hole to be punched is always identified. You don’t just punch anywhere on the ballot.

Typically a ballot has the names on the left and the punch holes on the right. In this case, the ballot had names on both sides with the punch holes in the middle. BUT, both Bush and Gore were on the left, where everyone would expect them to be. It is only candidates whose names were to the right of the holes that can complain about ballot design.

That county with the 19,000 double punched ballots could use more voter education. If a voter messes up or changes their mind, they should get a new ballot. Note that the voting machines only count “approved” punch positions. If you miss the “arrow” hole, then re-punch the ballot, the ballot will be counted correctly. It is only when you punch the “arrow” holes for two candidates that the ballot is invalid, since you can only vote for one.

8

There’s nothing that’s stopping Bush from asking for a recount too. If the claim is that the vote is so close and the method of hand counting is so error-prone that the vote will essentially switch back and forth randomly every time it’s recounted, then whoever loses a particular recount will have every reason to demand another recount, since he’ll have a 50% chance of winning the next recount. Suppose that the entire state of Florida is recounted a dozen times and the successive tallies are Gore by 17, Bush by 12, Bush by 18, Gore by 21, Bush by 20, Gore by 6, Gore by 22, dead even tie, Bush by 11, Gore by 8, dead even tie, and Bush by 3. It would then be apparent that the ballots used in Florida are so error-prone that in a close election no definitive winner can ever be declared. Who knows what a judge would decide in that case? Perhaps he should declare that Florida must redo the entire vote, and they must ship in voting machines so they can do it accurately this time.

9

If the counters were using what the voter did on the rest of the ballot to guess who they are voting for for President, that would be clearly wrong. However, if the problem is that the punching of a card is such an inaccurate procedure that many ballots where a voter intended to vote for a particular candidate aren’t recorded by the machine because it’s difficult for a person of normal abilities to be sure that they have completely punched out the holes, then I’d say that there’s a good chance that a judge would order a new election because Florida had such a badly designed ballot that no accurate total could be determined.

10

Not so at all. In Palm Beach County, at least, they are using pre-determined rules for the recount. There are standards for determining whether or not a computer ballot has been “punched” or not. If the “chad” (paper divot) is hanging by one to three threads of paper, it’s counted. Those where only two threads have been broken are not counted, and neither are those where the divot is merely indented (“pregnant”). This according to this morning’s Miami Herald.

This said, the standards used for recounts in different counties may be different, which is one aspect the Republicans are complaining about.

The reason only certain counties may be counted is that the Democrats got their challenges in in time. I believe in most cases challenges must be filed within 72 hours, so the Republicans may be out of luck. (Though I’m sure they’ll contest this). Personally, I agree that the whole state should be recounted, and let the chips fall where they may. That’s the only way for the election to have any credibility in the long run. But local regulations could forestall this.

Regarding the OP, the statistical argument is flawed. Statistical error only applies when you are sampling from a population. If you are enumerating the entire population, and some objective standards are applied to the enumeration, at least in theory it is possible to arrive at an exact count. In a recount such as the one in Palm Beach, you might have (1) disputes about the application of the objective standard to a particular ballot; or (2) errors in arithmetic. But these are not, strictly speaking, statistical errors.

11

To clarify, Florida law mandates a recount if the original tally difference is less than 1/2 of 1%. The mandated recount means that the ballots are retabulated using the same method originally used to count the votes. If the votes were originally machine counted, a candidate may request a recount by hand. Each county election board has the authority to grant or deny a request for hand count. A hand count is never required by law.

Oh, geez. I just disputed the answer of a well known and much loved (oft loved?) board Administrator. Oh, well. I never really liked it here anyway.
::bows head, awaits falling blade::

12

That’s not what I saw on the Fox News Channel on Sunday.

I wish I would have caught the guy’s name. It was a middle-aged man with strange hair who was giving a brief press conference about the PBC recount (and getting annoyed with people interrupting him, if that helps anyone remember). He was basically getting a lot of flak because he came out and said:

  1. They’d started the recount going with the “dimple” parameter
  2. Then they’d tried the sunlight test
  3. Then they went to whether part of the chad had actually been punched out.

In short, they didn’t really have a standard to compare the ballots with. This is when I got even more frustrated than I’ve been. So, they counted for the better part of a day with no consensus on what constituted a vote? Who decided the right standard in the end–why is that standard correct and not others? Were different hand counters using different standards? It also does sound as though they kept trying different parameters until they saw a result they liked. I’m not saying that’s what happened, but I am saying the appearance is mighty funny. And that’s leaving aside the question of having people try to judge the “intent” of anonymous voters.

Ah well, I guess I’ll go over here and watch my 401(k) dwindle a bit more…

13

According to this story in the LA Times at http://www.latimes.com/news/nation/20001113/t000108811.html

the people doing the recount in Palm Beach County used two different methods of counting until someone found a copy of the official county vote counting guidelines that were passed on November 6, 1990.

Once those guidelines were set, the counting was restarted a second time and completed using those guidelines.

14

In any measurement or count there is a margin of error. Take a million ballots and count them by hand or machine a hundred times and I doubt you’d come up twice with the same number. As has been said in some otehr post, it is usually the people who can’t balance their checkbooks who think you can just count once and arrive at a number which is certain.

15

Regarding the posts by Palandine and BobT, the reports you cite may well be correct. I was just going by what the Miami Herald said yesterday. Today they are describing the method differently. There are four points of connection of the “chad.” The diagram they published indicates that if even one of the four links is broken, the ballot is counted, but if it is only dimpled (or “pregnant”) it is not. But this is not the first time the Herald has screwed things up.

What’s the margin of error on counting 10 votes? On 100? And banks somehow do manage to get accounts balanced eventually, even thos of $1 million.

But regarding the OP, such counting errors are likely to be miniscule compared to the +/-1% cited. What would you say the average counting error on 1 million votes would actually be, if done carefully? 10? 100? For the figure cited in the OP to be correct, you’ld have to be miscounting, on average, by almost 60,000 votes in Florida as a whole.

As I stated before, such counting errors are different from from statistical errors, which conceptually are based on sampling a population, not on a full count.

Is there any truth to the rumor that an international commission composed of the ex-Presidents of Panama, Ecuador, and Haiti has been sent to monitor the Florida recount?

16

>> What’s the margin of error on counting 10 votes? On 100?

10 votes is a small sample so I would say the best answer is that it is 1/1000th of 10,000 votes. With only 10 votes in some cases it may be 0% and it could be 30% if you happen to have three ballots which are doubtful.

>> And banks somehow do manage to get accounts balanced eventually, even thos of $1 million

Yes, they balance them by force. They do not wait forever to clarify every error like they are trying to do in Florida. They have an account where they brush all these things into and they move on.

Some years ago a bank did not charge me for something I put on my credit card. Do you think they are still wondering where the money went? I bet they have balanced their books and moved on.

You fail to understand something which is that there will always be a certain margin of error in the recording and transmission of information. There is no way around this.

You can diminish it by building in redundancy and error checking. For example you could ask people to vote twice using two different types of ballots. Then you take the average of the two counts. Many web sites will ask you to type your email or passwaord twice just for this purpose.

Note that you can never eliminate errors, just diminish them by spending more time and resources. Look at the specs for any computer item and you will see the error rate. A CDrom has an initial error rate of whatever it is. It is very low by our standards but too high for computers so they have built in a number of protections in the way of introducing redundancy, error correcting codes and other things.

I can give ONE ballot to ten people and they can come up with different answers. Six may say it is a valid ballot for A while three may say it is a valid ballot for B and one says it is an invalid ballot.

If you think you can count a million votes and come up with a definite number, then you are just not understanding the scope of the problem.

17

sailor, we are talking about two somewhat different things here. You seem to be mostly emphasizing classification errors here, while I was primarily talking about counting errors. Classification would come in if one were deciding whether a particular ballot should be counted for Bush or for Gore, (or for neither). There would be no such classification errors, if, say, voters had handed in a black ballot for one and a white ballot for the other. It is only because there can be some question about whether the “chad” was actually punched that different people, or a computer, might give different answers in classifying the same vote.

You are correct in saying that classification errors may not be completely resolvable if the distinction between classes is somewhat difficult to discern. In the case of black vs. white ballots, one would hope that all observers would classify them the same way (but you never know, especially in Florida). In the case of the Florida recount, use of objective criteria should resolve the classification for the vast majority of ballots. But yes, there may be some ballots on which two observers might disagree on whether a particular corner of a chad is broken or not. (Though based on the Palm Beach criteria, it’s hard to imagine a ballot so screwed up that “Six may say it is a valid ballot for A while three may say it is a valid ballot for B and one says it is an invalid ballot.” If other criteria had been selected, such as a “dimpled” chad, that might have been the case.)

Counting errors are different. On a sample of 10 votes, unambiguously classifiable (e.g. black or white ballots), there should be a counting error of zero (I hope!). Likewise on 100. But yes, counting errors are bound to occur on very large samples. However, unless you do the count very carelessly, the counting error on even 1 million is not going to be anywhere close to +/-1%, the figure the OP cited.

And I never said there would be no classification errors or counting errors at all in enumerating a very large sample, but rather that these errors will not be remotely as large as that cited in the OP.

18

>> sailor, we are talking about two somewhat different things here. You seem to be mostly emphasizing classification errors here, while I was primarily talking about counting errors

Well, the point is you are always going to have both and you have to find a level of practicality.

The OP says:

My point is that is dumb. Counting and recounting does not get you any closer. well, I guess it does in the sense that you could specify that every election has to be recounted 100 times and the results averaged. Do you really think this is viable. Come on, every vote counts but not that much.

Yes, I am also sick and tired of hearing the “every vote counts” song these days. Well, I would amend that to “every valid vote counts”. If you are too dumb to punch a hole and the chad gets in the way, then tough cookies.

There are many reasons why people can’t vote and we don’t hold up an election for it. If you have a car accident on your way to vote and you can’t vote that day, though it’s by no fault of yours we’ll just have to say we’re sorry and better luck next time.

If we absolutely, positively must make sure every last person gets a chance to vote, then the system becomes impracticable.

Things cost money. How much money are you willing to spend on this? We could have machines which would “validate” the ballot before you cast it. That would cut back on bad ballots (like punched twice) but not on mistakes. We could have ballots which required marking the same name under two different forms just for confirmation. We could…

As I have said before, I think the people defending that position just do not have a clue of what it is like to work with numbers and demand a certainty in the results that is just not feasible even if God were doing the recount. These are the same people who have difficulty balancing their bank acoounts any month there are more than ten postings to their accounts.

These are the same people who often make a nuisance of themselves at condo and other associations because they demand an impossible perfection. When it is their turn to do it, then they usually do a much worse job. (I have an aunt of mine in mind right now.)

19

Hold on, sailor, I think we’re getting a little off the point of the OP. I would agree that mistakenly double-punched ballots should be thrown out. But the OP said nothing about people who weren’t “able” to vote.

The OP was basically about what the degree of variation of successive recounts might be relative to the actual difference between the candidates. I think the estimates cited in the OP are clearly wrong. But whether or not successive re-counts are “worth it” does partly depend on the “actual” difference between the candidates’ totals.

One the first state-wide recount, Bush’s margin of victory narrowed from c. 1,800 to c. 300. Therefore the combined counting/classification error was on the order of .00025 (.025%), or 1/40 the error of +/-1% cited in the OP. However, I suspect that on any sucessive recounts of the same ballots the difference from the second recount will be even less, as some sources of classification and counting error will have been cleared up.

However, one thing that is going on in Palm Beach is that ballots considered to be “blank” by the computer and hence invalid, are being re-classified as being valid votes for one or the other candidate (although some will still remain invalid). Gore’s main hope is that more of these “invalid” votes will be re-classified for him rather than for Bush. So in this case we are mainly dealing with a dispute about correct classification, rather than a counting error.

My feeling is that most of the difference between any successive recounts is going to be due to classification changes (whether certain votes are valid or invalid) rather than simple counting errors.

While I can’t substantiate this, my gut feeling is that on a statewide recount, true counting errors alone are unlikely to amount to 1000 votes, once the classification of each ballot has been agreed on (if it ever can be). However, counting errors might well be of the order of 10-100. If one candidate wins by 1000, I for one would feel it was reasonably credible. (Leaving aside the entire issue of people who made mistakes in punching their ballots.) If one wins by 20, well, I agree that would be pretty dicey.

OK, maybe not “every vote counts,” but every 100 do.

20

Colibri, I agree with you that it is “classification” and not “counting” where most of the variations occur but please note that when they say “recounting” they include both things. A ballot that was considered one thing last time it was counted can now be classified differently in the new count. So, according to your terminology, it is a reclassification and recount. They may call it recount but according to your terminology it is mainly a reclassification.

The thing is that machines are more impartial even if not so precise. They would have the same percentage of errors for all voters. A manual recount could probably be more precise but it is also subject to the subjective leanings of the counter. In the end they’ll settle on most ballots and a few will have to be taken to a judge for him to decide. I’m not saying it shouldn’t be done, just that it’s messy and costly.

I think the OP is clear that he feels every vote counts and therefore we should spend unlimited time and effort to find out what the issuer intended even if the ballot is quite confusing. My position is that it is not reasonable to do that.

I just wish all those people who are so outraged that their vote should be taken into account would have paid more attention when they were voting.

Even the Democrats are saying their voters turn in more invalid and faulty ballots because Republicans tend to be more literate. Well, it might be an argument in favor of recounting but it sure ain’t an argument in favor of the democrats.

Here in DC where I live, I have a neighbor who is an 85 year old woman who is almost blind and can hardly take care of herself. I have to help her with many chores including paying her bills as she can hardly write. I write the checks and she signs them.

This woman is confused by the simplest things. She doesn’t know if a piece of mail is a bill that needs to be paid or not. I have to explain everything to her.

I asked her if she was going to vote and she said, yes but if this woman is capable of issuing a valid ballot I would be surprised.

If the system slightly favors those voters who are more literate, better informed and capable of understanding what’s going on around them, then it cannot be entirely bad.