This is not meant to spark a political debate. This is purely a mathematical question for any statistics geeks out there:
If, say, 3 million votes are being counted by a less than perfect process which introduces a small but finite random error (for example, 2% of the votes randomly get thrown out as “no vote”), what is the standard deviation on the final count? Is it more than, say, 537 votes?
Or turn the question around: Suppose there were 6 million votes cast in an election, and, after the votes are tallied, the margin of victory of candidate B over candidate G is 500 votes. Given that there were errors in the counting process (purely random, not biased toward one candidate or the other), what is the probability that candidate B actually received more votes than candidate G? Is it much greater than 50%?
I ran a quick computer simulation (about a 20 line BASIC program) to try to answer the question. I gave each candidate (I arbitrarily called them “Bush” and “Gore”) the exact same number of votes (2970750) then had the computer count them, but each vote had a random 2% chance of not being counted. I ran the program several times. Here were the results:
In this case, using Y and N, you have the machine count Y votes and N votes. There are some that are invalid and not counted.
If the vote is close, you recount the Y and N votes, this time including ballot boxes found in the broom closet, but leaving out any ballot boxes left in the car trunk. Again, some are ruled invalid.
Since this is not a perfect world, you are not counting the exact same ballots the second time.
Then you get to use the 1-900 psychic hot line to determine the intent of the invalid votes, if possible. Here, the psychic changes as the counting goes on. This is normal learning. [“I’ve now seen that mark a lot, it must mean something so I’ll count it now.”]
[opinion]
It’s possible, nay probable, to ultimately select one of these guys for President. However the selection will necessarily be somewhat arbitrary. It is not probable that we’ll ever know, with reasonable confidence, who garnered the most votes, due to the margins of error, rejected ballots, and the poor voting process, in general. Not to mention that some of the evidence has now been tainted.
It’s like a photo finish at a horse race where you find that not only were there multiple camera angles with different results, but also the cameras turn out to be the pinhole variety made from oatmeal boxes and they used dental floss to trip the shutters… and then you find out your film is very old… and it’s over exposed in the developing process… and then the Democrats and the Republicans each want to use their own photo retouchers to “clean” up the images…
[/opinion]
A little semantic quibble - it may not be possible to determine which candidate received most popular votes beyond the maring of error, but it is possible to know which candidate has won - wait for the electoral college vote.
I would think that even with the best equipment/system, in a close elections, the random errors will be significantly more than the magority count. And if you vote electronically, how do you recount it?
In parliamentary systems like the U.K. and Australia (and probably in other countries) there have been relatively recent cases of tied votes and the electorate being decided on the toss of a coin or a draw from a hat. I don’t believe it has ever had an influence on which government was formed though.
Now there’s something to attract some prime time TV ratings. "Mr Thurmond, if you would please toss the coin now … remember ladies and gentlemen if it’s heads it’s President Bush, tails it’s President Gore.
The trouble with determining who received more votes isn’t one of counting them accurately. Given a set of agreed standards based on objective criteria, every voter’s ballot can be properly tallied; human error in keeping straight the process can be remedied with cross-checks, redundancies, etc.
Where the process in Florida has run into difficulty in reaching an agreed upon result is that the people involved, candidates and counters, cannot agree on objective criteria for counting votes. Mr. Gore and his supporters want anything that might even seem like a vote counted, confident that, since there were high numbers of ‘undervoted’ ballots in heavily Democratic counties, this ‘standard’ would result in the best chance of a victory for Mr. Gore. Mr. Bush’s camp has argued that any manual recount would necessarily involve subjectivity, making the result dependant upon who did the counting; his position appears largely based not upon reason, but upon the simple fact that, in the absence of manual recounts, vote totals would make him the winner. I don’t think there is anyone with real objectivity who believes that, if the facts were reversed, the positions wouldn’t be reversed.
All of which makes me think the voting machines we use here in Lucas County, Ohio (where Toledo is located) make a lot of sense. You can’t vote for more than one candidate for an office with ‘vote for one only’ criteria, and in order to not vote, you have to fail to pull any candidate’s lever. Recounting consisists of re-reading the numbers recorded on the machines and adding those numbers up. No chads, no stray marks on Scantron™ forms being incorrectly read (anyone who says such fill in the circle forms are inherently accurate has never scored a test using such a sheet). A vote or no vote, pure and simple.
Of course, the machines cost an arm and a leg, no one makes them any more, and the replacement parts are impossible to find…
Not to mention that the machine process isn’t perfectly error-free, either. This year, there were a number of precincts in the city of Boston that initially reported zero votes either way on some of the referenda. Turns out the poll workers were reading off the wrong dials on the backs of the machines. Those errors would not have been found if the numbers hadn’t looked suspicious.
COntinuing in that vein… Gore seems to have won twice as well…
woolly:
If managed properly, the random error factor can be mitigated. In many places the order of the candidates on the ballots are randomized. All machine counts and fixed ballot structures have some bias, but with randomized balloting, these random errors are distributed evenly between the candidates so it’s less likely that one candidate will suffer from a machine or ballot structure bias.
The most enlightening thing about this election is finding out that we’ve learned nothing from the scientific method in all these years… Of course, who ever claimed that the political process was in any way scientific??? Or even non biased, for that matter???
A election is simply a measurement. In this case, a measurement of voter preferences. Like any measurement, there is a margin of error, no matter how the measurement is taken. In almost every election, the measurement is outside the margin of error. (eg. Candidate X won by 100,000 votes, give or take 2000) In this case, however, the measurement is within the margin of error. We cannot determine factually who won. Therefore, we move from a factual question (who got the most votes) to a political question (who should win).
I have always thought that the main difference, generally speaking, in the world view between conservatives and liberals is factual vs. political. (Note - by factual I do not mean “correct”, I mean “concrete and provable”) Conservatives tend to lean toward the factual. They are “law and order”, and rely more on rules and authority. Liberals tend more toward the political. They are more relativistic and more interested on what “should” be.
A recent survey (no cite, sorry. I read it in the paper yesterday) says that Democrats are twice as likely to accept the legitimacy of a Bush presidency than Republicans are of a Gore presidency. I think this is because Democrats are more accepting of the legitimacy of the political process than Republicans. As the determination of the next president is a political one this time, Gore will have a much tougher time as president should he prevail than Bush.
Error can never be eliminated, even with the most sophisticated system. The American voting system is far from sophisticated, though. Old voting machines of ancient design and dubious reliability still serve because counties typically have much better things to spend their limited funds on.
Recounts could be handled even if voting was done electronically. Perhaps a printout of each vote could serve as a backup if you even wanted a hand recount.
An improvement in the reliability of the machines will reduce, but not eliminate error. Improvement in voting and ballot design techniques like JoeyBlades suggested, will help to reduce systematic error too.
If it comes down to it; I’m sure some sort of gladatorial combat between the two candidates would have much better TV ratings than court cases in the event of a tie.
Hey! Now your talking. The only problem is Bush wouldn’t stand a chance… having only served in the gladiator reserves and being absent for nearly a whole year of training, at that…
Yeah! Let 'em Rochambeau for it! On Pay-Per-View, to cover the costs, of course.
[Cartman voice] First I kick you in the nuts as hard as I can, then you kick me in the nuts as hard as you can, and the loser is the one who quits first[/Cartman voice]
I’m betting on Gore. The conservative is too compassionate.
