Elections are just Math. Really big, really important math.
Previous posts discussed polls and markets, two common ways of learning a group's preferences. Voting is another.
In the U.S. presidential election of 2000 many voters' preferences were not recorded properly or not included in the totals:
● machine error—400
● cast but not counted—155,000
● tried to vote but couldn't—2,000,000
That's 2% of the vote—lost!
Would a system that counted each voter's preference more accurately have made a difference?
In the 2000 election Bush beat Gore in Florida by 537 votes, out of 5,963,110 votes counted. (That's 0.01%.) On the other hand Gore beat Bush in New Mexico by 366 votes (0.1%), in Iowa by 4,144 votes (0.3%), and in Oregon by 6,765 votes (0.4%).
What is a vote? It is an effort to aggregate the individual preferences of the members of a group to determine the preference of the group as a whole.
A vote is not a "sample". Each member of the group is given a chance to express his or her preference. There are various ways of aggregating the votes of the individuals who actually do vote, none of which is perfect. The certified result is then declared to be the collective preference of the community. But is it? (In U.S. presidential elections the votes of the people are filtered through the Electoral College—but that's another story.)
In U.S. national elections we use the "first-past-the-post", "winner-take-all", "plurality" voting system. Whoever gets the most votes wins. Leaving aside whether this is really the fairest way of aggregating preferences or not, what does it mean to say a candidate "got the most votes"?
In the U.S. presidential election of 2000, according to the official tally (http://www.fec.gov/pubrec/2000presgeresults.htm ) George Bush received 50,456,002 votes and Al Gore received 50,999,897. Operation of the Electoral College gave the presidency to Governor Bush. There were a total of 105,405,100 votes tallied.
But do these figures really represent the preference of the voters?
● No vote-recording technology is perfect. Federal rules require that voting equipment have machine failure rates below 1 in 250,000 in order for the machines to be certified. (Some states have tighter standards.) That means that more than 400 votes for president could have been registered incorrectly, even if the equipment was working perfectly as designed.
● There were about 40 million registered voters who cast no ballots. According to estimates made after the election (by the Census Bureau) between two and four million of these potential voters did try to vote, but were prevented either by problems with the voter-registration system or difficulties with operation of polling places. Even at the lower estimate, those two million votes could have had an impact on the election outcome. (additional information at http://www.vote.caltech.edu/ )
● Even the most reliable voting methods (paper ballots and lever machines) show a "residual vote" (ballots cast where no presidential vote was recorded) of about 1.6%. Punch-card and electronic systems have a significantly higher rate. The overall "residual vote" rate for the presidential elections from 1988 through 2000 was 2.1%. Some voters, of course, may have intended to leave their vote for president blank. This number is thought to be about 30% of all "residual votes" (based on exit polling). But the rest of the residual vote is due to votes cast but not counted, votes not recorded due to voter error, or "overvotes" where more than one presidential preference was indicated, and so none was counted.
Those uncounted votes (that were not legitimate abstentions) totaled about 155,000 in 2000. Certainly enough to have affected the outcome, depending on where they were cast.
So in what sense does the outcome of a U.S. presidential election accurately represent the preferences of the voters? Well, it is a system that produces an outcome, which is in essence what a vote is supposed to do. But it is not perfectly accurate—what human endeavor could be?
Even considering only those who actually were able to cast a ballot in 2000, about 150,000 of them (0.1%) were not correctly recorded or counted.
But the much more serious problem is the two million voters who were not able to vote at all. Many of these denials were due to poorly maintained voter registration databases. (Need more and better nerds!—Quick!) The rest were due to confusion at the polling place, often due to poll workers being inadequately trained to help voters with unfamiliar machines, or inadequate polling locations or hours, leaving potential voters literally shut out.
Elections are counting and counting is math. Elections are really big, really important math.
Make your vote count!