A little bit about how error interacts with voting:
Counting is difficult. And yet, voting, which has such a huge impact in the United States, relies mainly on people’s ability to count. And, as I’m sure most people know, counting large numbers of anything always leads to mistakes; inherent in every election is error. Typically in elections, these don’t make much of a difference in declaring a winner because the error is much smaller than the difference in votes between the candidates. This means that if you take the error (let’s call it x) and add plus or minus x to the number of votes a candidate received, it would not change who won the election. It happens in every election that a few hundred votes go missing or are just miscounted, but typically these are ignored and never mentioned because they wouldn’t make a big enough impact on the election.
But there are those few elections in which the error made a huge difference. The example that comes to most people’s minds is the Bush v. Gore election in 2000. Many votes were miscounted because of poor ballot layout or because people filled out the ballots improperly. As Charles Seife writes, “Even under ideal conditions, even when officials count well-designed ballots with incredible deliberation, there are errors on the order of a few hundredths of a percent. And that’s just the beginning. There are plenty of other errors in any election. There are errors caused by people entering data incorrectly. There are errors caused by people filling out ballots wrong, casting their vote for the wrong person…[b]allots will be misplaced. Ballots will be double-counted” (163). When the winner is unsure, the first thing people do is order a recount, not taking into account that every single time they count, there will be errors associated with the end number, even if those errors are different among recounts. It is impossible to get the “correct” number of votes for each candidate.
According to Seife and many other political thinkers and mathematicians, the 2000 election was a tie; the error was too much bigger than the difference between the candidates to conclusively say one candidate one over the other. As Seife writes, “It’s hard to swallow, but…the 2000 presidential election should have been settled with a flip of a coin” (166). However, no one likes the idea that an election can be a tie, so we operate under the idea that we can find a real victor if we recount enough times.
Next in the series, the law of large numbers and probability!
Charles Seife, Proofiness
Jonathan K. Hodge, The Mathematics of Voting and Elections: A Hands-On Approach