In theory, elections are perfectly run. Voters make their voting intent perfectly clear. Election officials are perfectly incorruptible and infallible. And when polls close, every single vote is perfectly counted.
And so in theory, it makes no difference whether a candidate wins by one vote or by a million. Either way, he’s declared the winner and the loser graciously concedes. Simple as that.
But in practice? Not so simple. In practice, elections are not perfect. They’re messy and badly-run. Which means there’s plenty of room for error, malfeasance, and disputes.
And so in practice, there’s a huge difference between a one-vote and a 1M-vote margin of victory. If the margin’s a million, the loser will usually concede. That’s because in any semi-respectable democracy, no degree of error or malfeasance could possibly explain a 1M-vote shortfall. In contrast, if the margin is just one vote and the stakes are sufficiently high, then the loser will almost certainly dispute the result.
In theory, there is a very easy way to resolve disputes: Count and recount the votes until we’re absolutely sure who the true winner is. But in practice, the election may be so messy and badly-run that this is impossible, especially if the clock is ticking.
And so in practice, very close elections are decided not only by the “true” vote count, but also by other nebulous factors. Like who controls the courts and other positions of power. Who has the better legal team. Who’s prepared to fight a little harder and dirtier.
This was most vividly illustrated in the 2000 US presidential election, which came down to Florida. The first official count had Bush ahead of Gore by 1,784 votes or 0.03% of the nearly-6M Florida votes cast. In a perfect election, Gore would simply have conceded. But he didn’t. And so began the 36-day recount battle.
The final official result would be that Bush won Florida — and hence the US presidency —by a 537-vote or 0.009% margin. Most subsequent analysts agree Gore should’ve won. As one writer puts it: “there can be little doubt that more Florida voters who cast ballots in the 2000 presidential election preferred Gore to Bush and that a well-functioning electoral system would have accurately captured this preference, thus making Gore the winner of the presidency.”
The 36-day recount battle has been covered ad nauseam in books and even a HBO movie. Here we’ll simply mention three of the biggest controversies.
Controversy 1. The confusingly-designed butterfly ballot used in Palm Beach county. Depending on which academic analysis you believe, this confusing design cost Gore either several hundred or several thousand votes.
Controversy 2. Katherine Harris. Florida Secretary of State. Oh and also co-chair of Bush’s Florida election campaign. It is well-known that during the 36-day battle, she repeatedly hurried to certify Bush as the winner and stall recount efforts.
But an earlier abuse of power was probably more consequential. Pre-election, she incorrectly purged thousands from the list of legally-eligible voters. For example, a voter named Willie Steen was mistaken for a convicted felon named Willie O’Steen and thereby wrongfully disenfranchised. A disproportionate number of such wrongfully-disenfranchised voters were black and would’ve voted overwhelmingly for Gore.
And now for the darkest controversy. On Day 35 of the recount battle, five US Supreme Court Justices ruled to block all further recounts. This handed Dubya the Dubya and forced Gore to concede the following day.
No prizes for guessing these five justices’ political leanings.
Take Sandra Day O’Connor. According to witnesses at an election-night party, when the TV networks initially and incorrectly called for Gore, O’Connor was disgusted and exclaimed, “This is terrible.” Her husband then explained that “his wife was upset because they wanted to retire to Arizona, and a Gore win meant they’d have to wait another four years”, because she “did not want a Democrat to name her successor.”
Five weeks later, O’Connor would be one of the five justices that ended Gore’s presidential hopes. The five justices’ ruling was, of course, based entirely on sound jurisprudence, and had nothing to do with their personal interests or prejudices.
Now. Let’s go back to the puzzle of voting. In a perfectly-run election, there are two clear-cut scenarios where your vote matters.
But as we’ve just seen, real-world elections are NOT perfect. And so in real-world elections, what do we mean by your vote mattering? Does your vote even matter?
One possible answer is that your vote simply never matters in real-world elections. As Steve Levitt — Chicago economist and Freakonomics author — put it:
“If it’s even within thousands of votes, it’s not the votes themselves that decide the election, because nobody can figure out how many votes were really cast. It’s the courts that always decide, the judges who always decide.”
This though was just a passing remark in a podcast. For a more serious analysis, let’s take a quick look at the academic literature.
Two papers argue that your vote matters not when it creates or breaks a tie, but when it triggers a recount or eliminates the possibility of a recount. Doing the math, the papers conclude that your vote still matters, though less than it would in a perfect election.
A third paper argues instead that there is some grey area, where the vote is very close. Outside the grey area, either candidate wins for sure and your vote doesn’t matter. But within the grey area, both candidates have some chance of winning and your vote matters because it gives a tiny boost to your candidate’s chances of winning. Doing the math, the paper concludes that your vote matters just as much in a real election as in a perfect election.
The literature on the puzzle of voting is vast. But unfortunately, these few analyses are all I can find. Which suggests that very little thought has been given to the issue. Moreover, even these few analyses have produced three different conclusions.
So. When we ask, “Does your vote matter in real-world elections?”, we must unfortunately give the scientist’s most-common and most-unsatisfying answer: “We don’t know. More research is needed.”
In the next video, we’ll check out how tied elections are actually broken around the world.
 Ballot Battles: The History of Disputed Elections in the United States by Edward Foley (2016), p. 280.
 The seven books depicted are: Too Close to Call: The Thirty-Six-Day Battle to Decide the 2000 Election (2001) by Jeffrey Toobin; Supreme Injustice: How the High Court Hijacked Election 2000 (2001) by Alan Dershowitz; Breaking the Deadlock: The 2000 Election, the Constitution, and the Courts (2001) by Richard Posner; Bush v. Gore: The Question of Legitimacy (2002) edited by Bruce Ackerman; The Longest Night: Polemics and Perspectives on Election 2000 (2002) edited by Arthur Jacobson and Michel Rosenfeld; The Voting Wars: From Florida 2000 to the Next Election Meltdown (2012) by Richard Hasen; Ch. 11 of Ballot Battles: The History of Disputed Elections in the United States by Edward Foley (2016). The HBO movie is Recount (2008).
 Wand et al. (2001): “more than 2,000 Democratic voters [voted] by mistake for Reform candidate Pat Buchanan, a number larger than George W. Bush’s certified margin of victory in Florida.” Smith (2002): “A typical result shows a point prediction of 371 and a 95% prediction interval of 219-534.” Andres & Feuerverger (2005): “none of our point predictions for Buchanan’s vote exceeds 1000, with most lying well below this value” (Buchanan’s official tally in Palm Beach County was 3,407). There were also numerous hastier analyses by various academics during the recount battle — see this webpage.
 See NAACP v. Katherine Harris, “Vanishing Votes” (Greg Palast), “How the 2000 Election in Florida Led to a New Wave of Voter Disenfranchisement” (The Nation), and “Stealing An Election: Greg Palast Reviews How Florida Is Attempting To Disenfranchise Thousands of Voters (Again)” (Democracy Now).
 According to the Florida Ballots Project, had the limited recount of 61,190 so-called undervotes gone ahead, Bush would probably have won anyway. So in this sense, the 5-4 SCOTUS ruling, which concerned this limited recount, was not decisive.
However, if there had been a fuller recount that also included the 113,820 so-called overvotes, Gore would probably have won. See CNN’s summary. Note though that CNN’s summary limits itself to the narrow issue of recounts and doesn’t take into account other issues like the butterfly ballot or disenfranchisement.
 The blown calls by the networks was yet another bit of infamy in the Bush v. Gore saga. Most famously, when declaring the Gore win, CBS news anchor Dan Rather also added, “Let’s get one thing straight right from the get-go: We would rather be last in reporting returns than be wrong. If we say somebody’s carried the state, you can take that to the bank.” (Washington Post, New York Times.)
 See Isikoff, 2000, “The Truth Behind the Pillars”, Newsweek. See also Neumann, 2003, “Conflicts of Interest in Bush v. Gore: Did Some Justices Vote Illegally?”, Georgetown Journal of Legal Ethics.
 Bohanon and Van Cott (2002), “Now More Than Ever, Your Vote Doesn’t Matter”, and Heckelman (2003), “Now More Than Ever, Your Vote Doesn’t Matter – A Reconsideration”. Both in The Independent Review.
 Gelman, Katz, and Bafumi (2004), “Standard Voting Power Indexes Do Not Work: An Empirical Analysis” in British Journal of Political Science. See the one-page appendix.