Voting Power

Robin Hanson proposes a voting thought experiment:

Imagine that polls stayed open for a month before the election deadline, and that a random one percent of voters were upgraded to “super-voters,” who can privately vote up to twenty times, as long as they wait at least an hour between votes. When a super-voter votes all twenty times, their votes are doubled, and counted as forty votes. “Privately” means no one else ever knows that this person was a super-voter.

Having two votes is twice the power of a normal vote, and gives you twice the ability to choose a winner. In this scenario, if super-voters wanted to maximize their ability to change the outcome they would unquestionably vote twenty times. Yet Hanson suggests most people wouldn’t vote twenty times. I would suggest another way to imagine the thought experiment: given the ability to pay to be part of this one percent, how much would you pay to be a super voter? I’d bet the price would incredibly low. Why? Because even these “super-voters” have no ability to influence the outcome of elections.

At least for federal elections. In 2012, the closest state in the presidential election by percentage was Florida with Obama ahead by only 0.88% (Click on % or votes to sort respectively).

State Obama Victory Margin (%) Obama Victory Margin (votes) Electoral Votes Colorado 5.36 137,858 9 Florida 0.88 74,309 29 Georgia -7.82 -304,861 16 Maine, 2nd 8.56 28,783 1 Montana -13.65 -66,089 3 Nebraska, 1st -16.64 -43,939 1 Nebraska, 2nd -7.17 -19,087 1 Nevada 6.68 57,806 6 New Hampshire 5.58 39,643 4 North Carolina -2.04 -92,004 15 Ohio 2.98 166,277 18 Virginia 3.88 149,298 13

Several states or districts were actually closer in absolute victory margin than Florida, but not in percentage. Suppose that Romney had won Florida instead of Obama. This would have required an additional 74,000 people to vote for Romney or 74,000 Obama supporters to stay home, or half that number to switch from Obama to Romney. This isn’t out of the realm of possibility, but your puny 40 votes from Robin Hanson’s thought experiment would be worthless. Even if you could get Hanson to give you 74,310 votes instead of 40, all it would do would change Romney’s electoral votes total from 206 to 235, not nearly enough to win the presidency.

In fact, if you could strategically place votes, the least amount of votes you’d need to add to flip the outcome from Obama to Romney would be:

74,310 votes in Florida for 29 electoral votes

166,278 votes in Ohio for 18 electoral votes

149,299 votes in Virginia for 13 electoral votes

39,644 votes in New Hampshire for 4 electoral votes

That would get Romney to 270 electoral votes, winning 4 states by a single vote each, and requiring 429,531 votes in exactly the right places. So how much should you pay to get 40 votes in the 2012 election? $0, because 40 votes could literally do nothing to change the outcome.

Where Votes Matter

Needless to say, your single vote in a single state is even less valuable than 40 votes. There are some mitigating circumstances which would give your federal vote the chance at importance: you don’t know how close the election will be in your state and you don’t know which state will be the decisive one. But even this is only somewhat true; even though the 2016 election is months away, we are pretty sure that the most important states are Florida, Pennsylvania, Ohio, Virginia, and North Carolina. FiveThirtyEight does this by ordering all states on a scale of most likely to least likely to vote for a candidate; the state that pushes each candidate over 270 electoral votes is the decisive state. New Hampshire and Nevada are located near the others, but because they are worth fewer votes, they are not as likely to decide the election.

The problem for Romney in 2012 was that Florida was the closest state, yet his “tipping point” state was probably Colorado (or New Hampshire like we calculated earlier). People in Colorado actually had the decisive votes, yet their state was not competitive, so the election was largely over weeks before it actually happened.

This year, although there is still time, Trump is not competitive because he is losing badly in all the states mentioned above; he’s currently behind in not just Virginia and New Hampshire, but Ohio, Florida, Nevada, North Carolina, Iowa, and even Georgia. If Trump is in danger of losing Arizona even a few weeks before election day (recent polls have him ahead by only 2 percentage points), then the election will be over early.

Of course, things will change, and I suspect Trump will begin to lead again in North Carolina and Georgia. But to have a chance to be president, he’ll have to be competitive in Florida, Ohio, and likely Pennsylvania. If he’s not, he’ll end up like Romney with most votes cast on election day just fulfilling an already known outcome.

But irrespective of Trump’s competitiveness and barring unprecedented circumstances, if you don’t live in those mentioned states, your vote will be worthless regardless of what happens between now and election day. That’s an impressive fact. The purpose of the electoral college was to add a layer of indirection between pure populism and the presidency, but all it has succeeded in doing in make some states matter and others not matter at all.

Should You Vote At All?

There’s no getting around this question given how useless your vote is. The bottom line is that when it comes to presidential elections and pure cost-benefits discussion, if you don’t live in a swing state and your time is even marginally valuable to you, you should not waste time voting for president. People talking about your civic duty to vote convey a nice idea, but there’s no denying the electoral math.

Of course, this doesn’t mean you shouldn’t vote at all! The US is somewhat democracy obsessed, and there are usually very important other races to vote for. Senate and House races are often not very close, so you’ll have to check to see if your own local elections are projected to be close (the Cook Political ratings for House, Senate, and Governor are good places to start), but local elections and direct ballot referendums are much more likely to be competitive and will often affect voters’ lives more directly than federal elections. Of course, these also require a bit more research than presidential elections where information is plentiful.

The other point is that voting is fun. Americans love voting, because it feels like you’re involved in something bigger. Even if, mathematically, you’re not part of something at the federal level, you have the ability to make impacts on your local area.

Should You Vote For A Third Party?

We’ve already discussed that your presidential vote is worthless if you don’t live in a swing state (assuming they have any value at all). However, given that people can still find good reasons to vote in local elections, a local voter will already be in a position to cast a vote for president. The marginal cost of voting for president will be a matter of seconds. Given that, should you vote for a third party?

If you don’t live in a swing state, the answer is obviously yes. Of course, this assumes you actually prefer a third party to the normal Republican and Democrat choices. I don’t think this is too hard, and you can fill out surveys like isidewith.com and see what other political choices are available. Especially this year, there are plenty of people on the left disappointed with Hillary Clinton’s lack of integrity and hawkish foreign policy. And on the right, there are plenty people who would rather not vote for Donald Trump for any of several thousand reasons. If you don’t live in Florida/Pennsylvania/Ohio/North Carolina/Virginia, then there is no reason not to vote for a third party, as the outcome of non-swing states is already decided. If the outcome for any non-swing state is in danger, then the election is a landslide victory anyway (i.e. if Georgia is competitive, Hillary already won, so vote your conscience).

There’s also good reason to vote for a third party you like rather than leave that part of the ballot blank; Republicans and Democrats have been making it difficult for third parties to get onto the ballot for decades. The latest idea of the NeverTrump Republicans is to draft Evan McMullin to run for president. Well guess what? People won’t be able to vote for him in most states because of how difficult Republicans and Democrats have made it to get on the ballot. But people who vote for third parties in November will be directly helping those parties surpass ballot access requirements for the next election cycle. Many states allow automatic ballot access for the next election cycle if a party receives 3-5% of the vote in an election, depending on the state.

Should You Vote For A Third Party In A Swing State?

If you do live in a swing state, chances are you should vote for third party anyway! Most elections become less uncertain as we get closer to election day, and the chances of your swing state being both competitive and the decisive state are very low. In the last 10 elections, 2012, 2008, 1996, 1992, 1988, 1984, and 1980 were not particularly competitive. It actually didn’t matter who you voted for in these elections. In 2004, John Kerry needed over 100,000 additional voters (out of almost 5.6 million cast) in Ohio to win, and while in retrospect that’s a fair margin, it was within the margin of error for polls. It seems that most knew Ohio would be the big battleground state. But even if you combine all third party voters in Ohio, there’s not nearly enough to cover the margin. We could say that over 100,000 Bush supporters in Ohio could have voted for a third party without changing the outcome of the election. That’s a lot of people. In 1976, Ford only needed about 50,000 votes in Wisconsin and Ohio and he would have gotten 4 more years. It turns out that there were a substantial amount of third party votes for Eugene McCarthy, but it’s unlikely McCarthy voters were about to side with Ford over Carter. It seems we could say about 50,000 additional third party votes could have been cast in Ohio and Wisconsin instead of being cast for Carter.

Now the most famous case of third party votes changing an election is Florida in 2000. Here Bush beat Gore by around 500 or so votes, while Ralph Nader, the Green Party candidate, received almost 100,000 votes. We should not discount Nader supporters; they knew they had the option to support Al Gore if they wanted to. They decided they’d rather vote for Nader, which is certainly their prerogative. The question should be, if they had a choice, would 500 more Florida Nader supporters have favored Al Gore being president over George W. Bush? If so, the the Green Party caused the president to be someone Green Party supporters did not prefer. It’s also likely quite a few more than 500 Nader supporters would have wanted a Gore presidency over a Bush presidency with Nader being a far left-of-center candidate.

But we have to emphasize that the 2000 Florida situation is simply unlikely; most elections are not close, and even when they are, hundreds of thousands of voters are needed to change the outcome, not 500. If there is a chance of a swing state being the decisive state, and you happen to live in that state, and you have strong preferences between the two major party candidates, you could make an argument that you should vote for a major party over a third party, but that’s the only situation where there’s even an argument.

Another way I put it on facebook when discussing this year’s election with someone who opposed Trump:

“If Johnson voters would otherwise vote for Clinton, and if those voters live in a swing state, and if the election is close enough where 1 or 2 states could decide the election, and if Clinton were to lose by a margin smaller than the amount of Johnson voters who would vote for her, then a vote for Johnson is a vote that could cost Clinton the election. But it’s still not quite as bad as a vote for Trump.”

Remember, this is the only criteria for why you should vote for a Republican or Democratic presidential candidate. Even if you like them more than third party candidates, if it’s not a swing in a decisive election, it’s irrelevant that you vote for those candidates. The additional margin of victory changes nothing for them, and they already have ballot access.

The American electoral college was built to choose a president among many different candidates. Thus, in most states, you can vote for your ideal candidate without issue. The concept of “wasting” a vote on a third party makes no sense in most contexts because the electoral college will ensure that your vote is a “waste” already. If the election were a direct popular vote, voting for a third party would be a bigger issue (an issue that could be solved easily via instant runoff voting). But we don’t have that system. Anyone who claims that voting for Gary Johnson or Jill Stein is a “wasted vote” is just announcing that they prefer a main party candidate to a third party candidate. Trying to guilt voters who disagree with them to switch sides without convincing them why their candidate is actually better is an excellent political strategy. But as demonstrated here, there is no logic behind this reasoning beyond “I want my team to get more votes”. If their team isn’t worthy of getting your vote, don’t give it to them.

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Thanks to Stuart Langridge for his tips on making sortable html tables.

Picture credit: Gary Johnson by Gage Skidmore, licensed under CC-BY-SA-2.0