US Presidential Elections are Broken

 2016.11.09 -  Nat Tuck -  ~11 Minutes

The US just held a presidential election, and somehow Donald Trump got elected.

This didn’t happen because Trump was the best person for the job. It didn’t even happen because a majority of Americans prefer Donald Trump to the other contenders. Not only did Donald Trump get less total votes than Hillary Clinton, in the general election, but the majority of Republicans showed that they would have preferred someone else in the Republican primary.

US voters elected a president that the significant majority of them didn’t really want. And there’s a reason why this happened: That’s the completely predictable outcome of the rules of the voting system that’s used to elect US presidents.

The US voting system has a bunch of problems. Let’s go through some of them.

The Electoral College

There isn’t one general election for the US president. Instead, there are around 54 of them. One for each state, one for Washington DC, and a couple more for specific congressional districts in Nebraska and Maine.

Winning these elections selects electors, who vote to select the president later. The number of electors selected by each individual election is loosely proportional to the population of the area voting. This creates a couple of bad effects:

Unequal Voting Power

In 2016, the ~54 individual elections will select 538 electors. If the 538 electors were divided completely proportionally by population, there would be significant inaccuracy from rounding. But they’re not selected entirely proportionally - there’s a minimum of three electors per state.

  • Washington DC, Population ~660,000, 3 electoral votes = 220,000 people per elector
  • North Dakota, Population ~740,000, 3 electoral votes = 245,000 people per elector
  • California, Population 39 million, 55 electoral votes = 710,000 people per elector

We could say that a vote in North Dakota is worth more than 2 votes in California.

Winner-Take-All and Swing States

Most states assign all their electors to the single winning candate. This means that getting 40% of the vote and 0% of the vote are the same. This means that individual votes in predictable states simply don’t count. In a state like Massachusetts or Utah, even a well organized group of people have basically no chance of changing the outcome for that state.

Since the overall breakdown between the two parties is about 50-50 nationally (which will always be true with two parties, as we’ll see later), but some states have a sigificant preference for one party over the other, this means that only a few swing states will decide an election.

Trump won by:

  • ~60k votes in Pennsylvania
  • ~30k votes in Wisconsin
  • ~15k votes in Michigan.

Voters in those two states effectively decided the election. There were some other states that were reasonably close, like Ohio and Florida. New Hampshire was even closer, but its 4 electors didn’t end up being a deciding factor.

Media coverage of elections focus on ~10 swing states, and realistically individual votes can only have an effect on the election in those states.

What if it was changed?

This election is the fifth time in the history of the US when the electoral college and the popular vote disagreed. The last time was Bush vs. Gore in 2000.

If the president were selected by popular vote, Hillary Clinton would have won the 2016 presidential election. That would give us a more democratic outcome, but we’d still have some of the same problems with the result.

We know that over 40% of Democratic primary voters would have preferred Bernie Sanders to Hillary Clinton, but unlike the Republican primaries, the other candidates all dropped out early. We don’t know how many people would have preferred some third democratic candidate.

What we can say is this:

  • The actual election left at least 75% of people unhappy.
  • An election based on the popular vote would still have left at least 60% of people unhappy.

First Past the Post Voting

The method we use to vote itself almost guarantees that the majority will be unhappy with the outcome.

People voting for president are given a ballot with a list of candidates, and they can vote for one candidate.

This system works well for a two-candidate election, but as soon as there are more than two candidates it breaks horribly.

No Majority

Once you have three candidates, it becomes possible for no candidate to get a majority of the vote. Generally the winner is selected as whoever got the most votes, but this necessarily means that the majority of people will be unhappy with the result.

Spoiler Candidates

In the presidential election in 2000, the significant candidates were George Bush, Al Gore, and Ralph Nader. Al Gore won the popular vote. George Bush won the election by 5 electoral votes, with a margin of 537 votes in Florida. We can safely assume that most (at least half + 538) Nader voters preferred Gore to Bush.

If Ralph Nader hadn’t been on the ballot, Al Gore would have won the 2000 presidential election. This “spoiler effect” isn’t uncommon - it may have elected Bill Clinton over Bob Dole in 1996 due to the presence of Ross Perot.

And in this week’s election the third party candidate votes in most of the swing states exceeded Trump’s victory margin - but that’s less clear because we don’t know the second choice of Johnson voters.

The general issue that causes spoiler candidates is the issue of splitting the vote. Having another candidate that you support added to the election decreases the chance that any candidate you like will win, because votes for candidates you like will be split between all of them.

Strategic Voting and Political Parties

The vote splitting effect leads to strategic voting. Rather than picking your favorite candidate, a more impactful voting strategy is to predict the top two candidates and then vote for your preference among those two. That way you prevent the candidates that you expect to lose from influencing the election at all.

In the US election system, we have a mechanism to preselect the top two candidates: Political Parties. There are two major parties: Democrats and Republicans, and each party holds a primary election beforehand to select one candidate for the general election. Since the parties are popular, their candidates will be the top two contenders, and thus the two choices for a strategic voter.

This has the advantage that US voters get to select between more than two candidates, since they get to pick the final two candidates through primary elections. But there are two clear downsides: First, any serious candidate must win one of these primaries. Second, the primaries use the same voting mechanism and therefore suffer from the same issues.

In 2016, we saw two different failure modes for our “pick one” voting system.

In the Democratic primary, all but two candidates dropped out early to avoid any splitting of the vote. This means Democratic primary voters only had two choices to vote for - other views simply weren’t available as options.

In the Republican primary, there were a dozen candidates. Donald Trump pulled ahead early. Eventually Ted Cruz pulled ahead as the second place contender, but it was too late and he had already lost enough votes to vote splitting with other similar candidates to get a significant portion of the overall vote. Since Trump finished with less than half the votes, it is entirely possible that if it had been a simple Trump vs. Cruz primary that Cruz would have won.

The Effect of News Media

The correct strategy in a “pick one” voting system is to chose between the top two candidates.

So how do people determine the top two candidates? News coverage.

This has a relitively minor effect on the general election. News coverage influences people’s choice between the top two candidates, but with two major established parties the top two are determined by the primaries.

But in the primaries, the effect of news coverage on determining the top two is huge. It would be easy to argue that the US news media picked Donald Trump as the Republican candidate simply by their early and ongoing saturation coverage of everything he did and said. Further, none of the other Republican candidates were able to cleanly establish their position as #2 due to their lack of news coverage.

This effect of primary candidate selection by public opinion, and public opinion being largely driven by media coverage may be the most problematic element of the process.

Another more direct effect to consider is the possibility of biased polls. If you want to convince the public that you’re the top candidate in an election, having someone say you’re the top candidate is the easist way to do that.

Other Voting Systems

Ranked Choice Voting

This election, Maine voters approved a ballot question that would adopt a Ranked Choice   system to elect their future governors.

In this kind of system, instead of picking one candidate, each voter ranks all the candidates on the ballot from best to worst.

There are several voting systems of this general type, distingished by how they count the votes. The system that Maine adopted is the worst of the options, called Instant Runoff Voting.

In Instant Runoff Voting:

  1. Count the top-ranked votes.
  2. If there’s a majority winner, you’re done.
  3. Otherwise, drop the candidate with the least top-ranked votes, shift those voters choices up (so their second rank is now first).
  4. Repeat until someone has a majority.

This system solves the Bush-Gore-Nader problem. If most of the Nader voters vote { Nader > Gore > Bush }, then the vote will procedeed as follows.

  1. Count the top-ranked votes.
  2. Bush 49.7%, Gore 49.3%, Nader 1.0% - Drop Nader
  3. Nader ballots become { Gore > Bush }
  4. Count again.
  5. Gore 50.3%, Bush 49.7% - Gore wins.

If all third candidates are fringe candidates that are sure to lose, this works great. People can vote honestly, and there are no spoilers.

Unfortunately, when three candidates all get similar numbers of votes, the spoiler effect comes back.

Consider an election where you expect the following votes:

  • 3 people vote { Bush > Gore > Nader }
  • 2 people vote { Nader > Gore > Bush }
  • 2 people vote { Gore > Bush > Nader }

Your real preference is { Nader > Gore > Bush }. How should you vote?

If you vote your real preference, the election will come out as follows:

  1. Round 1 counts: Bush 3, Nader 3, Gore 2
  2. Gore is eliminated.
  3. Round 2 counts: Bush 5, Nader 3
  4. Bush wins.

If you instead strategically vote { Gore > Nader > Bush }, the election goes like this:

  1. Round 1 counts: Bush 3, Gore 3, Nader 2
  2. Nader is eliminated.
  3. Round 2 counts: Gore 5, Bush 3
  4. Gore wins.

The spoiler effect is back. Voting for Nader can elect Bush over Gore.

There are better ranked choice voting methods that solve this problem, but ranked choice voting methods are innately flawed. Math says that no such method can ever work perfectly.

Here’s a good video showing the issues with ranked-choice voting systems with better examples and more details:  

Range / Approval Voting

There is group of voting systems that does most of what we want from a voting system without being obviously broken: Range Voting.

In Range voting, your votes are like Yelp reviews: You give each candidate a rating in a range, like 0 to 4 stars. You give anyone you don’t want elected zero stars, you give your favorite candidates 4 stars, and maybe you give a couple stars to anyone you’d prefer over your bottom choices.

Counting is simple: Whoever gets the most stars wins.

This lets you express slightly less preference information than range voting. You can only chose from 5 different ratings for each candidate. If there are 10 candidates, you can’t give everyone a distinct rating.

But it solves the Bush-Gore-Nader problem. You can give Bush a 0, Gore a 3, and Nader a 4. As long as Bush’s lead isn’t more than 4 times the number of Nader voters, Gore will still win.

It also solves the “Anyone-but-Trump” problem from the Republican primary. You can vote for everyone but Trump, and give the highest rating to your favorites.

There’s still a strategic voting issue with Range voting. It’s strategically better to rate both Gore and Nader 4 to make sure you have a “full vote” for Gore - at least until Nader is doing well enough that he might win. But this strategy is obvious, and rarely leads to unexpected outcomes.

Given this strategy, a specific version of Range voting probably makes the most sense: Approval Voting. It’s range voting with a range of 0 - 1, you either vote for a candidate or don’t. The ballot looks just like the ballots today, except the instructs are “vote for any number of candidates”.

Range voting frequently elects compromise candidates. People don’t get their first choice, but victory goes to someone with broad support. This is probably a good thing.  


Our electoral system is broken in other ways. For example, moving to approval voting would also be good for congressional elections, but there are other even better options to consider there.

Hopefully I’ll get around to ranting more…