The number one argument against third parties is that they “split the vote,” but this doesn’t always hold water for ‘safe’ districts and parties outside the left-right spectrum.

## Third Parties Can Win In ‘Safe’ Districts

A ‘safe’ district is one where the Democratic or Republican party holds such a strong advantage that the other major party will never be able to win — even if a third-party splits the vote.

Let’s say there’s a district where the Democrat consistently gets 80% of the vote and the Republican gets 20%. Now, let’s say the Green Party comes along and runs a candidate, splitting the left-wing vote in half.

The Democrat and the Green would both have roughly 40%, while the Republican would still only have 20% — so a leftist would win, even though the vote was technically split. Increase the Green’s share of the vote, and they win; decrease it and the Democrat wins — the GOP is the real third party in this district.

## Mathematically Calculating if a District is ‘Safe’

So is there a way to calculate when the vote is impossible to split? Yes! The formula is simple:

If (ˣ⁄₂ > y)

X is the largest major-party and y is the other one. In this case: x is the Democratic Party and y is the GOP.

If (⁸⁰⁄₂ > 20) = if (40 > 20) = true

You can see it clearly works out with the theoretical situation we talked about above. Let’s see what happens when we lower x to 60, thus raising y to 30.

If (⁶⁰⁄₂ > 40) = if (30 > 40) = false

What happened? Half of 60 is 30, so the vote was split enough to allow the Republican to win. This tells us the upper-limit for x is above 60. To find it: let’s change our equation.

If (x > 66⅔)

This equation asks the same thing as above, but with only one variable: x, which stands for the largest major-party’s support. The number 66⅔ is 2/3 of 100 — so a major-party has to have more than two-thirds of the vote for the district to be immune to vote-splitting.

80 is greater than 66⅔, so it checks out, and 60 is less, so it checks out too! In terms of percentages: 67% is the minimum possible value for x (rounding to the closes whole-number). Let’s plug 67% into our first equation.

If (⁶⁷⁄₂ > 33) = if (33.5 > 33) = true

It worked! 33.5 is technically larger than 33, so this district is immune to vote splitting — at least on paper, since the vote shares of the two major-parties can fluctuate, and a third left-leaning party could screw-up the whole equation.

## Is Your District Safe?

Above is a map of districts where third parties can theoretically win, based on the 2020 US House of Representatives elections. Blue means the Democrat got over 2/3 of the vote, and red means the Republican got over 2/3 of the vote. (Desktop users can hover over the image to zoom.)

My US House district, AR-4, is immune to vote-splitting from the right — meaning a right-wing third-party could win here. Arkansas’ Senate seats ain’t safe, though.

## Syncretic Parties Can’t Split the Vote

One large exception to this rule is the Libertarian Party, which is left-wing on social issues and right-wing on economic issues — this means it’s impossible for an LP candidate to split the vote of either major-party.

So why don’t they win? People *think* they’ll split the vote, even though that assertion is false. Also, only 6% of Americans are Libertarians, so they couldn’t win, even if it was fair (sorry).

The same holds true for the opposite: parties that are right-wing on social issues and left-wing on economic issues, like the American Solidarity Party.

When a party doesn’t hold consistently left- or right-wing views, it’s considered to be syncretic. Sometimes, they’re falsely labelled as “centrist.”

The reason these parties can’t split the vote is because they tend to take votes away from both major parties. For example, the ASP would take a large chunk of Hispanic and Black voters from the Democrats, but also a great deal of populist Republicans from the GOP.

## Educate Voters!

The only way for third parties (or Independents) to win in safe districts, or for syncretic parties to win at all, is to educate voters that it’s impossible to split the vote. Explain the two-thirds rule, the fact that you’ll take votes from both parties, or both.

This won’t help in competitive districts unless your party is syncretic, but it can help you snag a few seats in Congress and get the ball rolling!

*Related article: How Third Parties Can Win Under First-Past-the-Post!*