When is a Vote a Wasted Vote?

Suggest to a Gary Johnson supporter, or a Jill Stein supporter, that voting for their preferred candidate is a wasted vote and you’re likely to get an ear full. But whether or not such a vote is actually a wasted vote depends on what you think of the other candidates.

What is a Wasted Vote?

As this 2016 presidential election has dragged on (and on) between two historically disliked front-running candidates, like campaign fingernails across a 16-month long chalkboard, heartfelt debates over how to vote are ubiquitous. And, as often as not, such debates get around to the idea of the wasted vote.

Everyone seems to know, intuitively, what constitutes a wasted vote. However, there is more nuance around this issue than many people consider. I’m reminded of a pithy quote, dating back to 1917:

“Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.” — H. L. Menken

Consider the recent blog post, The Power of the Wasted Vote, that begins with a pithy quote:

“I’d rather vote for what I want and not get it, than vote for what I don’t want and get it.” — Eugene V. Debs

Upon initial glance, the Debs quote seems quite reasonable, even wise. But, in fact, this is a perfect example of the type of explanation Menken was talking about: neat, plausible, and wrong. Let’s look a little more carefully to see why this is so.

When there are only two alternatives (i.e., candidates), this statement is, in fact, reasonable. Consider two alternatives A (the one you want) and B (the one you don’t want). In this scenario, not getting A implies getting B. Now, the Debs quote becomes:

I’d rather vote for A and get B than vote for B and get B.

In this scenario, you’re getting alternative B, period. So the statement can be refactored as:

I’d rather vote for A than vote for B. (But I’m getting B, regardless).

This really just expresses your preference for A, which is a given. So, in this scenario, it makes sense to register your preference for alternative A, in what might be called a protest vote, not because it will affect the outcome of this election, but because it might influence what happens after the election. (Don’t get hung up on the “protest vote” label. It’s just a label. If you feel that has a negative connotation, use any other label you prefer.)

The two-alternative scenario is easily analyzed. But the logic quickly becomes more complicated–less “neat”–when there are more than two alternatives.

To model the case of additional alternatives, we’ll continue to treat alternative A as most preferred. But now we’ll treat B as a list of alternatives B1, B2, …, all of which you don’t want. Now, as before, you’ll be ending up with B, but in this case, that means you’ll be getting one of the B1, B2, …. alternatives. In this case, a “protest vote” makes sense only if you have no significant preference between the B1, B2, … alternatives.

To see this, let’s make the example more concrete:

A = Getting kissed on the cheek by your biggest crush

B1 = Getting kissed on the cheek by your sibling

B2 = Getting kissed on the cheek by your other sibling

Now, following the logic of the Debs quote, you would vote for getting kissed by your biggest crush. However, you’ll actually end up getting kissed by one of your siblings, and you’ll leave that choice up to the other voters. This is okay because you don’t have a significant preference between B1 and B2.

A fundamental problem with the protest vote logic is when it ignores relative preferences between the available candidates. Let’s tweak the alternatives as follows

A = Getting kissed on the cheek by your biggest crush

B1 = Getting smacked in the face with a plastic ruler

B2 = Getting smacked in the face with a sledgehammer

We still most prefer A, but now, there is a strong preference between B1 and B2. In this case, it is very risky to leave the B1 vs. B2 choice entirely up to the other voters. In this case, if the race between B1 and B2 is at all close, a protest vote (i.e., a vote for A) is a wasted vote! It is wasted because it could have been used to influence a choice (B1 vs. B2) in which you have a strong preference. Put another way, the protest vote did not have maximum utility.

We can, and generally do, have more than one preference. In the example above we have the following preferences:

  • A > B1
  • A > B2
  • B1 > B2

And there is a fourth, less obvious preference:

  • We’d like to publicly register both A > B1 and A > B2, in the hopes to influence others, now or in the future.

But we only get to cast our vote once, for a single alternative. We should cast it in a way that maximizes its utility. That gets the most bang for the buck, so to speak. In order to do this, we must consider the relative strengths of each preference.

So, here’s my attempt to boil this whole idea down to my own pithy quote:

“I’d rather cast my vote where it has maximum utility.” — F. Andy Seidl

Photo credit: Robert Couse-Baker

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