Should I vote for an independent candidate?

This was a leading question on my mind when I started to write my own voting simulation. Years ago, a close friend of mine shared with me how he often votes. To choose who to vote for in high offices, he does a lot of research to find someone who is scarcely-known but who seems like someone he could fully support. He writes their name on his ballot. I’ve always admired this! It shows dedication and independent thought.

My friend once made a bold claim about this: “If everyone did their own digging and voted for someone they really liked best, we would all get much better people into office.” Is this true? Intuitively, it feels right.

His approach was an extreme version of “honest voting.” I’m not going to dig into exactly this approach here, because it’s more of a discussion of write-in candidates than anything else. Instead, here I’ll look at a more boring question. Should I vote for an independent candidate that I like best, or should I choose only between those candidates that seem likely to win?

Honest vs Strategic

Every voting method has:

• A ballot
• A method of determining the winner

How a voter expresses their preferences on their ballot is up to them. The most obvious way to mark a ballot is to answer the ballot question as directly as possible. This is an “honest” voter. For a plurality ballot, the question is (assumed to be) “Which option or candidate do you prefer above all the others?” I will cover some other voting methods, alternatives to plurality, further below.

Another obvious and common way for voters to mark their ballots is to consider it as a game of strategy. “How can I use my vote to have maximum impact toward my desired outcome? How can I most strongly improve the chances of a more favorable result to me?” What the ballot might be asking is irrelevant. What matters is the rules of the game: How is the winner chosen? In a plurality election, voters can pick only one candidate on their ballot to support. If a voter is able to guess which candidates ought to have the highest numbers of votes (the election hopefuls), then an optimum strategy would be to vote for their highest preference between those.

Again: Should I vote for an independent candidate if I prefer them to a major-party candidate? The self-interested voter is a strategic voter and I’ve already given you my answer: No. You would have more impact if you restrict your choice between those (usually two) candidates most likely to win.

While it’s obvious that self-interested voters ought to vote strategically, a more difficult question is: Do honest voters do better for themselves collectively than strategic voters? How should the community-focused voter play the voting game? Thinking a little in terms of game theory, strategic voting is the optimal strategy for the individual. But for the whole group, does honest or strategic voting provide better outcomes?

Do honest voters do better as a population?

By “do better” I mean: Are people more likely to elect candidates that best meet the (perceived) needs of the whole electorate?

In the chart above I have simulated 100,000 elections with an initial pool of seven candidates, which is narrowed down to four candidates through a primary election process. I have two axes of simulated political issues, one of which is more broad and somewhat polarized. Even though this is patterned off a political reality, I do not believe this simulation of candidates and voter preferences is very realistic. That said, these results seem to be typical of a broad variety of different configurations. There are 1,000 simulated voters for each election.

The vertical axis on that chart is average “voter satisfaction efficiency.” It is explained here — I liked Quinn’s idea and used it here. 100% score is achieved when the election method has elected the candidate who has the maximum total (perceived) utility among all candidates. I’ll claim that this candidate is the “ideal best” candidate for the group. This metric can be criticised, but I am encouraged by the way this tracks with many other aspects of voting that are ideal. Voting methods that meet a lot of important voting criteria tend to also do a good job of picking high-utility candidates. So unless you’re nitpicking about 1% differences here and there, I’ll stand by the claim that this metric is a good one.

And I didn’t say it in words yet, but YES – with strategic voters it looks to me like people do better, often much better, than honest voters given that the election method is plurality voting. In the simulations above, honest voters were getting results closer to die-roll elections than they were to actualizing the will of the people. But strategic voters got more than twice as close to the “right” answer, on average.

This is not an intuitive answer. Most people I’ve talked to feel like my friend’s instincts were correct: If everyone votes their heart, the system will work best. But with voting methods, intuition is not often correct. Why might it be better to vote strategically? Before I go there, I’ll look at some other voting methods.

How about for other voting methods?

Here are results for a few other methods from that same batch of simulations:

Instant Runoff Voting

I have no strategic version of this method. Strategies are very complicated for instant-runoff. See for example this paper. At the moment I can’t weigh in on this. I would very much like to try, but not today.

Borda

This is the classic voting method that has bad results when voters are strategic. Jean-Charles de Borda invented this (he was not the first or last inventor of it) and said what can be translated as “My scheme is intended for only honest men.”

My strategy for this method is really much too simple. (Not an optimal strategy.) Voters look at the top two leading candidates (from the honest election), rank their favorite of those two as their #1, and the other one gets ranked last. All other candidates get ranked according to that voter’s honest preference.

Another strategy that I have not simulated is for the voter to rank their most favorite candidate first, and the other candidates in reverse order of popularity. If only one (or a small contingent of) voter(s) does this, they do help their favorite as much as possible. But it reportedly produces absolutely terrible outcomes for the whole electorate if everyone does it. The most unpopular candidate gets ranked #2 on most ballots, and usually wins.

Borda is not a good voting method for political or other high-stakes elections. But for small informal groups making decisions that are not particularly contentious, the Borda count can work just fine. Not the best, but for a very small group where you need both a very simple method and for participants to be able to express more information than they could with an approval ballot, it’s a decent choice. Range voting would be a better choice.

Approval, Range, and STAR

These three methods are score-based (okay STAR is hybrid). A score-based voting system lets you score each candidate individually. Unlike ranked voting methods, voters can give the same score to multiple candidates. Range voting is similar to what Amazon, Yelp, Google Maps, etc use for ratings. Give something a rating, and find the thing with the highest average rating. Approval is a minimal score-based system: Voters score each candidate with either 0 (don’t approve) or 1 (approve). As long as you have, say, 100 or more voters, approval voting does better than I would have expected!

My strategy for all three of these score-based methods is the same. And much to my surprise, this strategy gives consistently better results for the population than honest voters! I did not expect this.

The honest voter, when scoring, will give their least-favorite candidate the lowest score, and their most favorite the highest score. Candidates in between will assign scores on a linear scale between worst and best, according to their own perceived utilities.

For a strategy, again look at the top-two vote-getters for the honest version of that same method. Find the score mid-point between these two, and add an artificial scoring gap there. Above and below the gap, scoring is linear. But the gap widens the voter’s score separation between the two most-hopeful candidates. The most extreme version of this has voters give the max score to their favorite hopeful candidate as well as all other candidates they like better. And the bottom score goes to all the rest. If all other voters do this, it gives the exact same results as strategic approval voting. No shades of grey. But for the Range and STAR results above, I used a strategy gap of 75% of the full range.

Both approval and range scoring (on a 1-10 scale) seem to do better when everyone uses this particular strategy. Yet again, this came as a shock to me!

But STAR voting already has an element designed to reduce the effect of any strategic voting. STAR stands for “Score, Then Automatic Runoff.” It uses a 6-point range-voting ballot – score each candidate from 0 to 5, inclusive. To find the winner, first add up all the scores. Find the top two candidates by score total. Then, count the number of ballots that score one of those top two higher than the other one, and vice-versa. (In this step it does not matter how different, just that the higher-scored one counts as a vote for that candidate.) This is a little bit like strategic range voting. The strategist gets a pre-election “poll” which is round #1 of STAR. Then they give the final preference info on their real ballot, which is like round two of STAR. In my simulations, STAR seems to do about the same with strategic and honest voters. But it has that final-two separation mechanism already built in, so this shouldn’t be surprising.

Do other studies agree with this?

Years ago I read an article about comparing voting methods by simulation. It presented a graph that indicated a range of performance for different voting methods according to how well each method picked winners that either did or did not maximize summed “perceived utility” scores of all the voters.

In this simulation and many others that Smith ran, a population of honest voters always got better results for the electorate than did strategic voters. That’s the opposite of what I’m seeing.

To compare this chart with the two I’ve shown: My 100% is pretty much the same as Smith’s Magic “best” winner on the left. My 0% is Smith’s “random winner.”

Later I found Jameson Quinn’s simulation results, which had strategic voting being an improvement under plurality and a few other methods.

So for this issue, I agree with Quinn but not Smith. If anyone knows of other studies of this, I’d be curious!

Why might strategic voting work well?

The main problem with plurality voting is that voters have to choose only one candidate to share their evaluation of. Because there is so little information on the ballots, the method (count all votes for each candidate) cannot often pick a candidate well. But there is some information, and when it comes down to the final candidates, the only remaining question is: which one do most people want? If you reduce a multi-candidate election down to a final two-candidate election, then all methods do equally well. So if voters know ahead of time what information is most important for that final pair, they can use their limited ballot to communicate only that bit of information that’s most needed.

This amounts to changing the question of the ballot. Instead of “who is your favorite?” The better question is “Which candidate do you feel most needs your support?” If it’s obvious ahead of time that an election will come down to two hopefuls, then that’s the best question to answer.

Now, this does not completely save plurality voting. Knowing what the final pair of candidates might be is another weakness of plurality. The strategic voting I’m describing here can’t fix that. Ultimately you need a method of getting some level of information from every voter about every candidate.

But in cases where two leading candidates are well-selected by honest pre-election plurality polls, strategic voters actually fix the worst, most glaring problem with plurality: The spoiler effect. I would suppose that fixing the spoiler effect (in many cases) is the main reason why strategic voting comes out to the benefit of all voters in plurality elections.

It should be properly shocking that approval voting does so well, at least according to the simulations I’m showing here. Approval voting is almost the same as plurality, with just one modification. Instead of “vote for exactly one candidate,” the approval ballot asks “vote for any number of candidates.” Punch away! But you can’t vote twice for the same candidate. That’s multi-voting, which (spoiler) does not do as well. But voters can share one bit (0 or 1) of preference information about each and every candidate. Voters don’t have the awful choice to make of which one candidate they weigh in on.

And strategic approval voting takes a basically good method and actually makes it better. My version of strategic approval voting is to use the free parameter – where a voter draws the line between “approve” and “disaprove” – and sets it to the optimum value for each voter to communicate that information that’s most needed. When you compare this with plurality voting, voters get the best of both worlds. They can vote honestly and strategically at the same time. “I like this hopeful candidate, but I also like this other candidate that is in fact my most favored. I approved of my favorite, which is all I can do anyway, but since it will probably come down to these other two, I’ll weigh-in on that too.”

I want to write more about Condorcet methods here, but I don’t want to have to explain it all here first. If you know about Condorcet voting methods, you’ll also see how these automatically include all pair-wise preference information. So again if all voters can somehow (magically) find the right top-two candidates before voting, and communicate their final preference as a strategic vote, then strategic voting with plurality would effectively turn it into a Condorcet method (whenever a Condorcet winner exists). All of the Condorcet methods I have simulated seem to do about as well as the score-based methods in terms of voter satisfaction and lack of a center-squeeze effect. For another post.