Strategic Straightforwardness

Which is simpler: Approval Voting (where you vote for as many candidates as you like and whoever gets the most votes wins) or Instant Runoff Voting (single-winner Ranked Choice Voting, where you rank the candidates, candidates get eliminated, and votes get transferred from eliminated candidates)? The case for the simplicity of Approval Voting is obvious; the ballots are much simpler, it’s far more difficult to spoil your ballot, the tabulation is utterly trivial, and it’s easy to describe it in a single sentence.

The case that Instant Runoff Voting (IRV) is simpler is more interesting. To vote in an IRV election you rank your favorite candidate #1, your second-favorite #2, and so on — there’s no obvious need to consider which candidates are the most likely to win or how much more you like one candidate than another. In contrast, voting in an Approval election basically requires you to think strategically and consider which candidates are the most likely to win. Simple ballot instructions (e.g. “Vote for ALL the candidates you approve of”) are inadequate — for example, if you like every single candidate then following these instructions would imply that you should throw your vote away altogether by voting for all of them. More generally, in order to have your vote matter you need to vote for at least one, but not all, of the viable candidates. This is impossible to do reliably without knowing who the viable candidates are.

Even with perfect knowledge of who is and is not viable, strategic considerations are a significant aspect of casting an Approval ballot. Suppose there’s a three-candidate election in which you like Alice a lot, think that Bob is moderately worse than Alice, but can’t stand Carol. Bob seems like the frontrunner, but you think both Alice and Carol also have a real chance of winning. It’s obvious that you should vote for Alice, but it’s not obvious whether or not you should vote for Bob, and the ideal strategy involves more math than most voters want to perform. In general, Approval prompts far more strategic thinking than IRV.

I call this difference between IRV and Approval voting strategic straightforwardness. Loosely speaking, a voting method is strategically straightforward if (a) it doesn’t make voters feel like they have to take strategy and polling data into account when casting their ballots, and (b) if voters who just jot their options onto their ballots with no consideration of strategy whatsoever have almost as much influence as voters who put a great deal of thought into voting strategically.

Apparent and Actual Strategic Straightforwardness

The conditions (a) and (b) above don’t always coincide, and for a more rigorous analysis it’s important to disentangle them. I call these separate concepts apparent and actual strategic straightforwardness. Apparent strategic straightforwardness is about what voters feel like they need to consider and how much of a mental burden they feel is imposed on them by strategic considerations. Actual strategic straightforwardness is about how much strategic voting actually amplifies the power of the ballots of strategic voters. Creating a mathematical definition of apparent strategic straightforwardness is probably impossible, but actual strategical straightforwardness can be described like this:

Consider three possible options for a voter:

• Casting a strategically optimal ballot, where “strategically optimal” is based on the best available polling data, prediction markets, etc. — but not on some magically perfect knowledge of how everyone else is voting.
• Casting a valid ballot with zero thought to strategy, polls, etc.; this can be thought of as simply jotting down one’s opinions. This is trivial to define for ranked ballots and Plurality, but there are multiple reasonable definitions for cardinal voting methods like Approval and STAR.
• Abstaining

Call these options S (strategic), N (naive), and A (abstaining), and let E() denote the expected utility of each option. We can define the actual strategic straightforwardness of a voting method by (E(N) - E(A))/(E(S) - E(A)). Basically, this number says what fraction of a strategic voter’s voting power is possessed by a naive voter who doesn’t consider strategy. If a voting method has a strategic straightforwardness of 1, strategy doesn’t matter in it at all; if a voting method has a strategic straightforwardness of 0, there would be absolutely no point in going to the polls if you weren’t going to be strategic. This mathematical definition of strategic straightforwardness is dependent on a host of factors in addition to the voting method (what information is available to voters, the distribution of voter preferences, the strategies employed by other voters, etc.), and it can be difficult to compute since determining the ideal strategy is often difficult. But it’s easy to estimate it within a computer simulation if you assume (or can prove) that some strategy is strategically optimal.

A voting method can have excellent apparent strategic straightforwardness without having great actual strategic straightforwardness. While voting in an IRV election feels straightforward, there are a couple reasons why strategy can matter a fair amount. First, there are often more candidates in a race than available rankings, so, if you prefer a lot of longshot candidates to the frontrunners and vote honestly, you may not have any rankings left for the frontrunners, and your ballot would be wasted just as if you had voted for a non-viable candidate in a Plurality contest. Second, it can be best to rank broadly acceptable candidates above polarizing candidates, even if there’s a polarizing candidate you really like, in order to avoid a center squeeze; here are some examples of this from Australia. The actual strategic straightforwardness of IRV is still better than that of Plurality or Approval, however.

Similarly, a voting method can have better actual strategic straightforwardness than apparent strategic straightforwardness. I think STAR Voting is a prime example of this. The expressive scoring ballot means that voters have a lot of reasonable-sounding options for how they should vote, and it’s not obvious which of these options is the best. However, the difference between these reasonable options in their expected effect on the election tends to be very small. I have spent several hours designing and programming strategies for STAR Voting and have found it quite difficult to beat a basic naive strategy by an appreciable margin. The best strategy I’ve invented does substantially better than the zero-information naive strategy when there are a large number of candidates and only some of them are viable, but this is largely a result of harvesting some very low-hanging fruit: you should always give one viable candidate a 0 and one viable candidate a 5, where “viable” needs to be defined such that there are always at least three viable candidates. In three-candidate elections, voters are actually better off using the naive strategy than the more sophisticated strategy I designed.

Strategic straightforwardness of single-winner voting methods

Evaluating apparent strategic straightforwardness is necessarily subjective, and I have not done all the simulations required to assess actual strategic straightforwardness. (Also, such simulations would have to take into account the possibility of there being fewer allowed rankings than candidates.) All of these scores are subjective and the uncertainty is often substantial.

• Plurality: Apparent 4/10, Actual 0/10: Plurality makes it far easier to throw your vote away than other voting methods, and it’s rather obvious that identifying the frontrunners is important.
• Approval: Apparent 3/10, Actual 5/10. Compared to Plurality, Approval offers an additional way to throw away your vote (i.e. voting for every viable candidate), but this is overshadowed by a vastly reduced chance of a wasted vote when there’s a non-viable candidate you really like. Another important factor is that if you accidentally throw away your vote under Approval it’s evidence that you didn’t care a great deal about which of the frontrunners would win anyway.
• Approval + Runoff: Apparent 3/10, Actual 8/10. It’s possible to throw away your vote in the general election, but not in the two-way runoff.
• Score: Apparent ???, Actual 1/10. In Score, voters who use intermediate scores are at a disadvantage, and the ballot design encourages the use of these scores.
• STAR: Apparent ???, Actual 9/10.
• IRV: Apparent: 10/10, Actual 8/10.
• Condorcet: Apparent 10/10, Actual 10/10. It’s very rare for it to be strategically optimal not to vote honestly; strategy only matters in weird corner cases or when massive numbers of voters coordinate.

I view the difference in strategic straightforwardness as the strongest argument there is for preferring IRV to Approval Voting (though I think the difference in third party visibility and performance in the center squeeze are more important).

Is strategic straightforwardness a good thing?

There are a few obvious arguments for wanting a voting method to be strategically straightforward:

• Most people prefer not to have to worry about strategy, and we should make voting feel as good as possible. Relatedly, strategically straightforward voting methods may be more likely to be adopted and less likely to be repealed.
• Some demographics will do better at strategic voting than others. If a voting method has low strategic straightforwardness, lower-income voters and other disadvantaged groups will have less of a voice.

The argument that (actual) strategic straightforwardness is undesirable goes as follows: Informed voters make better decisions than uninformed voters, and voters who are good at math are better at assessing different tax policies, knowing whether we should be more worried about mass shootings or suicides, and evaluating the relative dangers of terrorism, global warming, and future pandemics. The greater the advantage of voters who are mathematically literate and follow the polls, the greater the effective mathematical literacy, political knowledge, and average intelligence of the electorate. If half the electorate is good at math and half is bad at math, and we use a strategically non-straightforward voting method that gives each good-at-math voter 50% more influence than each bad-at-math voter (an unrealistically large effect size), this is somewhat similar to a massive education campaign that makes 60% of the electorate good at math instead of 50%. But it’s not that similar, because the massive education campaign would result in the set of good-at-math voters being more representative of the entire electorate.

Using a voting method with low strategic straightforwardness can also be compared to testing for basic knowledge as a requirement for voting. This has the potential to yield a more informed electorate and therefore better policies, but there’s a dark side: if a group of people can write a test to determine who is allowed to vote, that group can disenfranchise anyone they want. Such a policy is infinitely abusable, but using a voting method with low strategic straightforwardness is different: there’s nobody making up a test that can be interpreted ambiguously or changed from year to year; all you have is a fixed algorithm that people need to understand in order to have the greatest influence possible.

Overall, whether you want high or low actual strategic straightforwardness depends primarily on two factors: The extent to which you view politics as a zero-sum game over who gets what vs. a collaborative attempt to make everyone better off, and whether you think a more diverse group of less competent individuals makes better decisions than a less diverse group of more competent individuals.

• If politics is primarily a zero-sum game over dividing a fixed pie, a more strategically straightforward voting method will result in a more equitable division.
• If politics is primarily about identifying the best policies for advancing our shared values and having a more knowledgeable and intelligent electorate is more important for this than having a diverse electorate, using a voting method with low strategic straightforwardness will result in better policies.
• If politics is primarily about identifying the best policies for advancing our shared values and having a more diverse group of decision-makers is more important than having these decision-makers be competent as individuals, using a voting method with high strategic straightforwardness will result in better policies.

As for apparent strategic straightforwardness, it seems best for it to be as high as possible so long as it doesn’t somehow deceive voters into throwing away their votes. When people vote in a strategically sensible manner it’s usually good for the electorate as a whole, and we want to encourage it.