Monday, October 10, 2016

Why use ranked-choice voting over approval voting

Example of a ranked-choice voting ballot.
Voting is not an easy task for a voter.  I don't mean taking time off work, getting to the polls, and waiting in line, etc.  I mean, when you are standing there in the ballot box, you have to decide what vote you want to cast given the options presented to you.  For example, a Jill Stein supporter may be torn between supporting her favorite candidate and voting for a candidate who has a better chance of winning the election.  I'll refer to this as the cognitive burden of expressing your vote.

In this post, I'll address the cognitive burden of three different types of voting:
  1. Plurality voting (i.e., selecting one candidate)
  2. Approval Voting
  3. Ranked-choice voting
OpaVote supports all three of these voting methods if you want to try them out yourself.

Plurality Voting

Plurality voting is very simple, a voter simply picks one candidate.  There is, however, a cognitive burden when there are more than two candidates.  A voter presumably wants her vote to matter.  Accordingly, a voter should not necessarily select her favorite candidate, but instead select her favorite candidate who has a reasonable chance of being elected.

Consider the current U.S. Presidential election.  I'm a big supporter of the Green Party, but Jill Stein is not going to win the election.  I'd like to vote for the Green Party, but instead I'll vote for Hillary because that is the best way for my vote to make a difference.  Others will vote for the Green Party out of principle.

Where there are more viable candidates, the cognitive burden is much higher.  The French 2012 elections for President had ten candidates in the first round.  A voter thus needed to consider which candidates had a chance of winning, and then select her favorite among those who had a chance of winning.

Approval Voting

With approval voting, a voter has the option to approve as many candidates as they like. The candidate with the most approvals is the winner. For someone whose first choice is Jill, the voter may, for example, approve of Jill and Hillary and not approve Donald and Gary.

Approval voting, like plurality voting, is very simple in practice.  A voter just selects one or more candidates.  But Approval voting suffers from similar cognitive burdens as plurality voting.  How do you draw the line between candidates you approve and candidates you don't approve?  

Consider a voter whose true preferences are: 
  1. Jill Stein
  2. Hillary Clinton
  3. Gary Johnson
  4. Donald Trump
Clearly, this voter will approve Jill and will not approve Donald, but what should she do with the other two candidates?  Should she also approve Hillary?  Giving Hillary an approval may help Hillary beat Jill, but she would certainly prefer Hillary to Gary or Donald.  Similarly, this voter may not like Gary, but she may dislike Donald so much that it is worthwhile to approve Gary to minimize the chance that Donald is elected.

Phew... that is a lot of thinking to do.  It would be even harder if Jill and Gary had better chances of being elected.

In sum, approving any candidates other than your favorite can hurt your favorite. Not approving candidates can help your least favorite get elected.  Approval voting thus creates a significant cognitive burden for voters.

Ranked-Choice Voting

With ranked-choice voting, a voter ranks the candidates in order of preference, similar to the picture above.  In my view, this has the least cognitive burden among the three methods discussed here.  It is easy for a voter to pick her favorite candidate, pick her second favorite, and so on.  This kind of ballot has low cognitive burden because a voter doesn't have to consider which candidates are viable.

But, you may ask, "Doesn't a voter have to think about whether their second and later preferences might hurt their first preference? For example, should a Jill Stein supporter not rank Hillary second because it might help Hillary beat Jill?"

The great thing about ranked-choice voting is that the answer to this question is a clear and resounding NO!!! Your second and later choices cannot harm your first choice! Your second preference is only ever considered at all if your first preference has definitively lost. Voting geeks call this the later-no-harm criterion.

Voters thus need to be educated that later choices do not hurt earlier choices so that voters are encouraged to rank as many candidates as possible.  The more candidates a voter ranks, the greater influence the voter has in the outcome of the election.

Accordingly, ranked-choice voting has the lowest cognitive burden.  A voter simply needs to select their first choice, second choice, and so forth.  The voter does not need to consider which candidates are viable.

(For voting geeks who are leaping out of their seats to make points about other voting systems criteria, please keep reading.) 

Other Stuff...

In my view, it is extremely important to make it as easy as possible for voters to vote, and, for the reasons described above, ranked-choice voting does this better than both plurality and approval voting.

I want to briefly address another form of ranked voting called Condorcet voting.  Condorcet voting also uses a ranked ballot, but the votes are counted in a different way.  Condorcet voting doesn't satisfy the later-no-harm criterion mentioned above, so it is possible that your second and later choices could hurt your first choices.  The possibility, however, that your second and later choices hurt your first choice is so small that, for practical purposes, a voter to cannot take this into account, and thus Condorcet voting has the same cognitive burden as ranked-choice voting.  While Condorcet voting is a great voting method, I still prefer ranked-choice voting for public elections, and I'll address that in a future blog post.

Another point to mention is that detractors of ranked-choice voting complain that ranked-choice voting does not satisfy other voting systems criteria, such as the monotonicity criterion.  While this is certainly true, for practical purposes, a voter cannot take the monotonicity criterion into account when casting a vote.  It is just far too complicated and you would need to know how everyone else is going to vote.  The non-monotonicity of ranked-choice voting thus doesn't create a cognitive burden.

Please let me know what you think, especially if you disagree.  I am happy to post any well-reasoned dissent as comments or even give you the opportunity to write your own blog post in rebuttal.


  1. Exactly! It's nearly impossible to pin down Approval Voting advocates on what *instructions* voters are to be given. They usually start by saying "vote for those your approve", but when you start asking what "approval" actually means --- including whether it means the same thing to every voter --- and the possibilities of "approving" could lead to a "wrong" result (e.g. Stein and Johnson supporters bullet-voting their candidates), they'll admit what they really want is for voters to use a particular strategy. The strategy they want relies on voters having access to accurate polls, which precludes using it effectively in many local and state races, particularly primaries, where there is no public polling. Approval voting takes complexity out of the ballot and tally and places it on the voter instead; thus, the cognitive burden you highlight.

  2. First off: thank you, Jeff, for a thought-provoking piece. I'm going to disagree with you on some points, but it's clear that you're arguing in good faith.

    Second: I'm sorry, but I really can't bear the name "RCV" in a voting methods discussion. I know that's what IRV is frequently called in actual laws, but to me "ranked choice voting" is obviously the correct term for the whole class of voting methods which includes Condorcet, Borda, and IRV; not just for IRV alone.

    So, on to the body of your argument: that (according to you) the cognitive burden of IRV is lower than approval, Condorcet, or plurality.

    I agree with you on one point: thinking in terms of cognitive burden is an important, and productive, way to consider voting systems. I also acknowledge that approval's apparent simplicity is less of an advantage than one might think, once you consider the cognitive burden.

    However, I strongly disagree with you that IRV has a low cognitive burden in practice, for two reasons.

    The first, and most important, is that IRV does not actually remove the need for strategic thinking. Yes, it obeys LNH, so once you've decided to rank your favorite in first place, you have no reason not to include your second choice on the ballot too. But there's an important, and predictable, class of election scenarios where it's strategically crucial NOT to rank your favorite first: center squeeze scenarios. If you have two candidates at ideological opposite points, with a third candidate in the middle near the median voter, it is actually quite common for the center to have the lowest first-choice support and get prematurely eliminated. This kind of thing happened in Burlington 2009; in multiple recent French elections; tragically, in Egypt 2011; and would have happened in the US 2000 if Nader had gotten over 25%. In this case, the correct strategy for one group of voters is to rank their true first choice in second place. Understanding this, and correctly seeing when it applies, is a HUGE cognitive burden for IRV voters.

    Second, IRV requires strict ranking. That's a nontrivial cognitive burden when there are more than a handful of candidates. If there were 15 candidates in a race, how should a voter decide exactly which of them to give 8th preference? It's much easier to use absolute grades, as in Majority Judgment. (Behavioural research bears this out; strict ranking is harder than rating, for anything more than 3 or 4 options.)

    On the other hand: is the strategic burden for approval voters actually that high? I think not. Consider the rule used by Ka-Ping Yee in his voting system visualizations: a randomly-assigned strict threshold. This requires no strategic doublethink, yet leads to near-ideal outcomes under his assumptions. My point is that under approval sophisticated strategy is not nearly as important as under IRV.

    But still, I think you have a point. Approval does have a cognitive burden, and we should account for that. That's precisely why I've been working on MAS (majority acceptable score) as an option: it's a simple 3-level voting system with an absolute minimum of cognitive burden. I believe that under MAS, in basically all everyday voting scenarios, a naive sincere ballot will be strategically optimal, or close enough to it that most voters wouldn't care.


    ps. You mention Condorcet, and argue that the strategic cognitive burden is higher than IRV. I disagree; but since Condorcet comes with a higher cognitive burden in just figuring out why a given candidate won, I agree that Condorcet methods are probably not best for large-scale elections.

    1. I agree that the terminology is difficult and that RCV could and perhaps should apply to any method where votes are ranked.

      When you say that "it is actually quite common for the center to have the lowest first-choice support and get prematurely eliminated," we need to clarify "quite common." If you mean 5-10% of the time, then I could believe that, but if you mean 50% of the time, then I would disagree. It would be really interesting if a statistician could collect the data and present results.

      I can't comment on Burlington or Egypt. For the French elections, the center candidate is generally in the top three of 10-15 candidates (depending on the year). Candidates that came later than that top 5 have very little support.

      My main point here, however, is that, except in rare situations, voters are not capable of voting strategically to account for a center candidate out of the top two (and by this I mean normal voters, not the people on this list). First, it isn't clear how often the center candidate is out of the top two. Second, voters would need to think deeply about how the voting system works. third, you need precise polling information. Fourth, if you are too successful in your strategic plan, it backfires. There is this middle ground where enough voters have to vote strategically to get their desired result but not so many that you overshoot and still elect the wrong candidate. A few people (like the people on this list) may consider such a scenario when voting, but I think it is far too complicated for any significant subset of voters to consider it.

      Regarding the difficulty of ranking a lot of choice, that makes sense, but I don't think it matters so much. For most RCV elections, nearly all ballots end up at one of their top 3 or 4 choices. Rankings after this don't matter much. Also, if a person has trouble deciding who to rank 7th and 8th, then perhaps the person doesn't have a strong preference between them and would be equally happy (or more likely equally unhappy) with either.

    2. I have found the following directions to be helpful to voters:

      Rank candidates in the order of your choice by writing a "1" by your first choice, a "2" by your second Choice, a "3" by your third choice, and continue ranking until you don't care who wins among the remaining candidates.

    3. Melvin, thanks for sharing. Those are good instructions for voters.

  3. Publishing comment on behalf of Mike Sawyer:

    Homunq asks, “IRV requires strict ranking. That's a nontrivial cognitive burden when there are more than a handful of candidates. If there were 15 candidates in a race, how should a voter decide exactly which of them to give 8th preference?”

    Brian Zurowski of Davidson College and I are collaborating on some voting theory issues. We have been looking at using pods with various voting methods as a way to relieve the cognitive burden. By “Pod” we mean any collection of choices of unknown, indistinguishable or equal values (Pod – from the proverbial “like peas in a pod”). We were wondering if you had looked at pods (perhaps by some other name)? To see the logic of using pods you need only imagine you are voting (say instant runoff) on a list of restaurants for your groups luncheon tomorrow. Your preference is Mexican cuisine and you see three Mexican restaurants on the list, but you’ve been to none of them, so you group them in a pod and rank the pod first on your ballot. It’s not that just any one will do, but your best bet is the one others rank highest. This is tallied by counting one first place vote for each choice in the pod reducing the chance that any of the three will be eliminated. This is in effect an approval vote followed by individual rankings.

    You might have ranked this pod in second place in which case it (with its surviving members) becomes an “approval pod” only when your first choice is eliminated. In fact a ballot could have multiple pods by simply stringing together consecutive choices that have only trivial differences. An RCV ballot with five choices would have not just 120 voter profiles but 520 (if I did that right). “Approval Pods” (or perhaps Coombs disapproval pods) should be possible with most single winner RCV, Condorset and (with additional steps) STV algorithms. Effective use of approval pods may gain a small strategic advantage for more flexible voters, but for the most part the choice is a trade-off sacrificing “selection” (the ability to choose between “peas” or pod members) in exchange for “protection” (greater assurance that at least one pod member, [the one most liked by the voters] will survive). Generally we want to avoid methods that allow strategic voting, but I see this as productive strategic voting as opposed to counterproductive results seen with plurality voting. The simple rule of thumb for deciding when to form a pod is “ignore trivial differences.” We appreciate your thoughts.

  4. This is an old post but I'd disagree with you that non-monotonicity is not a problem with voting system like IRV. Take the absolutely most common situation Left is running against Center and Right and all of them are reasonably close. Most of Left's voters have ballots that look like Left-Center-Right, and Right's voters Right-Center-Left. In short because the vote is close Center can come in 3rd or 1st but he can't come in 2nd.

    That means if Left is winning, but doesn't have an outright majority Left's best strategy is to make sure that Center gets eliminated before Right. This is especially important since if Left is winning, it most likely follows that more of Centers voters look like Center-Left-Right than Center-Right-Left. Because of this, it pays for a small group of Left's voters (activists) to vote Right-Left-Center even though Right is their least prefered candidate.

    That is to say the best strategy for disciplined voters is to cast a highly dishonest ballot. And note they don't have to know exactly how the other voters will vote they just have to be correct within a few percentage points most of the tie for that strategy to payoff handsomely. Similarly you have strategies like this when the candidates are HardLeft, SoftLeft, SoftRight, HardRight.

    I noticed you commented on this a little above. General voters can vote honestly. It is the 10% or so that are politically involved that can be safely instructed when to vote a dishonest ballot that make IRV potentially extremely destructive.

  5. Just my 2d. One of the arguments against Ordinal is that they are non-monotonic therefore will on occasion give the wrong result and that weakness can be exploited for tactical voting.

    1) Why is a non monotonic result "wrong"?

    2) I've never heard a convincing argument about how it can be exploited.

    The argument that it causes cognitive dissonance for voters is strange.

    You look through the candidate list and put a one next to your favourite candidate, then put a two next to your favourite remaining candidate, repeat until you run out of candidates or run out of candidates you know about.

    None of the quirks of the voting system should cause you to vote tactically. How can they? I challenge a critic to give just one example of a secret ballot where a political representative was being chosen with an electorate over a thousand where due to tactical voting the "wrong" candidate won. I'll give you a clue, there isn't.