Some Arguments in My Book for the Claim that Approval Voting is Superior to its Rivals

There has lately been what could be called a glut--indeed, a veritable superabundance!--of writing on proposed election law reforms, with a good deal of it finding its way to the email boxes of interested readers through the offices of Rick Hasen's Election Law Blog or the Substacks of a half-dozen scholars like Ned Foley, Rick Pildes, and Steven Hill. The most popular proposals these days seem to be Instant Runoff Voting (IRV), including both Ranked Choice and Condorcet methods. And the supporters of the various versions of these ordinal methods are, if I may say so, nearly at each other's throats. For what it may be worth, it's my view that all of these folks are, in a word, "barking up the wrong tree."

I haven't the slightest doubt <ahem> that all my readers here have already enjoyed (no doubt quite heartily!) my book on democratic theory. I suppose, however, that it is possible that several of you, after finishing that work and (fondly) laying it aside, have been kind enough to forward their copies on to friends without taking the trouble to memorize its most important passages first--a grievous, but perhaps forgiveable error. Well, despair not generous readers! There is now no reason to purchase another copy solely because you can't quite remember why Approval Voting is claimed therein to be superior not only to such ordinal rivals as IRV and RCN but also to Score Voting. 

Oh Frabjous Day! But....How is such good fortune even possible? Well (and please, there is absolutely no need for thanks!) it is managed by my reproduction below of one key section devoted to that subject. [Of course, if you'd really rather pick up another copy to refresh your memory of the entire argument, you can get one here. (I note that while link is specifically to the paperback version, there are, of course, also hardback and digital versions easily found nearby. I will also mention that the Brams/Fishburn book pictured above is also for sale there.) 

In any case, I haven't the slightest doubt that each of you DOES remember how I move on from soda choices to political candidates and from thence to the additional need for a multiple winner procedure--and what that should be--so I won't repeat any of that here. I will muse (regretfully) only on how much better off we would be in the U.S. today if people had listened.

Extract from Ch. 7 on Approval Voting

Suppose eight people (A, B, C, D, E, F, G, and H) are having a party and are trying to decide what soda to bring. (For simplicity, I here require a single winner by adding the assumption that, for whatever reason—maybe it would be a major hassle or much more expensive for there to be more than one choice of beverage at the party—only one sort of soda may be bought.) Now, let there be four possible choices: Cola, Lemon-Lime (“L-L”), Orange and Root Beer (“RB”). There is no unanimity among the planners and, being the good (small-d) democrats they are, they think that the majority ought to have its way and plan a vote to decide the matter. One of the eight is made secretary and, as we shall see, keeps careful track of the votes cast. Here is the result when they are asked to give their favorite soda of the four (here designated with check marks):

While Cola receives a plurality of the vote, no flavor gets a majority. One member of the group therefore suggests a run-off election among the first and tied-for-second contenders only, leaving off RB all together since it did so poorly. Here are the results of this run-off election with ‘A’ indicating an abstention): 

 

Obviously, this second vote does not help. There has been no movement at all because voter H absolutely loathes all the flavors except RB and refuses to pick any of them as even passable choices for the party. The revelers aren’t completely stuck though, because there are other possible voting schemes. I will suppose that they are skeptical of ranked choice voting (“RCV),[i] not because they have heard criticisms of it involving vote splitting, non-monotonicity, or insincerity,[ii] but because they worry that it may not get party-goers what they actually want. They take this to be a possibility because someone might prefer one flavor to another even if she really dislikes both of them. So, perhaps unlike other democracy investigators, our group’s dismissal of ordinal methods does not involve concerns that the unavailability of intersubjective measuring sticks might allow for a huge divide between one person’s 1st and 2nd choices and hardly any at all between another person’s two top picks. Instead, they just doubt whether a collection of preference orderings can ensure that they will meet their goal of landing on a beverage that the party-goers actually want to drink, something that will be a “successful choice” for the participants generally. This concern can be taken to be a recognition that a sort of cardinality is required here, something that, at the very least, allows the assignment of a Yes or a No to each flavor, where a “Yes” means “this is better than nothing” and a “No” means “this is useless or worse.” Such assessments can correctly be said to mean the same thing to everyone. They reliably correlate in a way that ordinal preferences do not.

Two members of the group have suggestions. One has been swayed by literature she has received from a group advocating Approval Voting (“AV”),[iii] and the other is a sports and cinema fan and understands that rankings of teams and movies usually use some form of Score Voting (“SV”), where each voter gets to assign a number of points (or stars) to each candidate, and the points are summed to find a winner or produce a ranking. This two-member sub-committee decides to allow points to be assigned, but only if the system excludes everything that seems to them impossible to compare. That is, they agree to keep out any allotments of point differentials that might suggest “a little better than” to one voter but mean “much, much better than” to another. In their search for additional trustworthy information, they come up with the following (arguably cardinal) scale:

BOTH ENJOYABLE AND THE BEST OF THOSE LISTED                  4 PTS
GOOD ENOUGH (WOULD DRINK IT IF AVAILABLE)                       3 PTS
PASSABLE (NEVER HAD IT BUT WOULD TRY IT IN A PINCH)    2 PTS
NOT OK (NEVER HAD IT AND WON’T TRY EVEN IF THIRSTY)    1 PT
REALLY DISLIKE IT                                                                                0 PTS

The AV supporter insists on an additional condition. She agrees with the use of this scale only if the assignments of 4, 3, or 2 points are also counted as “Approvals,” and assignments of 1 or 0 are considered disapprovals. This is settled upon as well, and the third vote is duly taken. The secretary represents the approvals here with a check mark, and circles the two sums representing the highest number of points and the most approvals $$$

The results are disturbing. While the Plurality victor was Cola, the SV winner is Orange and the AV winner is L-L!

Perhaps it will seem that this embarrassment of winners is the result of the weirdness of there being so many “never tried it” votes with respect to what seem like common carbonated drinks. But it is important to realize that an attitude of “I really don’t know much about her (or it)” toward a political candidate or proposal is not unusual at all. Look at the secretary’s registers above again, but this time, think of them as the results of a political election for a representative, each of whom is put up by a different party. (Perhaps replace “Cola” with “Corporatist”; “L-L” with “Liberal”; “Orange” with “Outsider” and “RB” with “Republican.”) We can also think of the individual partygoers above as voting blocs. This may make it clearer that there can be a large number of decisions in which the assignment of the sort of SV points allowed by our party-goers would largely be a function of the varying amounts of risk that voters are willing to take. Some people will be OK with this or that relatively unknown candidate or proposal; others will not be willing to take their chances.

Brams and Fishburn 2007, perhaps the most complete and ardent work written in support of AV, does not say very much about what “approval” means. They merely note in passing that it is “voting for” something/someone or “finding it acceptable.” It is important to recognize that in some cases we may find none of the candidates “acceptable” even though one or two seem to us a bit better than the others. In such cases, do we “approve” of any of them or not? Should we understand approval to mean Is OK with? Thinks is pretty good? Supports? Hopes will win? something else? Couldn’t each of these understandings of “approve” produce different results in an election?[iv] This is a matter, discussed in previous chapters with reference to CHOICE, that I believe to be central to the question of what matters when one votes. And it is my view that the soda story above is quite helpful here. We have taken the first three on this list to be approvals:

BOTH ENJOYABLE AND THE BEST OF THOSE LISTED                  4 PTS
GOOD ENOUGH (WOULD DRINK IT IF AVAILABLE)                       3 PTS
PASSABLE (NEVER HAD IT BUT WOULD TRY IT IN A PINCH)    2 PTS
NOT OK (NEVER HAD IT AND WON’T TRY EVEN IF THIRSTY)    1 PT
REALLY DISLIKE IT                                                                                0 PTS

This is because, ex ante, we do not think our lives will be better off if anything satisfying either of the bottom two lines is picked. We might say that those two bottom lines seem to us to be Equal to Or Worse Than Getting Nothing at All. On this view, those only are the unsuccessful choices, and all others may be called successful—even though we may not particularly look forward to the of obtaining those we deem only “PASSABLE” and would admit that we may discover that we hate them. That is how affirmative votes (or approvals) should be understood throughout this book. It is a conception tightly connected with the concept of success. Notably, it does not involve favorites or preferential orderings, and so, perhaps, could not be used to construct an indifference curve. A choice should be deemed “successful” at time t if and only if its result is expected by the chooser to provide something that, at t, seems like it would be better than nothing at all. Of course, this is consistent with the unpleasant fact that when we make poor choices, our lives may get worse in spite of that “success.”

So, who (or what) should the authentic majoritarian take to be the winner in this election? The Corporatist (or cola), because he (it) is the favorite of the largest number of voters? The Outsider (Orange), who/which got the highest score? Or the Liberal (Lemon-Lime), who/which most voters found to be at least minimally palatable? In my view the third answer is best: it is the number of approving voters that the best democratic practice should take to matter most. Why? Just as we ought not to be stuck at parties with nothing we can stand to drink, we ought not to be stuck with ruler/representative A when more people among us can stomach candidate B. This is the position that I believe produces the nearest thing to a consensus victor and, is thus more likely to knock out the sort of outliers who are most discordant with anything that might be considered a general will. So, it is my view that if it is to be used to determine what the people do or do not want, aggregation should be taken to be the counting of approvals, where each person’s approval is given the same weight as everyone else’s, regardless of how enthusiastic or tepid it is.

Surely this tack will be more conducive to stable regimes than ones according to which candidates whom a majority of the populace absolutely do not want may get to take office. Obviously, I cannot insist that nobody could mean anything else by “consensus” or that “egalitarian democracy” simply must require AV. But I believe that mine is at least a reasonable approach that not only does well against known competitors, but captures much of the common sense understanding of “consensus.”

AV has some obviously desirable characteristics besides being uniquely competent to reflect the principles that motivate CHOICE. First, while it can countenance more than two candidates in a single-winner election, it is not susceptible to transitivity cycles, since it allows us only the choices of approval and non-approval. Thus, in a situation with seven candidates, whether we approve one, three, or six of them, there is never a danger of intransitivity. Second, it is consensus-building/revealing by its very nature. Indeed, in legislatures and committees, substituting simultaneous approval votes on alterations of proposals (placed beside both the original proposal and “no bill at all”) for the current practice of successive votes on amendments would vastly democratize procedures by eliminating the absurdly inappropriate power now held by agenda-setting moderators (Riker and Weingast 1988). Finally, it is easy to understand.[v]

Criticisms of AV[vi] have focused on a claimed likelihood of producing unsatisfactory results if voters bullet their favorite candidates in violation of the system’s explicit instruction that all approved candidates be voted for. Perhaps it would help in the effort to resist the lure of preferentism to put specific instructions on ballots indicating that what is wanted are bare approvals only: indications of which candidates are "passable."[vii] Thus, perhaps:

 

Vote for every candidate you think would be minimally OK, i.e., you would give a grade of PASS to them if they were considered strictly on a PASS/FAIL basis.

 

Insisting that such instructions will always be resisted in favor of doing whatever one can to elect one’s favorite[viii] is an empirical assertion of psychology, and those making it should understand that if they are right, the irrationality of social choices is inescapable, and reaching consensus will always be mere luck. This is because, as Arrow has shown, use of ordinal scales provides no possible means of coherently determining what would make a populace relatively content with governmental actions.[ix] Fringe candidates that most voters find abhorrent could always be selected. In the next chapter I will suggest a way one might overcome preferentist defeatism of this sort by buttressing minority voices in government.

It is interesting to consider Lindsay’s appraisal of theories that deliberative consent is a solution to the main problem of democracy in light of AV. Lindsay was a strong proponent of small group, Protestant-style deliberation as the best model for democratic practices. But he saw the limits of unanimity-building when he indicated that the margin between most and all must be filled. Why? Consider a church group of 50 people that cannot agree on whether to tear down their building and put up a new one, fix up the current one, or do nothing at all. Suppose the split is 35 for repair, 10 for tear-down, and 5 for nothing whatever. They debate and debate but make no progress. What happens? Do the five (“do nothing at all”) folk win if unanimity is never reached, or do we excommunicate them as “others” as Schmitt would have advised, and achieve unanimity that way? One devout Calvinist to whom I put this question, responded that, “Usually the dissenters get tired and concede or move on. Often folks just smile and ignore them like you do with a crazy old uncle.”

But, of course, there are two ways to “ignore” this group of five. One is to pretend they are not there, the other is to halt the proceedings until these dissenters retire or die off, which would, in this case, be allowing the proposal with the fewest supporters to win the day. Lindsay saw the hopelessness of the “perfect accord” approach in such situations and so might have supported AV, according to which the church would have been repaired—the moderate position. The “do-nothing” group would not have gotten their way, but, assuming adequate and fair deliberation took place, they would have had their appropriate say both prior to and within the election. It would not be might that made the result right, but the group’s fairly-assessed and aggregated desires, since nothing else (that the vote might have missed) is “really right.” As I will discuss further below, I don’t believe that AV is quite enough to guarantee the entire filling of Lindsay’s margin between most and all within large, necessarily non-deliberative groups like U.S. voters in large electoral districts, but I do think it is a crucial first step.

 

---

[i] Under RCV, voters rank as many of the choices as they would like. If no candidates receive enough first-choice votes to win, the candidate receiving the least first-choice votes is eliminated, and the vote counters see what the second choices were of the voters who most liked this eliminated candidate. Those second-preferences are then distributed as if they were first-choice votes. This process is continued until some candidate(s) have/has enough votes to win. RCV is thus a way to conduct iterative instant run-offs, dropping the bottom candidate each time. Without specifying more complete preference orderings of the party-goers, it is impossible to determine which type of soda would come out on top pursuant to RCV.

[ii] See Brams and Fishburn 2005.

[iii] The voting rule for AV is quite simple: Vote for all and only those candidates you minimally approve of by making a mark next to the name of such candidates. These votes/marks will be summed. The candidate getting the most votes wins.

[iv] I have benefited from discussions with Kevin Zollman on this matter.

[v] It will likely be observed that everyone who writes about voting rules seems to have her own particular favorite. Sometimes such promotion stems from the calculation of likely outcomes given various estimates of voting strategies among the electorate. But theorists also attempt to demonstrate that their pet mechanisms provide the most accurate aggregations of individual preferences over a set of more than two options. But AV is not intended for that purpose at all: it maps (much easier to sum) approval profiles rather than preference profiles. In the next chapter we will look at another mechanism that eschews ordinality, but does so for a different purpose. Both procedures reflect my view that general wills are not ordinal rankings.

[vi] See, e.g., Nagel 2007.

[vii] Notwithstanding current television ads insisting that "Just OK is not OK," most people will agree that a grade of Pass is better than having to retake a class. What is actually “Just OK” or acceptable/approvable need not be BEST, anybody’s favorite, or even terribly good.

[viii] Caleb Huntington has speculated in conversation that this predilection might be related to the utility gain, for primitive hunters, in choosing only one antelope in the herd to focus upon and chase, even though any number of others would do just as well.

[ix] With respect to compiling ordinal lists, I agree with Riker and Weingast (1988, 382) that “tinkering with the mechanism” is pointless. There simply is no coherent way to sum individual rankings to determine what a group wants. In my view, to find the general will, one must scrap preferentism completely.