Approval Voting:
Solving the Vote-Splitting Problem

by Tom Burrows
April 2, 2012
Version 2.1


Most current single-winner political elections use an election method called plurality voting in which you vote for a single "preferred" candidate. When there are more than two candidates in a race, plurality voting can cause problems like vote-splitting which lead to large-scale public dissatisfaction with election results. You know this is true when the vote splitting going on in some election is as big a story as the actual issues.

Both major parties have been affected by this; recall Ross Perot and Ralph Nader. The problem is even worse in primary elections, where you routinely see large fields of similar candidates splitting the same voter base.

Many methods have been proposed that are considerable improvements over plurality voting. They produce results more in line with the voting public's intent by providing ballots upon which voters can more explicitly express their intent. Instead of merely checking off one candidate, you can score or rank the candidates in various ways. Although election method theorists argue about which of these other methods is best, there seems to be a consensus that plurality voting is unacceptable and should be abandoned (for single-winner elections).

Approval voting is one of these election methods which are far superior to plurality voting. Specifically, it is the simplest of the score (a.k.a. range) voting methods just mentioned. A complete description requires only two sentences: Check off all the candidates you approve of. The winner is the candidate who is approved by the most people. (Again, we shall be talking about single-winner elections throughout this paper. Multiple-winner and apportioned-winner elections have different optimal voting methods.)

In addition to being trivial to describe to voters, approval voting has the least impact on clerks & recorders of all the big-improvement voting methods: It uses the same ballots and counting machines as plurality voting; and the only software difference is that "overvotes" are allowed and recorded. (I'm told that allowing and recording overvotes can be done by setting an option in some existing software.)

More complex election methods that are claimed to be even better than approval voting are not better by much, if at all. Some of these, like Instant Runoff Voting (IRV), calculate winners with complicated procedures harboring problems which can produce unintended consequences instead of actually reforming the election process.

The rest of this paper will describe in detail how approval voting addresses the problems created by plurality voting, and thus why we should be using it for single-winner elections.

Problems with Plurality Voting

When there are more than two candidates on the ballot, plurality voting frequently results in vote splitting and related issues like spoilers and "throwing your vote away" if you vote for the candidate you really prefer:

Taking the last two points together, we see that plurality voting can harm major and minor parties alike.

How Approval Voting Solves These Problems

Approval voting avoids vote splitting and its related problems:

Taking the last two points together, we see that approval voting can benefit both major and minor parties alike.

Eliminating the Need for Pre-Primaries

We have seen that general elections using the plurality method can be spoiled if more than two parties appear on the ballot. They would be spoiled even worse if multiple candidates for each party appeared on the general election ballot. In order to prevent this second level of spoilage, it is usual to prune the field in advance using primary elections.

But this only partially solves the problem. Primaries, even more so than general elections, have ballots populated by large numbers of similar candidates splitting the same voter base. Thus, when plurality voting is used in primaries, we still have a big problem with vote splitting—the problem primaries were supposed to solve.

This now snowballs into a need for pre-primaries to pre-prune the field at yet another level.

In Colorado these pre-primaries take the form of a complicated system of conventions attended by delegates who are chosen using yet another system of pre-pre-primaries known as caucuses. This system is almost impossible to explain to the public and is collapsing under the weight of its own complexity. An added problem is that, for reasons which are explained in a companion paper (Making Our Primary Votes Count in Colorado), the results of the convention process have only a tenuous connection to the intent of the original voters.

If approval voting were used in the primaries, then we could tolerate a large population of candidates on the primary ballot, the second level of pre-pruning would not be necessary and the pre-primary system (delegates and conventions) could be eliminated.

The conclusion is that the place where approval voting is most urgently needed as a replacement for plurality voting is the primary election process.

The Campaign Environment

When similar candidates run against one another under plurality voting, they are forced to wage war against one another with a ferocity that may cause embarrassment to their cause.

Suppose we have two roughly equally matched factions, and that one faction has two comparable candidates A and B on the ballot and the opposing faction has only one we shall call C. With plurality voting the outcome is destined to be roughly A:25%, B:25%, C:50%. Assuming that A and B are not likely to convince C's base (which is a different faction) to abandon their own political philosophy en masse, the only way A or B can get enough friendly voters to pump them up to the 50% needed to compete with C is to cannibalize each other. No one will be surprised if A and B spend more time slinging mud at each other than campaigning against their real philosophical opponent C.

Under approval voting, similar candidates running against a common philosophical enemy have an incentive to advance their common cause in ways that win approvals for their faction as a whole; and this will lift their approvals together like a rising tide.

Minimizing Complexity

On the surface, the instructions you follow to cast your ballot are equally simple whether the plurality or approval election method is used. The former's instructions are "Check off the one candidate you prefer" and the latter's are "Check off all the candidates you approve."

However, plurality voting is actually more complicated in the sense that you must frequently wrestle with the dilemma of whether to vote for your favorite candidate or go with a candidate who is less desirable but more electable. With approval voting, you simply vote for both.

Expressing Intent with Approval Voting

This leads to the following strategy you can follow when using the approval voting election method: Approve the best "electable" candidate and, in addition, approve all other candidates (if any) that are actually preferable. Approving the best electable candidate minimizes the chance of a feared candidate winning. And approving the candidates that are preferred even more not only "makes a statement"—one of them might actually win.

A simpler situation is when there are multiple candidates who are all equally "good" and electable, running against candidates you don't care for. Just approve all of the good ones. With plurality voting, you would need to guess which good candidate is other people's favorite (of the good candidates), "pile on" with your vote and hope other voters of like mind do likewise to avoid splitting the vote and handing victory to one of the "bad" candidates.

There are more strategies you could use with approval voting; but they typically boil down to having different thresholds for what is considered "approvable." E.g., if your attitude is "anyone but X", you could maximize the probability that X loses by voting for every candidate but X. At the other extreme, you might have such a high threshold that only one candidate is considered worthy of approval.

Note that a voter who does not understand that approval voting is in use and votes in the usual manner will still cast a valid and reasonable vote, since what they are doing is equivalent to simply voting with a very high threshold of approval.

Further Reading

The Center for Election Science []

Approval Voting: A Better Way to Select a Winner, by Steven J. Brams []

ApprovalVotingUSA [] (Frank Atwood's web site.)

The Center for Range Voting [] (Note: Approval voting is a type of range voting.)