Expressiveness in Approval vs. Ranked Ballots

Introduction

At first glance, a ranked ballot appears more expressive than an approval ballot. Here's an example of an argument favoring a ranked ballot:

"Approval voting means you give the same score to the candidate you love, the one you like, and the one you hold your nose for. Not very representative of voter preference..."
~Anonymous IRV advocate

Response: Consider Accuracy & Efficiency

This argument is actually partially correct. A ranked ballot indeed has more potential expressiveness than an approval voting ballot. However, that's only one factor governing the ultimate representativeness of a voting method. The other two are:

  1. The accuracy of the information the voter puts on the ballot
  2. The efficiency of the tabulation algorithm used by the voting method

When these additional factors are taken into account, approval voting is more representative than IRV (as well as the other commonly discussed ranked methods, in general).

Ballot Accuracy

A ballot's potential for expression is only as good as the accuracy of the information the voter puts on it. Unfortunately, all deterministic voting methods give voters an incentive to put insincere (i.e. inaccurate) information on their ballots. This is true for both IRV and approval voting, but the tactical incentives with IRV are substantially more detrimental to its performance.

To explain why this is, the general tactic with virtually every deterministic voting method is to identify the two most likely winners, and give the more favored one as much support as possible, while giving the other as little support as possible.

With approval voting, that still leaves the voter free to approve everyone he sincerely prefers to the frontrunners, making it quite resistant to tactical behavior. Whereas this is not possible with any voting method which forbids giving equal support to multiple candidates. Hence those methods, particularly IRV, tend to degenerate toward plurality voting in practice.

Tabulation Efficiency

Here's a simple way to understand the importance of the tabulation algorithm. Imagine a ranked voting method in which the winner is the candidate with the most first-place votes. In effect, that would be identical to plurality voting, because all the rankings coming after the first would be ignored. Despite the representativeness of the ranked ballot used by this system, the representativeness of the election would be no better.

IRV is not quite as bad as that theoretical method, but it does throw away a lot of data, unlike approval voting.

Approval Voting Election Results Are More Representative

There is an objective "economic" measure of the representativeness of voting methods, called Bayesian regret, which simultaneously incorporates the aforementioned factors with an objective weight. The following graphic of Bayesian regret values is taken from page 239 of the William Poundstone book Gaming the Vote. It provides a simplified look of the relative performance of several voting methods.

Note that score voting (aka "range" voting) and its simplified form, approval voting, both far exceed the performance of IRV with any ratio of strategic-to-honest voters, i.e. approval voting is better with 100% tactical voters than IRV is with 100% sincere voters.

Chart comparing common voting methods by simplicity and group satisfaction

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