A Superior Voting System

by Robert Z. Norman | 10/17/05 5:00am

The subject of voting procedures in alumni elections has been the topic of several opinion pieces and letters to The Dartmouth in the past five months. The current draft of a new Association of Alumni constitution proposes a change in the voting system for the election of alumni trustees.

As an emeritus professor of mathematic who taught at the College from 1956 to 1992, and continues to work with undergraduate students through the Math and Social Sciences Program. I have studied the practice and theory of voting for many years and have taught courses on the subject at Dartmouth. It is one of my principal areas of research. I would like to comment on the proposed change.

In 1990 the Alumni Council decided that there should be at least three candidates for the election of a member to the Board of Trustees candidates. The Council recognized that in an election with two or more candidates, there are many well-known faults with the most common method of voting, Plurality Voting, in which voters can vote for only one candidate.

I was pleased to be consulted at that time by the committee studying this issue. After much deliberation the committee recommended Approval Voting for future elections. In Approval Voting, voters may vote for as many candidates as they want to support, and the winner is the candidate with the most votes.

The current proposed change is to a system of Partial Preference Voting in which a voter "may vote by ranking his or her First Choice and Second Choice." If any candidate has a majority of the first choices on the ballots, that candidate wins. If no candidate has a majority, then the candidate with the fewest first choice votes is scratched from the ballots and the process is applied to the resulting ballots. A candidate must have a majority to win; if none has a majority, the process is repeated until some candidate has a majority.

I believe that the current system, Approval Voting, is significantly better than either Plurality Voting or Partial Preference Voting.

In electing a Trustee, one hopes to find the most preferred candidate of the voters. This sounds simple, but when there are three or more candidates it isn't. Kenneth Arrow, who won a Nobel Prize for his work more than 50 years ago, showed that while it is easy to describe characteristics that "most preferred" should satisfy; it is impossible to satisfy all of them. However, some voting systems have more faults than others.

Consider this problem: Suppose Anderson, Baker, and Cook are candidates in an election using Partial Preference Voting in which Cook is the winner. If some of the voters who rated Baker first and Cook second had, instead, voted Cook first and Baker second, wouldn't you still expect Cook to win? It is hard to imagine that someone getting more first place votes ought to lose because of that, but, under Partial Preference Voting, it can happen -- despite these additional votes, Cook would lose and Anderson would win instead!

Imagine the story the next day: "Cook won last night's vote, but if he had received more first place votes, he would have lost." Proponents of voting systems like Partial Preference Voting claim that such anomalies almost never happen, but in close elections they can happen often enough to be troubling. This anomaly cannot occur under Approval Voting.

One other problem with Partial Preference Voting occurs in a polarized voting body. If candidates Diver and Farmer are polar opposites and each attracts first-place votes from a little less than half the electorate, an attractive third candidate Edson might be rated second by most of them, even though Edson gets fewer first-place votes than Diver or Farmer. Under Partial Preference Voting, Edson would be eliminated, and Diver or Farmer would win, leaving a large number of voters dissatisfied. Under Approval Voting, by contrast, if Edson is appealing enough to generate a lot of second approval votes, Edson would win the election as the compromise candidate. Thus, Approval Voting is more likely to produce consensus candidates than either Partial Preference Voting or Plurality Voting.

A major fault with Plurality Voting is that when voters come to believe that their favorite candidate doesn't have a chance, they will dump their favorite and vote strategically for another candidate they like less well. Thus their vote doesn't reflect their true preference. Similarly, under Partial Preference Voting, voters are apt to give their first choice to some other candidate, demoting the one they most prefer. Under Approval Voting, even if they vote for fewer or more candidates, they will still vote for their favorite.

Some critics of Approval Voting claim that the ability to cast more than one vote gives voters who do so an advantage. Since every voter can vote for several candidates, that option is fair to all. But it is easy to show mathematically that sometimes casting only one vote is optimal, especially if you have a clear favorite. On the other hand, if you're relatively indifferent between two candidates, you do best by voting for both of them, helping either one to win. Also, if your favorite does not seem viable, Approval Voting gives you the opportunity to vote for a second choice to try to prevent a worse choice from winning.

Other critics of Approval Voting claim that it is confusing to voters. However, it is quite possible to clarify the system for Dartmouth alumni through instructions and information. The idea is, "Vote for as many candidates as you want to support."

I have found that a substantial majority of academic experts, a list that includes Nobel Laureates, favor Approval Voting over systems that use successive eliminations, especially ones like Partial Preference Voting that limit expressions of preferences.

In my opinion, Approval Voting is like democracy itself -- flawed but still a better system than any other, and Dartmouth alumni should stick with it.

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