Voting to select or rank-order alternatives
For management teams, the most common method of selecting an alternative is to engage in a period of discussion and then put the matter to a vote, usually by asking for a show of hands. However, as we will next see, there is much more to voting than a simple show of hands. Management teams that want to make the most of their collective judgment would benefit from knowing it.
Voting theory (also called "consensus theory" or "social choice theory") is the mathematical study of how democratic groups construct a social preference from a set of individual preferences. At first glance, voting theory may strike you as much ado about nothing. After all, how tough can it be for a group to choose between two alternatives? All they have to do is employ a majority voting procedure, i.e., choose the alternative that receives more than half of the votes. Or, they might employ a three-fourths majority vote in which the winning candidate must receive no less than 75 percent of the votes. Either way, the process is pretty simple.
Voting is simple when there are only two alternatives. But when there are more than two alternatives, things get a lot more complicated—so much so that Stanford economist Kenneth Arrow was awarded the Nobel Prize for proving that there is no consistent method of making a fair choice among three or more alternatives. Arrow’s “Impossibility Theorem” establishes a number of fairness criteria and then proves that it is impossible to devise a voting method that doesn’t violate at least one of the criteria.
Before we go on, note that the terms candidate and alternative will be used interchangeably. Whether we are voting for a person (often referred to as a "candidate") or a proposed action or idea (generally referred to as an "alternative"), the issues are fundamentally the same.
Plurality Voting
While Arrow's Impossibility Theorem says that no voting method is without problems, some methods are better than others. Plurality voting is considered the worst of the lot. Most people are familiar with plurality voting because it is used in the United States’ presidential election system. With this method, each voter casts one vote, and the candidate or alternative that receives the most votes is deemed the winner. For example, in the following election candidate A, with 40 votes, is the winner.
Candidate A 40 votes
Candidate B 35 votes
Candidate C 25 votes
Total 100 votes
The problem with the plurality method is that the plurality winner can be everyone else’s least favorite candidate. As voting theorist Donald Saari puts it, "The plurality vote is the only procedure that will elect someone who's despised by almost two-thirds of the voters."
Plurality Voting with Elimination
A somewhat better process is plurality voting with elimination. With this method, the winner must receive more than 50 percent of the votes. If the condition is not met, the alternative with the lowest number of votes is eliminated and voting is repeated. Had this method been used in the foregoing election, candidate C would have been eliminated and a second election held. Look who wins this time around.
Candidate A 45 votes
Candidate B 55 votes
Total 100 votes
Approval Voting
Approval voting dates back to the 13th century, when Venetians used it to help elect their magistrates. With this method, each voter can cast one vote for every candidate he/she approves of. The candidate that receives the highest number of votes is the winner. Thus, in an election with 100 voters, it would be theoretically possible for each candidate to receive as many as 100 votes. A more likely outcome, however, would be something like the following.
Candidate A 35 votes
Candidate B 80 votes
Candidate C 55 votes
Total 170 votes
An advantage of approval voting is that a voter can express support for a dark horse candidate without feeling that he has "wasted" a vote. It also provides voters with various ways of expressing themselves. For example, if a voter prefers a candidate above all others, he can better express himself by voting for that candidate and no other. Or, a voter who hates a particular candidate can express himself by not voting for the hated candidate and voting for all of the remaining candidates.
Borda Count Voting
The Borda count was used in the Roman senate. Although it sounds obscure, sports fans will recognize it as the method used to rank college sports teams. In a Borda count, each voter ranks all the candidates from top to bottom. If there are, say, five candidates, then a voter's top-ranked candidate gets 5 points, his second-ranked candidate gets 4 points, and so on. The points from all the voters are added to determine the winner.
For example, let's assume that three people vote for three candidates named A, B, and C in the order shown below. Candidate A with two first-place votes and one second-place vote wins with a total of 8 votes (3+3+2=8). Candidate B with one first-, second-, and third-place vote comes in second with 6 votes (3+2+1=6). Candidate C with one second-place and two third-place votes comes in last with 4 votes (2+1+1=4).
Order Voter 1 Voter 2 Voter 3
1 A B A
2 B A C
3 C C B
Like all the methods, Borda count voting has strengths and weaknesses. Its principal strength is that it avoids certain paradoxical results that occur with the other methods. One of its weaknesses is that it is more complicated than plurality and approval voting. It's also more susceptible to manipulation by strategic voters who want to "beat the system." A third weakness is that voters may be very certain about their most- and least-liked candidates, but wishy-washy about candidates in the middle range. As a result, middle-range candidates may be chosen more or less randomly, especially when the list of candidates is a long one.
Pairwise Comparisons
Using the method of pairwise comparisons, each alternative (or candidate) is compared with each other alternative. The alternative that wins is given one point and the alternative that loses is given no points. In the event of a tie, each alternative receives a half point. The candidate with the most total points is the winner.
As before, let's assume three candidates and three voters. The results of each pairwise comparison are shown in the following table. Alternative A wins in four comparisons, ties in one, and loses one, so it scores 4.5 points (1+1+1+1+.5+0=4.5). B wins in one comparison, ties in three, and loses twice, so it scores 2.5 points (1+.5+.5+.5+0+0=2.5). Alternative C wins once, ties twice, and loses three times, so it scores 2.0 points (1+.5+.5+0+0+0=2.0).
Matchup Voter 1 Voter 2 Voter 3
A vs. B A A Tie
B vs. C B Tie Tie
C vs. A C A A
Pairwise comparison voting satisfies what is known as the Condorcet criterion, which states that the winner of an election should be the candidate who defeats all the others in a head-to-head matchup. As a practical matter, pairwise comparison can be very laborious because of the large number of comparisons that are required, which equals n(n-1)/2. It also lends itself to inconsistent evaluations.
Weighted Voting
Any of the foregoing methods can also be used in a weighted vote. A weighted voting system is one in which the preferences of some voters carry more weight than the preferences of others. An example is shareholder voting, where shareholders are allocated one vote for each share that they own. Thus, larger shareholders have more votes, or weight, than smaller shareholders.
Ranking Procedures
Ranking procedures are used to provide a complete ranking of the alternatives from first to last place. Two ranking methods can be used with any of the foregoing voting methods. The extended rankings method involves running the election and ranking the candidates based on how they did relative to the other candidates. The recursive rankings method entails the following steps: a) run the election, the winner gets first place overall, remove the winner from the list of candidates, b) run a new election, the winner gets second place overall, remove the winner from the list of candidates, and c) continue until all candidates are ranked.
So What? Who Cares?
The concept of voting is so strongly associated with the idea of electing people to office that it's hard for most people to see how it applies to decision-making and problem-solving. In order to make the leap from electing a candidate to selecting an alternative, it will help to look at a couple of unique applications of Borda count voting.
The first application has to do with space flight. In 1973, scientists used a Borda count vote to choose among several possible trajectories on the Voyager missions to Jupiter and Saturn. The second application pertains to computerized character recognition. One method that computer scientists employ is to have different computer programs vote on different interpretations of a character. For example, they might vote on whether the character should be interpreted as an "8," "6," or "3". Error rates drop from one in 166 characters using the majority voting method to one in 1,000 using a Borda count.
Substitute "strategies" for "trajectories" and you begin to see how voting theory can be profitably applied in a business context. A team of managers might improve their performance by using Borda count voting to combine their judgments when choosing among several possible strategies. Use "explanation" instead of "character" and you start to understand how voting theory might be used to interpret a particular situation. Would error rates drop if the team were to use Borda count voting to cooperatively assess three possible explanations of some situation or phenomenon?
Organizations would do well to add voting theory to their skill set. As you now know, there's much more to the process than simply asking, "Can we have a show of hands?"
Kevin W. Holt, the founder of Co.Innovation Consulting, is a strategic planning consultant and meeting facilitator based in Phoenix, Arizona. He works with commercial, government, and nonprofit organizations to develop innovative strategies and solutions. His strategy consulting and meeting facilitation practice centers on the use of proven processes mapped to collaboration technologies (e.g., electronic brainstorming) and specialized software tools (e.g., the Blue Ocean strategy canvas). The technologies enable him to serve as both an offsite meeting facilitator and a virtual meeting facilitator for strategic planning workshops, innovation labs, brainstorming sessions, feedback sessions, and other types of meetings. Kevin is the author of Differentiation Strategy: Winning Customers by Being Different, published by Routledge in June 2022.