Groups need to make decisions. You and your friends need to pick where to eat dinner; a country needs to choose its leaders. When the right choice isn’t obvious and we want to be fair, we often turn to voting. The problem is, voting isn’t always fair. There are many causes for bad outcomes in elections, of course, but an often-neglected issue lies in the method of voting itself.
In most cases, groups use a very simple system of one vote per person. This is easy to understand and implement, but unfortunately, it’s not very good at selecting the best decision for everyone. Let’s take a simple example of ten friends choosing a restaurant for lunch. If six of them want to eat pizza and the other four want burgers, the group should probably go to a pizza place. However, when the votes come back, there’s a surprising result: three votes for Pizza Bella, three votes for Pizza DaVinci, and four votes for Brown Bag burgers. The burger place wins with the most votes, even though picking either of the pizza places would have made more people happier.
This problem of “splitting the vote” is well-known, and the normal solution is to hold a primary. That is, the six pizza lovers should get together before the main vote and decide as a group whether they want to go to Pizza Bella or Pizza DaVinci. When the actual election rolls around, they vote together and win six-to-four against the burger folks.
Primaries are an okay answer, but what if there are three different pizza places? Or ten? Then they’re back where they started, trying to pick from one of many options. They could hold a primary before the primary, or a triple-primary, but that quickly gets impossible to sustain. In fact, Student Senate recently voted down a motion to make primaries mandatory for large student government elections this GM Week, since holding a primary takes significant extra resources.
Let’s take a step back: What makes a voting system good or bad? We need a way of measuring “goodness” for a group of people—this is what economists call utility. A system that produces more utility (think satisfaction or happiness) for more people is preferable to one that produces less.
This applies directly to voting. Consider a big election for Grand Marshal with five candidates, where three identify as Green Party members, one is affiliated with the Purple Party, and the last is an independent. Theoretically, each student voter has a preference for each candidate—a mental “rating” of how satisfied he or she would be if that candidate wins the election. (Calling it a rating is a little bit misleading, and one person’s rating isn’t exactly comparable to another’s, but thinking about it like that isn’t too horrible of an approximation in this case.)
Suppose that Grand Marshal election is run on the simple one-person-one-vote system, with a primary to pick the best Green Party candidate before the general election. To make things easy, let’s say the student body is split cleanly into Purple Party members and Green Party members. Purple Party members would be most happy if the Purple candidate wins, but they’d still be pretty satisfied with the independent candidate (although they’d be very unhappy with a Green Party winner). The Green Party thinks the same way: Green winner is best, independent is almost-as-good, and Purple is really bad.
It’s pretty clear where this goes—in the general election, either Green or Purple will win by a few percentage points. Half the electorate will be very satisfied, and half will be very unsatisfied. The total utility, however, is pretty low; the gains made by the winners are almost canceled out by the losses by the other side.
If we could hand-select a candidate in this example to maximize utility, the obvious choice is the independent. The entire electorate would be only a little bit less happy than if their favorite candidate had won and no one is unsatisfied, so the total utility is pretty high—at the very least, it’s higher than a winner from Green or Purple. (Of course, this conclusion is just for the hypothetical example; I’m not saying everyone should always vote for third-party candidates. Sometimes, though, a really good independent candidate gets passed over because he or she doesn’t have a chance in a general election.)
There are a number of alternative voting systems out there that try to achieve a higher utility than one-person-one-vote and primaries. One example is called Instant Runoff Voting, which is actually used in Australia and India. The idea is that voters should rank candidates in order of preference on the ballot. If no candidate receives a majority of first-choice votes, then the candidate who received the least number of votes is eliminated and another “round” takes place, using second-choice votes where necessary. (The process continues until one candidate has a majority.) However, while this is more efficient than running a series of primaries, it still doesn’t produce results with a much higher total utility. An Instant Runoff Vote in the Green/Purple example would still elect either a Green candidate or a Purple one, rather than the optimal independent.
A better solution is something called the range vote. It takes the utility model and translates it directly into a voting system. Each voter gives each candidate a rating, say a number of stars from one to five. The candidate who receives the highest average rating wins the election. When we use this system on our example race, we’d most likely see the independent candidate win with an average rating of maybe four stars (whereas the Green and Purple candidates would have ratings of around three each, as an average between the fives from supporters and ones from the other party). The reason range voting works so well is that it literally works on the idea of “the greatest good for the greatest number.” The voters describe their preferences in their ratings, and the winner is the candidate that makes the most people happiest (as described in their ratings). The system isn’t perfect—five star ratings aren’t an exact measure of utility—but it’s close, and it’s definitely better than anything else out there.
It’s not hard to understand, either—anyone who’s been to Amazon.com knows how to rate things. In fact, thinking about it in terms of a service like Amazon makes a lot of sense. Using one-person-one-vote in an election is like only letting users rate one book each on Amazon, and then only with a thumbs-up or thumbs-down. It ignores a lot of information and produces worse results.
However esoteric this all sounds, it’s important. There are a lot of problems people like to talk about with voting, but the math behind it isn’t one of them—and it should be. We can’t expect democracy to function correctly if our voting system doesn’t accurately capture the will of the people. It’s hard to effect this sort of change on a national scale, but anyone can step up in a club or school election and get people to consider a better alternative like range voting.
Seriously, next time you’re electing club officers, bring this up. Talk to people in charge; amend your bylaws. Make it an issue next year for GM Week—talk to Student Senate candidates that might join the Rules and Elections Committee. This is a technical school; we should vote like it.