The citizens of Flatland need a new president. Having seen the problems with first-past-the-post voting though, they also need to come up with a way to elect that president and still ensure a couple things. First, all the shapes wish that they could vote for whoever they support, without having to think about how everyone else is going to vote.
Second, there can only be one president. And third, a spoiler candidate should not change the results of the election, if multiple candidates from the same party wish to run.
After much deliberation, they decide to host the next election with an approval method of voting. In approval voting, rather than pick one candidate that they wish to win, voters can put a check next to each candidate’s name, indicating that they would not mind having this individual in office. They can check as many candidates as they like, or none at all (though this doesn’t affect the outcome, so it’s the same as not voting). Essentially, an approval system gives voters one vote per candidate: for or against.
As it currently stands in Flatland, the population is divided up politically into five parties: 35 percent are Square partisans, 36 percent are Triangle partisans, 7 percent are Circle partisans, 10 percent are Star partisans and 12 percent are Parallelogram partisans (Figure 1). Triangle and Square still make up the major political parties and the majority of all voters, so in a first past the post system, one of them would certainly win.
However, things turn out a bit different in an approval system. Square voters support Square, obviously, but they also approve of the policies held by Parallelogram, so they “approve” of him too on election day. Triangle supporters don’t like the policies of any other parties, so they only approve of Triangle.
Circle supports herself and Parallelogram. Star voters are somewhat in between Triangle and Square and as such approve Star, Triangle and Parallelogram. Parallelogram approves of themselves, Square and Star candidates.
When all these approval checkmarks are tallied up, Square is supported by 47 percent of the population, Triangle by 46 percent, Circle 7 percent, Star 22 percent, and Parallelogram is supported by a winning 64 percent (Figure 2)! This is a surprising result, since Parallelogram is not a major party; both Square and Triangle have about three times as many supporters.
But by appealing to a wide range of voters, Parallelogram was able to get many differing political parties to approve of him and thus could win the election. The advantage of this system is that the majority of voters (64 percent) have a president that they approved of on election day. The disadvantage, however, is that a relatively small percentage (12 percent) of the population had their first-choice party elected.
Beyond this simple election, though, approval voting is more resilient than first past the post: If another member of the square party was to run in the election, not much would change. The square voters could approve of both candidates, and subtle differences between the two candidates would lead to some voters giving approval to one and not the other, thus giving the better-liked candidate a greater chance to win. So spoilers do not upset elections in approval systems.
Plus, perhaps the best part of approval voting is that no tactical voting strategies are required. You can’t “waste your vote” on candidates that are unlikely to win; each voter just votes for the candidates that shapes support.
Inspired by this new presidential election system, the citizens of Flatland decide to redo the way they elect their congress in order to reduce the effects of gerrymandering and allow voters to not have to think about who everyone else is voting for. To do this, they’ll have to implement an entirely new concept of what a vote means: the single transferable vote.