Single transferable vote leaves no vote behind

The citizens of Flatland, inspired by their new presidential system, decide to revamp how representative elections are done. They do have a slight issue with a straight approval system though: it doesn’t give a way for voters to indicate that certain candidates are preferred to others; voters can only give a candidate approval or not. So to make its new congress as representative as possible, Flatland uses a new system of voting, single transferable vote. The single transferable vote system, or STV, works by having each voter rank the candidates.

Implementing a STV system requires a few changes to Flatland, though. Instead of having a bunch of small districts which each elect one representative to congress, the country is refactored in a few large districts, each of which sends several representatives to congress. Then, on election day, each voter ranks the n candidates on the ballot from 1 to n. Let’s look at one district in Flatland. Each party votes as shown in Figure 1.

After voting, votes are tallied according to each party’s first choice, similar to first past the post [Figure 2].

However, simply having the most votes does not guarantee a victory. Since this district sends three representatives to congress, a candidate must have (100 percent / representatives + 1), or 25 percent of the vote, to win. In this election, Square has 35 percent of the vote, so it instantly wins one spot. In traditional first past the post, the other 10 percent of the votes for Square would be wasted. This is not the case in single transferrable vote. Those votes go to the voter’s second choice. In this case, Square’s voters’ second choice was Parallelogram, so that’s where the extra votes go [Figure 3].

Since not enough candidates have hit the 25 percent threshold yet, we now eliminate the candidate with the least number of votes. In this case, that would be Circle. Circle’s voters’ second choice is Square, who’s already elected, so the votes can’t go there. Instead, we look to their third choice, Parallelogram. The votes are redistributed, and the new distribution is as follows [Figure 4].

Parallelogram has now won the second spot, despite starting with only 12 percent of the vote! In fact, getting Circle’s votes pushed it over the boundary, so the extra 6 percent of votes are redistributed to Circle’s next choice, Triangle [Figure 5].

This last batch of votes pushes Triangle up over the threshold, so he wins the final spot, thus concluding the election.

This election provides a prime example of the qualities single transferable vote lauds. Under STV, it is not as important to cater directly to a smaller group of voters to become its first choice, as is the case under first past the post. Instead, an optimal strategy is to be well liked by all voters. Although Parallelogram had very few direct supporters (ranking second last in this category), it placed fairly highly on the vast majority of voters’ rankings. The merits of this system in practice can be debated. (Will a candidate who wants to please everyone get anything done or just try and maintain the status quo that got them vast support at election time?) But the candidates’ motivations are not the real strength of STV.

Single transferable vote radically differs from many current voting criteria in that it does not require tactical voting. In STV, how everyone else votes doesn’t affect how you should vote. A voter does not have to worry about wasting their vote by putting a smaller, less likely to win candidate first: If this candidate doesn’t make it, then the vote is simply transferred to the next candidate on the card. You cannot waste your vote on a minority party, which makes minority parties much more viable than in plurality systems. Similarly, there is no need to “vote against” a certain candidate to make sure he or she is not elected. Simply put him or her at the bottom of your ranking, to ensure your vote goes to people you would rather see in office. In fact, some versions of STV allow voters to stop ranking candidates at any point, thus ensuring that their vote will never go to a candidate that they don’t want in office. Although it initially seems much more complicated than first past the post to a voter, to the informed voter, STV is actually much simpler. You just vote for who you want, without worrying about who everybody else is voting for.

Post Author: tucollegian

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