Week 8: Bump in the Road

After 7 weeks of relatively smooth sailing, I came upon my first major hiccup. In weeks 3 and 4, I explained how some of the voting systems that I was working with weren’t designed to work with truncated ballots, so I had to tweak them. Unfortunately, I messed up – or so I thought.

After taking quick glances at the data from the simulation that I ran last week, it seemed like the Bucklin voting method was behaving unexpectedly. There were two features that caught my eye, but the most glaring one was that, unlike every other voting method, when elections were truncated by one ballot, the winner didn’t match the “true” winner. 

First, I looked into whether there was a bug in my code, but after many thorough glances I moved on from that possibility. Since that wasn’t the issue, I decided to test my implementation of the voting system in other ways, such as manually calculating election results from profiles that caused Bucklin to find different winners from elections truncated by 1 candidate. 

Everything seemed to be working correctly, so I talked to my off site advisor about it. He explained a few things to me, which sorted my confusion. The fact that Bucklin elections truncated by 1 candidate produced winners differing from the “true” winners” was actually expected. 

As a quick refresher, Bucklin finds its winner by tallying up the first round of preferences, and if a candidate achieves a majority, it is declared the winner. If no candidate has a majority, the number of times each candidate was preferred second gets added to their first place tallies. If any candidate’s sum of first and second place votes is greater than 50% of the total ballots in the election, then they are the winner. This addition goes on until a candidate reaches a majority of votes, or every preference on every ballot is tallied, at which point the candidate with the plurality of votes wins.

I had rushed to assume that truncating ballots by 1 candidate shouldn’t affect the election outcomes. However, since voters don’t rank every candidate, there is no guarantee that a majority will be reached, which means that the last round of voters actually does affect the results.

Ultimately, It turned out that there weren’t any issues, which I was happy about, or else I would have needed to rerun the simulation, which took over a week to complete. Sorting out this situation took up my entire week, but I’m glad it’s behind me. Beyond what was described above, there are other interesting results that I will cover in the paper that I produce at the end of this project. Stay tuned!