Computing the winner under different voting rules with access to partial preference information.

What is it about?

When choosing between many options, it's hard for people to rank every single one. To make the process easier, we explored voting methods where voters only give their opinions on a smaller number of options. Our research focuses on a group of voting systems called "positional scoring rules" and looks at which of these can still work with limited input from voters. Surprisingly, some well-known systems, like plurality voting (where you vote for your favorite option), don’t fit this framework. We also found similar limitations for other voting methods, like single transferable vote (where the least popular option gets eliminated in rounds). These findings highlight fundamental limits in how much we can simplify voting without losing essential information. For methods that do work with fewer inputs, we calculated how many questions we need to ask to identify the winner. While we have precise answers for certain methods, figuring out the exact numbers for others, especially when randomness is involved, remains an open challenge. We did, however, make progress on one specific case.

Featured Image

Photo by Phil Hearing on Unsplash

Photo by Phil Hearing on Unsplash

Why is it important?

Voting is a powerful tool for making decisions, but it can become overwhelming when there are too many options. Imagine being asked to rank dozens of candidates or opinions you barely know about. Research shows that in such situations, people often feel frustrated, make random choices, or even opt out entirely. This is especially true in settings like large elections or online platforms where users are asked to weigh in on many opinions or ideas. To address this, some systems simplify the process by only asking voters about a few options at a time. While this makes voting easier, it raises a big question: can we still trust the results? Our research tackles this issue by identifying which voting methods work reliably when voters only provide limited input. We also explore how many questions we need to ask to confidently determine the winner. Understanding these limits helps design better voting systems that balance simplicity and fairness, ensuring that everyone's voice is heard—even in complex decision-making scenarios.

Perspectives