Nicola Lo Russo

nlorusso [at] ethz.ch Nicola Lo Russo
Different Voting Systems and How They Yield Different Winners

Different Voting Systems and Their Outcomes

Why This?

In my undergrad, I started studying voting theory — and it blew my mind how the same group of people, voting honestly, can end up with completely different winners depending on the system used. This is a small intro, not too formal, just to play around with ideas and see for yourself how messy (and fascinating) collective choice can get.

The Voting Systems

Here's a quick tour of some common (and not-so-common) voting rules:

  • Plurality: Everyone picks one candidate. Most votes wins. Simple, but often unfair.
  • Borda Count: Voters rank candidates. Higher ranks get more points. Think of it like Eurovision.
  • STV (Single Transferable Vote): Ranked voting where the least popular gets eliminated and votes get transferred until someone gets a majority.
  • Llull's Rule: Every candidate is matched one-on-one with every other. Win the most pairwise duels to win overall.
  • Plurality with Veto: You vote for someone and veto another. Winner has best net score.

The Condorcet Winner

This is a key concept in voting theory. A Condorcet winner is a candidate who would win a one-on-one match against every other candidate. In other words, if we did head-to-head duels, this candidate would beat all opponents.

Sounds like a fair winner, right? The problem is — a Condorcet winner doesn’t always exist. In some elections, preferences are cyclical: A beats B, B beats C, but C beats A. This is known as a Condorcet cycle, and it shows just how tricky collective choice can be.

We’re including a check for the Condorcet winner, if there is one. You’ll notice how some voting systems choose them — and others ignore them entirely.

Try It Yourself

Change the preferences below and hit compute. You’ll see how each method picks a (potentially different) winner.