Here is a 3-paragraph summary of the blog post "A Referendum Puzzle" for mathopen.com:
Imagine a town of 801 residents who vote on 9 different questions. For each question, every resident votes either "Yes" or "No," and whichever option gets more votes wins. A resident is considered "happy" with a particular question if the outcome matches how they personally voted. This setup, posed as a puzzle by Konstantin Knop, leads to some surprisingly counterintuitive results about voting and satisfaction.
The central question the puzzle explores is how many residents can end up happy or unhappy with the overall results across all 9 questions. Even though the majority always wins on each individual question, it turns out that a significant portion of the population can end up dissatisfied with most or even all of the outcomes. This highlights a fascinating tension between individual preferences and collective decision-making.
The puzzle sits at the intersection of combinatorics and voting theory, making it a great example of how mathematical reasoning can shed light on real-world democratic processes. Working through the problem requires careful counting and logical deduction, and the answer is likely to surprise you. It is the kind of puzzle that is easy to state but demands creative thinking to fully solve.