In this short note, the probability of the event that in a first-past-the-post voting system, the party winning the maximum number of seats loses in terms of popular votes, is studied under a few simplifying assumptions. It turns out that the said probability is roughly 20 per cent. That is, one-fifth of the times, the said event will happen, on the average.
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DeyP. & NarahariY. (2015). Asymptotic collusion-proofness of voting rules: The case of large number of candidates. Studies in Microeconomics, 3(2), 120–139.