2000 character limit reached
Better-than-average uniform random variables and Eulerian numbers, or: How many candidates should a voter approve?
Published 5 Mar 2024 in math.PR and math.CO | (2403.02670v1)
Abstract: Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but distinct from, the well known fact that the integer part of the sum of independent random numbers uniform on $[0,1]$ has an Eulerian distribution. One motivation for this problem comes from voting theory.
- Leonhard Euler. Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. Vol I. St. Petersburg, 1755. http://www.math.dartmouth.edu/~euler/pages/E212.html
- Werner Meyer and R. von Randow. Ein Würfelschnittproblem und Bernoullische Zahlen. Math. Ann. 193 (1971), 315–321.
- Warren D. Smith. Examples in which best Range Voting strategy is ”dishonest” approval-style. http://rangevoting.org/RVstrat2.html.
- Warren D. Smith. Completion of Gibbard-Satterthwaite impossibility theorem; range voting and voter honesty, 2006. http://rangevoting.org/WarrenSmithPages/homepage/newgibbsat.pdf
- Warren D. Smith. How many candidates should a voter approve? 2022. http://www.rangevoting.org/HowManyApprove.html
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.