This is a demonstration of a vote for a numerical value, such as the monthly dues of a private club. We compare computing the winning result using median vs. using average (a.k.a. "mean").
Conceptually, the same issues should apply to elections in which we are choosing a single winner from a set of human candidates. However, the "purity" of this example might better illuminate the distinction between median and average in this context, given that the concepts are more directly definable and observable when speaking of numerical results.
I consider this example to be like the concept of "perfect competition" in the study of economics: a theoretical benchmark to which real life structures can be compared. Like perfect competition, an election for a number is simple to understand, elegant and, to me, ideal.
There is also a story which more-or-less accompanies this, something I wrote over 10 years ago, which is the idea of the members of a Moose Lodge voting for their monthly dues. Although it briefly discusses average vs. median, it was written with the assumption that the difference would be obvious without going into much detail. The story mostly attempts to illustrate how poorly designed voting systems (such as plurality, a.k.a. first past the post) can cause things to get polarized, especially as people learn to strategically exploit the flaws.
Note that election methods that select a single winner (typically a human candidate) may use some form of median or average in their tabulation logic, for instance Majority Judgement uses median (specifically to discourage tactical voting), while Score voting uses average. Other methods, such as Condorcet methods and Borda count, might be considered to have "median seeking" and "average seeking" tendencies while not explicitly using median and average in their tabulation.
Nonetheless, this demo is not attempting to advocate for one or another single-winner election method. It is simply to establish a very-much-needed baseline for discussion -- both philosophical and mathematical -- with an awareness of how easily such discussions can go off the rails.
You may copy and use this however you wish.
rob brown, 2018
rjbrown @ gmail