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## 9 Counting Votes -- RCV

This is the promised discussion of counting ballots in a
system of Ranked Choice Voting (RCV) discussed in the prior post.

**First story**:--Consider a sports club that is
voting on a location for its annual picnic. Among four alternative locations,
the meadow wins the balloting. After the vote, someone suggests yet another
location. When the vote is repeated with five locations, two votes shift away
from the meadow; the baseball field emerges as the winner. Why should a
seemingly irrelevant, unpopular alternative change the location of the picnic?
In RCV, the two unsuccessfully shifted ballots revert to their second choices,
restoring the original winner. *The two "unsuccessful" voters have the
satisfaction that their votes did contribute to the result they wanted if they
could not have their first choice*. Their votes were not wasted.

**Second story**:--Consider a mathematical
streamlining process. This story is set in a country where all taxes are paid
with coins that are accurately equal in weight. There is a reliable report
that the tax collector in one province has rubbed off exactly one gram from *every*
coin he submitted. The problem is to learn which collector cheated. The long
solution is to weigh a coin from every province. The short solution is sampling:
since counting is faster than weighing, take one coin from the first province,
two from the second, and so on; weigh all those selected coins in one single
step. The number of grams shortage is the ordinal number of the faulty
province. (For example, if the second province is at fault, the shortage is
two grams because there are two altered coins in the sample.)

This story illustrates efficient data collection. A *single*
test (weighing) suffices because the *sample* is designed for that method
of analysis.

**Third story**:--A single-elimination tournament
bracket starts with a simple lineup of all the teams. Of every pair of teams
in the first level, only one progresses to the second level. The process of
elimination continues until one team reaches the final level. In this system
there is the nagging possibility that a team was eliminated in the first level
by an unusual circumstance. In a different sequence of contests, that team
might have reached the top. A much more thorough testing process is the round
robin in which every team plays every other team (usually twice, once at home
and once away). The final winner is based on accumulated successes, not single
instances.

**Suggestion**:--The first story encourages finding an
intuitively satisfying outcome with no abrupt surprises. The second story
motivates thoughtful planning of a process for reaching the outcome. It
compresses the research into a single selection step; it is unitary. The third
story serves as a model for scoring and ranking based on the most complete
available data set.

Combining the stories might lead to this formula: Give
every candidate a score that is the inverse of ballot ranking, then find the
highest total score. If there are four candidates, the highest (first) ranked
candidate scores four and the lowest (fourth) ranked candidate scores one. (In
an incomplete ballot, unranked candidates receive no score.) The total score
is a measure of overall support for a given candidate, making this counting
system logically appropriate.

Let us soon implement an agreed form of RCV that will
deliver the advantages laid out in the prior post: (1) avoiding wasted
ballots, (2) eliminating repeat elections, (3) expanding discourse among
multiple viewpoints. This is our easiest step to better democracy.

Being For Others Blog copyright © 2020 Kent Busse

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