"What is Democracy?" Video Series
"Democracy Versus Game Theory" Book
Preferential ballot elections allow voters to specify a 1st choice, a
2nd choice, a 3rd choice, and so on. Since they collect more
information from voters, preferential ballot elections often produce
winners who better represent voters than single vote ballot elections,
in ways that can be made mathematically precise.
However, since more information is collected from voters, the
question of how to determine the winner of a preferential ballot
election is more complex, both mathematically and philosophically. This
is the topic of Professor Bray's book, "Democracy Versus Game Theory: The Case for Preferential Ballot Elections", coming out soon. Until then, watch his "What is Democracy?" Video Series.
One of the subtleties is that there are many ways to determine the
winner of a preferential ballot election, and often these different
methods lead to different results. More importantly, each vote counting
method has its own game theory, which incentivizes candidates and
voters to behave in certain ways.
For example, single vote ballot elections incentivize candidates to
join one of two major political parties to avoid "splitting the vote"
with other candidates who have similar political positions.
Furthermore, voters are incentivized to vote for one of the two major
polical parties to avoid "throwing their vote away." This
mathematically precise effect, known as Duverger's law, is very evident
in American politics, which has favored two major political parties for
most of its history.
The algorithm this web page uses to determine the winner (and
ranking of all of the candidates) is the Ranked Pairs algorithm. This
algorithm is used because it is Condorcet, clone invariant, monotone,
and last place loser independent. These properties incentivize voters
to vote more honestly and candidates to seek more centrist positions.
They also decrease the influence of political parties and fringe
Condorcet means that a candidate who wins every head-to-head
contest against every other candidate, if such a candidate exists,
should win the election, thereby rewarding centrist candidates. Clone
invariant means that similar candidates do not penalize (or reward)
each other (for example, by splitting the vote), thereby making
political parties less necessary. Monotone means that if a voter ranks
a candidate higher, this should not ever hurt the candidate, allowing
voters to vote honestly. Last place loser independent means that if the
candidate who came in last place drops out of the election, the outcome
does not change, thereby minimizing the influence of fringe candidates.
The only major preferential ballot vote counting method with all
four of these properties is Ranked Pairs. Philosophically, Ranked Pairs
chooses the ordering of the candidates which gives the highest priority
to the greatest margins of victory in all of the head-to-head contests
(where only two candidates compete at a time). Professor Bray's book,
among other things, compares and contrasts this method to the other
major methods, ultimately arguing the the Ranked Pairs method is the
best preferential ballot vote counting method to use in most
situations, for the reasons just described.
A brief review of other algorithms: Instant Runoff Voting is
neither Condorcet (and hence not good at picking centrist candidates)
nor monotone (so that, for example, voting for a candidate can actually
decrease their odds of winning, in some circumstances). The Borda Count
is monotone, but is still not Condorcet, and incentivizes voters to
vote very dishonestly in some cases, including highly ranking
candidates that they don't like, as a way of hurting candidates they
view as competition for the candidate that they do like. Neither of
these methods should be used to select a single winner,* if the above
considerations are a concern. On the other hand, the Schulze method,
which is Condorcet, clone invariant, and monotone, is a reasonable
method, even though it is not last place loser independent. However,
while it always determines a winner, it does not always provide a
ranking for all of the candidates, even when all ties are broken, which
could be a problem for some applications.
(* Instant Runoff Voting is okay when there are many winners, in
certain circumstances where a broad diversity of winners is desired.
However, for single winner elections, it is only slightly better than a
single vote ballot election at selecting centrist candidates and, in
general, has a very complicated game theory, thereby making it more
vulnerable to manipulation. There is also a chaotic element to Instant
Runoff Voting, where relatively small changes in the votes can lead to
the single winner being drastically different.)