[EM] A much too complicated sporting analogy

[LAYTON Craig]

This is just an interesting exercise (boom-boom) in looking at election
methods from a different perspective.

I think that almost any voting system can be translated into the following
scenario, and anything (as far as I can tell) that can fit into this
scenario can be translated into a voting system;

You have to design a method to pick the winner of a particular sporting
competition, with a number of players (say four) and any number of contests
between the players.  Additionally, any number of players can be on the
field at once, and can play in teams, or individually.  The players are very
consistent and always perform exactly the same way (depending on variables
such as who is in their team &c.) so there is no point repeating exactly the
same contest.

Each voter's vote is a goal for a particular team.

Here is some translations of some major voting systems;

Plurality - there is a single match between all contestants on the field at
once (all playing for themselves).  The contestant with the most goals wins
the competition.

IRV - All the contestants play on the field at once.  This is followed by a
match with all the contestants except the one who got the least number of
goals in the last game.  The team who wins the grand final (the match
between the last two contestants) wins the competition.

Condorcet - every contestant plays every other contestant in one-on-one
matches.  If there is a player who is undefeated, that player wins the
competition.  Otherwise, you use one of a number of ways to decide on the
winner based on how many goals each competitor scored, and how many were
scored against them.

Approval - every contestant is on the field in every game.  The contestants
are always organised into two teams.  You play every match possible without
repeating one (for four players, this is 7 matches, representing the 14
possible ballots).  You add up the goals from all the matches, and the
player with the most goals wins (when players are in teams, the whole team
scores).

Cardinal ratings - This is tricky.  I would describe as like plurality but
instead of playing against one another, all the players play as if they were
on the same team.  Every time a goal is scored, each player is given a score
based on how much skill they demonstrated and how much they contributed to
the goal.

Most other methods are fairly easy to translate (easier than CR anyway).