[EM] A much too complicated sporting analogy

Bart Ingles bartman at netgate.net
Wed Apr 4 20:46:13 PDT 2001

How about a foot-race analogy?

Approval:  Each runner starts in a separate lane.  There is one heat,
and the winner of the single heat is the overall winner.

Plurality:  Runners start at opposite ends of a single lane.  The one
who gets farthest before colliding into someone else is the winner.

Instant Runoff:  Similar to Plurality, but the race is aborted as soon
as the first two runners collide.  The colliding runner judged farthest
behind is eliminated (even if both are ahead of other runners at the
time).  This is repeated until the final two collide head-on, and the
one who got farthest in the final round is the winner.

LAYTON Craig wrote:
> 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).

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