- Joined
- Jun 21, 2003
OK, so evidently “Mario Cart” is some kind of Nintendo game where players assemble and race go-carts. I happened upon a serious piece of mathematics that uses something called the Pareto Front to figure out the optimal combination of super-chargers, etc., that you can put on your cart to maximize your chances of winning.
Vilfredo Pareto was a 19th - early 20th century Italian economist who also made contributions to social choice theory.
How is this relevant to figure skating? The knock against the old 6.0 ordinal scoring system, and the case for the IJS, is summed up in a result called Arrow’s Impossibility Theorem (Nobel Laureate Kenneth Arrow, 1951). This states that no system of ordinal or ranked voting can possibly work every time. By “work” we mean that certain “obviously” desirable conditions should be met. For instance, no “flip-flops.” A flip-flop occurs when skater A is beating the pants off skater B on a majority of judges’ score cards, but then skater C skates and suddenly skater B vaults ahead of skater A. This is unsettling, especially if you are skater A.
Another (related) condition is called the Pareto Condition and was first examined by this guy Pareto in a economic setting: If a proposed change to economic policy will benefit some members of society while not hurting any members of society, then society is better off to adopt the new policy. Pareto showed that paradoxically sometimes society as a whole might be better off keeping the old policy even though every individual member of society is either better off or no change with the new. That is, if every individual judge thinks that skater A was better than skater B, then the scoring system as whole should give the prize to skater A. The Impossibility Theorem says that it not possible to invent a ranked voting system (that has at least two judges and at least three skaters) that will simultaneously satisfy all the desirable conditions in every conceivable contest. – not “majority of ordinals,” not “one-by-one,” not any variation on ordinal judging.
But the Code of Points does. If skater A gets more points than skater B on every judges card, then skater A will alwaysplace above skater B, no matter what skater C does.
www.mayerowitz.io
Vilfredo Pareto was a 19th - early 20th century Italian economist who also made contributions to social choice theory.
How is this relevant to figure skating? The knock against the old 6.0 ordinal scoring system, and the case for the IJS, is summed up in a result called Arrow’s Impossibility Theorem (Nobel Laureate Kenneth Arrow, 1951). This states that no system of ordinal or ranked voting can possibly work every time. By “work” we mean that certain “obviously” desirable conditions should be met. For instance, no “flip-flops.” A flip-flop occurs when skater A is beating the pants off skater B on a majority of judges’ score cards, but then skater C skates and suddenly skater B vaults ahead of skater A. This is unsettling, especially if you are skater A.
Another (related) condition is called the Pareto Condition and was first examined by this guy Pareto in a economic setting: If a proposed change to economic policy will benefit some members of society while not hurting any members of society, then society is better off to adopt the new policy. Pareto showed that paradoxically sometimes society as a whole might be better off keeping the old policy even though every individual member of society is either better off or no change with the new. That is, if every individual judge thinks that skater A was better than skater B, then the scoring system as whole should give the prize to skater A. The Impossibility Theorem says that it not possible to invent a ranked voting system (that has at least two judges and at least three skaters) that will simultaneously satisfy all the desirable conditions in every conceivable contest. – not “majority of ordinals,” not “one-by-one,” not any variation on ordinal judging.
But the Code of Points does. If skater A gets more points than skater B on every judges card, then skater A will alwaysplace above skater B, no matter what skater C does.
Mario meets Pareto
Discover how to find the best Mario Kart 8 build using the Pareto frontier method. This interactive guide explores multi-objective optimization of speed, acceleration, and other key stats to help you beat your friends on the race track.
www.mayerowitz.io
