It IS Fair

 

To Close For Comfort

Be firm and be fair, be absolutely sure, beware
On your guard, take care, when there's such temptation
One thing leads to another
Too late to run for cover
Much too, too close for comfort now

And more important than being fair, be certain!

In any fair game there are three outcomes: Win, Loss, OR Tie. Tie breakers are often employed after regulation time, but sudden death, extra innings, overtime, shoot outs, etc. do NOT change the fact that during regulation, the game ended in a tie. Thus in any two-player game, there are three outcomes even if one of those outcomes results in another, or a continuation of the current, game.

When a jury renders a verdict, it is Guilty or Not Guilty; NOT Guilty or Innocent. On a 12-member jury there are 2¹², or 4,026,  possible outcomes of Guilty and Not Guilty. Only one of these is unanimously Guilty, which makes means it will only occur 00.02% of the time and its certainty is thus 99.98%. For all other outcomes, at least one member of the jury had reasonable doubt. Thus it only APPEARS that there are two outcomes, even though there are really more than three outcomes. In a classic two-player game, with no punishment for lying, cheating, or stealing, if one player lies, cheats, or steals then that player’s choice may be the winning choice. The certainty however is always 100% minus the probability of one (NO lying, cheating, or stealing) outcome. It will never be 100% certain unless the number of outcomes is infinite.

There are various ways to increase certainty that include: increasing the number of games or members; seeding; ranked choice voting; awarding of points in the inverse order of the finish; group stages followed by knock-out stages; double elimination tournaments, etc. The issue is that dominance is NOT certainty. Complaining about the outcome by saying that if you don’t win it is not fair might merely shows that you do not understand the difference. Dominance is the probability of all winning outcomes. Certainty is the inverse of the probability of a single outcome. Being dominant does not mean that the outcome is certain. Certainty is fair, dominance isn't.