Dominance

 

I'm Comin' Home Again

The poets cry for dreams they never saw
The only certainty is nothing sure
And nothing stays the same
Go back where they came

Forget about certainty, is dominance sure?

There is a difference between dominance and certainty. Dominance is about who won a game or series. Certainty is about whether that winner is also expected to win again. If a game is Heads I Win/Tails You Lose, there will always be a winner, and that winner will show dominance. But just because there is a winner in one game, it does not mean that this winner is going to win the next game or series. In a one game series, the probability is 100% that there will be a dominant winner, but there is only a 50% chance that the dominant winner will win the next game. That is why there are multi-game series. As the number of games increases, the chances that the winner of the series will also win the next game also increases. The table below shows the dominance and certainty of the outcome of a series of  games based on the record of that series. For example in a 5-game series, there is a 100% chance that the winner of a 4-3 series shows dominance, but there is only a 73% chance that this dominant winner will win the next series. A 0-7 record in a 7-game series means that there is a 99.22% chance that the loser with that record will also lose the next game.

Games			Games			Games			Games
1	Dominance	Certainty	3	Dominance	Certainty	5	Dominance	Certainty	7	Dominance	Certainty
1-0	100%	50.00%	3-0	100%	87.50%	5-0	100%	96.88%	7-0	100%	99.22%
0-1	0%	50.00%	2-1	100%	62.50%	4-1	100%	84.38%	6-1	100%	94.53%
			1-2	0%	62.50%	3-2	100%	68.75%	5-2	100%	83.59%
			0-3	0%	87.50%	2-3	0%	68.75%	4-3	100%	72.66%
						1-4	0%	84.38%	3-4	0%	72.66%
						0-5	0%	96.88%	2-5	0%	83.59%
									1-6	0%	94.53%
									0-7	0%	99.22%

 A series may stop after dominance has been achieved. If a 7-game series stops after 4 wins have been recorded, then if all games had been played, the final record could have been 7-0, 6-1, 5-2 or 4-3. Those records each have a different certainty, but they also have a different probability of occurring. The certainty of a winner of the series also winning the next game should thus be weighted, and not a simple average. The certainty that the dominant winner of the series will win the next game, i.e. is certain, is thus as shown in the table below

Series	Dominant is Certain
3 games	45.83%
5 games	59.79%
7 games	70.31%

 The same logic also applies to voting members, say by justices of a 9-member Supreme Court. A 9-0 opinion might be just as dominant as a 5-4 opinion, but that 9-0 opinion is more certain.

9	Dominance	Certainty
9-0	100%	99.80%
8-1	100%	98.24%
7-2	100%	92.97%
6-3	100%	83.59%
5-4	100%	75.39%
4-5	0%	75.39%
3-6	0%	83.59%
2-7	0%	92.97%
1-8	0%	98.24%
0-9	0%	99.80%

 This also holds true for jury votes. A 12-member jury which reaches a unanimous decision of Not Guilty is 99.98% certain. However unless there is an infinite number of members on that jury, the certainty will always be less than 100%. The goal in jury trials is to achieve as close to certainty as possible. Should that not also be the case in Supreme Court decisions? The goal is to increase certainty, not decrease it. A 5-4 opinion which overturns a 7-2 opinion decreases certainty. It does not increase it.

Dominance is BACKWARD looking. Certainty is FORWARD looking. Is there any wonder that MAGA  (where the second “A” stands for “Again”) wants to return to Trial by Combat which can only show dominance? This was abandoned in the Middle Ages which is longer than even MAGA generally considers.