Truth V

 

The Three Bears

Just then, Goldilocks woke up
Broke up the party and beat it out there
Bye-bye, bye, bye, said the daddy bear
Goodbye, bye, said the mamma bear
Hey bubba-rebear, said the wee bear
So ends the story of the three bears

So, don't forget children, whatever you do
Don't go down to the woods tonight
Because the bears'll get ya!

Never mind Goldilocks and the Three Bears, what about Absolute and The Three Zeroes.

In a previous blog post I proposed that there are three zeros: 1) absolute zero, 2) relative zero and 3) repeating zero. If one of the four cells in an outcome matrix is an absolute, then the other three cells must be zero if the entire outcome matrix is also to be absolute. Let’s assume the rows of the outcome matrix are wins and losses and the columns of the outcome matrix are true and false. Then if any of those four cells are absolute then the other three cells must be one of the three zeroes.

If Quadrant I ( Quadrant numbering follows standard mathematical  conventions: Top Right is Quadrant I, Top left is Quadrant II, bottom left is Quadrant III and bottom right  is Quadrant IV) of the outcome matrix are true wins, then Quadrant II are false wins, Quadrant III are false losses and Quadrant IV are true losses. the outcome matrix is certain if all four cells sum to 100% and the outcome matrix is an absolute when any one of the four cells is 100%. If the absolute is a true win,  then Quadrant 2 must also be a False Win and an absolute zero; Quadrant III must be a False Loss and a relative zero, and Quadrant I must be a True Loss and a repeating zero. An absolute win is identical with an absolute loss. However an absolute win does not also have to be true. It is only true if the members of the group are also true. If there are N members of a group then if a group is going to function as an absolute, then N must be equal to three ( if N→∞ is 1, 100%, then Quadrant II is N/3 according to L’Hôpital’s Rule.)

If the outcome matrix is to be certain AND true, then the Quadrant I must be N/3, and the sum of Quadrant I and Quadrant III must also be true. This  makes the zero in Quadrant III an absolute zero. The zero in Quadrant IV, a False Win, must be a relative zero since it is offset from an absolute zero. This means that the zero in Quadrant II, a False Loss, must be a repeating zero. Thus there are four outcomes if an absolute is certain: Absolutely true; absolutely false; absolutely a win, and absolutely a loss.. If the absolute must be certain and true , then there is only one matrix that satisfies this and as stated previously, Quadrant I must be N/3. If all cells of the outcome matrix must also be between zero and one, then non-negative values can be found for Quadrants II, III and IV that can satisfy the certainty of the outcome matrix if the members of the group are greater than 3. If the number in the group is 3, it IS consistent with the absolute. If N, the members of the group, is only 1 there are NO non-negative values of Quadrants I, II, and IV that can e found that are also true. If the number of members of a Group are 2 and Quadrant II is zero, then the group can be true OR false depending on the values for False Wins and False Losses. If the value of False Losses is between zero and 1/6 and the value of False Wins is also between zero and 1/6,  and the value of False Losses plus False Wins is equal to 1/3 then the group is true. To satisfy both conditions, if N=2, only Quadrant II=Quadrant IV=1/6 is possible. This means that the sum of values in Quadrant II and IV, which remember is only the stand-in for ties, is a normal distribution. Otherwise the win is ABnormal. If the percentage of True wins is 2/3, 66 2/3%, and the sum of False Wins plus False Losses, i.e. ties,  follow a normal distribution.   The maximum positive normal skew is 96%, the False Wins are 2% and the False Losses are also 2%. The minimum normal skew would be 46.53% and the False Wins and False Losses would be each 26.785%. However any value for False Wins less than 25%  is also certainly false. This means that 91% of the normally distributed values with a Quadrant II of 2/3 are true and 9% are false.

An absolute appears consistent with groups with three Members, a trinity. A group with more than three members can always be true, a group with only 1 Member will always be false. Groups with two Members can be either true OR false. Groups with two Members (for example a two  party systems according to Duverger’s Law), which are normally distributed with a location parameter of 2/3 and a range parameter equal to ½ are true 91% of the time, including all those that are positively skewed, but are false 9% of the time, including the maximum negative normal skew.

A normal win in a real election with two group (e.g. parties) indicates that the win is true 91% of the time. If the distribution of False Wins and False Losses (whose sum is ties) are normally distributed, it  will be false 9% of the time including some negatively skewed normal distributions. The maximum positive skewed normal distribution for a group of two has a win certainty of 98%, and a truth certainty of 96%, That is almost identical to the absolute value of 100%.

Things that are assumed in making wins true.

1 The members of the group should approach the absolute, i.e., N→∞. All measures that decrease N, such as voter suppression, reduce the chances of the win being true.

2.  Ties have to be allowed. Zero-sum games assume than a contest will always result in a win and that all other outcomes are a loss. Thus contests that include a fixed sum, such as fixing the size of the House at 435 seats, the number of Supreme Court justices at 9, or fixing the currency to a commodity standard, should not be allowed. It is noted that if rather than the current method of allocating Congressional House seats, a method which apportions of one seat to the smallest state by population and all other seats based on the ratio to that state, currently Wyoming. This is why the popular name for this rule is the “Wyoming” rule.

3.  There must be three choices accommodating the three outcomes of win, loss, and tie. Since Duverger’s Law says that in the current single representative for a district system used in the United States will tend to two parties (groups) , this can be satisfied if each of the two parties nominates two candidates in each election. Otherwise voting might only indicates opposition to a candidate, not voting for a candidate.

4. Rank choice voting, as currently used in Alaska, should be include in all elections where the winner is by plurality rather than majority. In the 2024 Presidential election, at least the state votes in Michigan (Trump 49.7%) and Wisconsin ( Trump 49.6%) were by less than a 50% majority.

5. The electoral college is intended to elect a President based on the people’s choice AND the state’s choice. Thus awarding electoral votes should be done by Congressional District AND by states, as is the case currently only in Nebraska and Maine. It is not commonly reported what the people’s portion of electoral college vote would have been in all other states if they were awarded by Congressional House District. 

Even if all of these measures were in effect, it is noted that a normal election with two major parties is only absolutely true in 91% of all cases, based on statistics and game theory. Knowing the difference in the three zeroes makes it possible to solve for truth even when some of the Quadrants are NOT zero.  And it in reality, where there are both, 2, sides not being normal is not being truthful.