The Yes Vote Distribution

The Random Yes Vote Distribution

The Standard Normal Distribution is a statistical distribution described by the Encyclopaedia Britannica as: The Normal Distribution is the "most common distribution function for independent, randomly generated variables. Its familiar bell-shaped curve is ubiquitous in statistical reports, from survey analysis and quality control to resource allocation, " adding elsewhere in the Encyclopaedia Britannica  "the standard normal probability distribution, which is a normal probability distribution with a mean of zero and a standard deviation of one. A simple mathematical formula is used to convert any value from a normal probability distribution with mean μ and a standard deviation σ into a corresponding value for a standard normal distribution. The tables for the standard normal distribution are then used to compute the appropriate probabilities. "

In Mathematics, the Normal Distribution can be written as ND(mean, Standard Deviation), and the Standard Normal Distribution = ND(0,1) 

Since in mathematics, the interval on the x-axis goes from minus infinity to plus infinity written as  -∞ to ∞ written as [-∞ , ∞ ], in probability talk that normal humans understand, the interval for a probability is 0% to 100%  or [0% , 100%]. It is easy mathematically to change the complex interval [-∞ , ∞ ] to  [0% , 100%] so normal people can understand the mathematics more easily. That is what is done here. The Standard Normal Distribution is changed from the interval  [-∞ , ∞ ] to  [0% , 100%] written in mathematics the interval is [0, 1] where 1 = 100%, so that you can understand it. That is why I created "The (Random) Yes Vote Distribution". Before I explain more, below is "The (Random) Yes Vote Distribution", and it is focused purely on the percent of support in a vote. For example, if in an election or a vote, the percent of "yes" support is 65%, then you look at this distribution and see if this amount of support is acceptable on a standard score that ranges from 0 to 4. The scientist does not care about the vote subject or the politics involved! This is a purely mathematical issue. You will see that a vote that does not cross the 75% "yes" support is not acceptable! Why? Because there is something called Confidence Level, and scientists require this Confidence Level to be 95% as a minimum. Therefore, you will see in the graph that a 75% "yes" support in a vote has associated with it a 95% Confidence Level. Of course this is the minimum, and there are other factors involved we will discuss later and others are on the website, especially the newly developed "Vote Accuracy" measure.

When you look at a vote that has 50% "yes" support, it is at the center of the graph, at 0.5 or 50%, you see that the Confidence Level CL = 0%. This should be logical, because if you imagine two opposed groups, the "yes" group fighting the "no" group in a tug-of-war rope pulling situation, a 50% "yes" implies the opposition is 50% "no", and we have a net 0% as the result of this opposed pulling. Similarly, when the "yes" group has 60% it implies the "no" group has 40%, and the result is computed as "yes" percent minus "no" percent = 60% - 40% = 20% which in statistics is called the "mean" (or average) of the vote. The average of a vote 60% "yes" and 40% "no" is NOT 50%! Why? The opposition "no" voters are pulling in the opposite direction of the "yes" voters, which is negative direction! Therefore the value of the "no" portion is -40% not 40%! In mathematical language it is called a vector. To describe a vote as 60% to 40% is improper mathematically and leads to misunderstanding. It is a 60% to -40% vote; therefore the Vote Mean or average is the sum of all the votes divided by voters total number = 60% + (- 40%) = 20%. Here is a detailed simple example of computing a Vote Mean: 10 persons vote with 6 persons voting "yes" and 4 persons voting "no" ; the vote therefore has the data set = (1, 1, 1, 1, 1, 1, -1,-1,-1,-1) where 1 represents a "yes" vote and -1 represents the opposite vote "no". The Vote Mean or Vote Average = sum of the votes divided by the total number of voters = 6 + (-4)= 6 - 4 = 2; diving 2 by 10 total voters we get 20%. Experiment with the calculators on this website, such as the Election Accuracy Calculator by trying few examples, and see the very detailed explanations and graphics. Therefore, the Vote Mean or Vote Average = "yes"% - "no"%. From this simple but extremely important equation, we can get a feel that the higher the "yes" group percentage is, the more confidence we have in the vote win. That is why at 50% "yes" support the Confidence Level CL is 0%, and at 62.25% "yes" support the Confidence Level CL is 68% {red interval}, and at 75% "yes" support the Confidence Level CL = 95% {orange interval}, and from 75% to 87.5% "yes" support Confidence Level CL = 99.73% {green interval}, and at 100% "yes" support Confidence Level CL = 99.99% {blue interval}. CL does not increase in a straight line, and you can ignore this until you learn more formal statistics. The Confidence Level CL is a probability. So saying a vote with 75% has CL= 95% implies this vote has 95 percent probability of not being a random vote. What is a random vote? A Random Vote is a vote where ALL the voters vote with their eyes closed when selecting from { yes or No} vote answer options. Therefore a Random Vote serves as a reference. If all voters voted with their eyes closed, we expect the vote results to be 50% of the voters vote "yes" and 50% of the voters vote "no". That is why at the 50% "yes" or 0.5  level on the graph, you have a CL = 0%. At 50% "yes" you can see the graph has highest height. In essence, the height of this graph tells you how random a vote is. At 50% "yes" the vote has maximum randomness.  For humans, deciding randomly is equivalent to deciding with eyes closed, which is a stupid thing to do. So you can see in the graph that as you move away from the 50% "yes" support, randomness decreases from its maximum. When randomness decrease, intelligence or knowledge, the opposite or compliment of randomness increases. The less randomness the better.

Since a regular person, and even many highly educated people and scientists are not aware of the fact that the mean of a vote is no the "yes" proportion, I created this distribution to make it easier for all to understand voting. With this distribution, you do not need to compute the Vote Mean or average; Just get the "yes" proportion of the vote, let say a vote had 68% "yes" support, and you look at the "Yes Vote Distribution" above, on the x-axis, and you will see this value is in the orange area range, which implies the vote has less than the 75% "yes" support which is the minimum support required in science (95% Confidence Level, or a Z_Score = 2, or is more than a two Standard Deviations Away from the random mean 50%.) The "Yes Vote Distribution" above is the easiest to understand and is less technical than the "Vote Distribution" elsewhere on this website.

An important question to ask about a vote is this: Is 95% Confidence Level CL good enough in important decisions? 95% probability of being correct implies 5% probability of being incorrect or in error. So will you sentence a person to death with this much probability that you are incorrect?

Another question to ask is this: 1% chance of error implies 1 person out of 100 persons is injured or damaged by your vote decision, and since in political elections or creating laws, the entire country's population is effected by the error in the vote, this implies a 1% error causes damage to 1% of the country population. So a 1% error for the USA with a population roughly 400 million produces injury and damage to 4 million USA persons. Now with CL =95%, we have 5% error. Therefore the injury or damage to the USA population is 5% * 400 million = 20 million person from a vote adopted by 75% "yes" support. 

You should begin to understand the amount of damage being done by electing a person to office by 51% or creating a law by 51%. The error is almost 100%. Is this real or imagined mathematics. I tried my best to explain these things, but political interests and economic interests must be huge, that such simple mathematics is being kept out from the public somehow. Now, go talk to your statistics professor, or ask a university statistics student or a scientist if this mathematics is true or not, and if true, what is going on that the public does not know of it?????????????????

There are other factors involved, such as the Vote Accuracy, and you should take time to explore this website in full, if you care about understanding basic voting issues, because your vote does not only effect you, it effects the life of others, and if you do not care to educate yourself about the amount of damage you are causing me and others with your ignorance, why should I or they care about you? Literally! If you are such a person that does not care about how your actions affect others, you can drop dead, and it will be a positive event in my life and the life of some others.

Mathematical note: The Yes Vote Distribution above is a Standard Normal Distribution ND(1,1) where the Standard Deviation is scaled from 1 to 1/8 to map its [-∞ , ∞ ] interval  to the [0% , 100%] interval; to become ND(0,1/8). 1/8 = 0.125. The distribution mean is then shifted from 0 to 0.5 to be understandable easily by the public that is unaccustomed to probability being on the negative part of the x-axis. The Yes Vote Distribution therefore becomes ND (0.5, 1/8).  Now the 0 mean that previously implied randomness for a Vote Mean, moves to the 50% "yes" or 0.5 "yes" point on the [0 , 1] interval, which can be understandable by the common person. A common person usually says the vote had 50% "yes" support, instead of the proper mathematical talk of saying the vote had a mean or average equal to 0, because such a person usually ignores the "no" portion of the vote which is a part of the "mean" equation. The colors are added to show danger zones with red and orange being dangerous zones where the number of Standard Deviations is less than 2, thus failing to meet the minimal required Confidence Level of 95%. The intervals are broken to 4 Standard Deviations associated with Z = 1,2,3,4 (Z = Z-Value) and their corresponding Confidence Level values of 68%, 95%, 99.73%, and 99.99%. Read other material on this website for very precise details.

Jamil Kazoun is the developer of The Yes Vote Distribution and many other mathematics equations and tools highly relevant to human well-being and to accurate decision making, as presented in his book "A Mathematical Foundation For Politics And Law" among other books.