Vote Scope Limit

The Vote Scope Limits Principle

The Vote Scope Limits, Poll Scope Limits, Or Decision Scope Limits are the number of distinct issues that compose the subject of the poll. 

Note: If you are not a mathematician, you can skip the next few paragraphs in italics and scroll down to the very easy explanations for the average voter."

The number of distinct issues in a poll subject is discovered by:

1. Orthogonalization of the subject components, and restricting subject (data point) dimensions to 1 dimension, through requiring mathematical orthogonal representation of the subjects involved. This makes each component in the subject independent, and requires breaking the poll into multiple polls, with each poll covering only one independent component of the subject. In this manner, we are guaranteeing the most accurate result for the Poll Accuracy equation. This is in order to preserve maximum accuracy in the vote result. Otherwise, poll accuracy cannot be known. A data point is proper if it has one indecomposable subject dimension. Therefore, this is the most important requirement for a poll to be valid or proper. A break of this restriction should prevent any poll from being conducted.

Wikipedia defines the orthogonalization process as: “In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1, ... , uk} that generate the same subspace as the vectors v1, ... , vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span.”…  “Local orthogonalization: To compensate for the loss of useful signal in traditional noise attenuation approaches because of incorrect parameter selection or inadequacy of denoising assumptions, a weighting operator can be applied on the initially denoised section for the retrieval of useful signal from the initial noise section. The new denoising process is referred to as the local orthogonalization of signal and noise. It has a wide range of applications in many signals processing and seismic exploration fields.”

This is beyond the scope of this book, but awareness of it is extremely important for advanced study, and though it sounds very complicated, it can be understood easily from the examples I will give bellow.

2. A Poll Scope Limits is Proper if it blocks all bargaining and compromise between voters.

Note: Mathematical proof needs to be presented that: Accuracy generated from of a data sample of size n, decreases as the data point dimensions increases.

Example: If a vote by parliament is regarding the public schools education budget, the scope of the vote would be strictly related to this subject, and maybe for example, “Do we agree to spend 1 million dollars on school education?” Any other issues would not be allowed to be a part of the subject of this vote (poll), whether it is explicitly or implicitly included in the vote. Therefore, the vote subject would not allow including “the farming budget” or “the military budget” issues, etc. This limits the subjects (data point dimensions) to 1, which is the subject of public school education, and blocks bargaining between voters interested in education and those interested in military issues or farming issues. Therefore, a vote by 10,000 people (in a public vote, in parliament, congress, senate, or a committee) on "should we increase the budget of public schools education, and farming, and military budget?" would violate the Principle of Vote Scope Limit, because the voters are asked to vote on several independent subjects in the same poll question, and the poll would be blocked from proceeding. Let us look at how breaking the Vote Scope Limits prevents being able to measure poll accuracy to the maximum amount possible:

If 33.33% of voters in congress support a public school education budget, and 33.33% other congressmen support a farming budget, and 33.33% other congressmen support a military budget, none of these congressmen factions succeed in polls, and no spending budget would be adopted. Let us see why:

Poll 1: Do you support a public school education budget? Poll Results: YES = 33.33%, NO = 66.66%. Accuracy < 0%, which would fail poll adoption. Implication is that this is a bad idea, or inaccurate idea.

Poll 2: Do you support a farming budget? Poll Results: YES = 33.33%, NO = 66.66%, Accuracy < 0% which would fail poll adoption. Implication is that this is a bad idea, or inaccurate idea.

Poll 3: Do you support a military budget? Poll Results: YES = 33.33%, NO = 66.66%, Accuracy < 0% which would fail poll adoption. Implication is that this is a bad idea, or inaccurate idea.

Poll 1, 2, and 3 have results and we can measure these polls’ accuracy properly, because each poll is related to a distinct subject, that cannot be decomposed into smaller subjects. All three polls failed because they represent three unacceptable or bad ideas.

If the three voting factions in congress are allowed bargaining, thus breaking the Vote Scope Limit, they can agree to trade votes and support each other. They say to each other: “Vote for my subject and I will vote for your subject, and this way, we are guaranteed to win!” Therefore, all three groups agree to a bargain, the results can be a wining or a unanimous vote. Now a single poll is held on the question:

Poll: Do you support a public school education budget, and a farming budget, and a military budget?” 

Poll Results:  

YES = 33.33% + 33.33% + 33.33% = 99.99% = 100% support, 

NO = 0%, 

Accuracy is approximately YES – NO , because the voters group size is large and we can ignore the Group Size Error of  4/√n. Therefore, the Poll Accuracy = 100% -0% = 100% (approximately). YES =100%, NO= 0% which wins poll adoption. 

Three bad idea ideas that cannot win individually based on their own merit, now win with great success when combined, giving a false sense of merit to them. Three bad ideas that would never be adopted, are now adopted, causing damage to the voting process, because the Vote Scope Limit has been violated. The poll can no longer measure accuracy properly, and the accuracy equation usefulness has been destroyed because of this violation!

Limiting the Vote Scope, the 3 subjects (dimensional data points) are reduced to 1-dimension votes, and now we are forced to have three votes instead of only one vote:

Poll 1: Should we increase the education budget? YES = 33%, NO = 67%, Accuracy < 0%

Poll 2: Should we increase the farming budget? YES = 33%, NO = 67%, Accuracy < 0%

Poll 3: Should we increase the military budget? YES = 33%, NO = 67%, Accuracy < 0%

None of the 3 polls would be adopted when we apply Vote Scope Limit. The bad results from "limiting voter selection ability, or choices, or freedom" which limits accuracy are avoided, and Poll Accuracy is measured correctly.

Example 2: Public elections of officials. Three individuals run for parliament offices in a country. None of these individuals is a good candidate, as surveys show:

Survey 1: Would you elect person 1 to office? YES = 33%, NO = 67%, Accuracy < 0%

Survey 2: Would you elect person 2 to office? YES = 33%, NO = 67%, Accuracy < 0%

Survey 3: Would you elect person 1 to office? YES = 33%, NO = 67%, Accuracy < 0%

These three individuals know these secret or public surveys, and decide to join together on a “List” as some countries allow in their voting system, or using proportional division of poll results, etc. These three individuals decide to join forces as one group or party (list) etc. This act violates the Vote Scope Limit, because the public is now limited to voting on a group or party, instead of individuals. Voters' freedom of choice has been restricted. At election time, the public is asked in the election poll: Do you approve of electing political party A (composed of person 1, person 2, person 3) to office? 

The public votes YES = 33.33% + 33.33% + 33.33% = 99.99% = 100% support, NO = 0%, Accuracy is approximately YES – NO , because the voters group size is large , and Accuracy is now near 100%, and the party composed of these 3 persons wins, and each of these three candidates gets a parliament seat.  This is clearly a very bad result. Vote Scope Limit requires breaking a poll into its smallest component. Therefore, there should have been three questions in the poll at election time:

Question 1: Would you elect person 1 to office? YES = 33%, NO = 67%, Accuracy < 0%. The person fails to be elected. The public is spared this bad person.

Question 2: Would you elect person 2 to office? YES = 33%, NO = 67%, Accuracy < 0%. The person fails to be elected. The public is spared this bad person.

Question 3: Would you elect person 1 to office? YES = 33%, NO = 67%, Accuracy < 0%. The person fails to be elected. The public is spared this bad person.

None of these individuals, who lack merit, would be elected, because the voters were protected by the Vote Scope Limit principle. The bad results due to "limiting voter selection ability, or choices, or freedom" which limits accuracy are avoided.

Many countries or systems of voting allow block representation voting, party representation voting, proportional representation voting, etc. Proportional Representation systems aim to allocate seats to parties approximately in proportion to the number of votes received, but they violate severely the Vote Scope Limit principle. For example, if a party wins one-third of the votes then, according to proportional representation, it would gain about one-third of the seats. The vote is not broken down to its smallest part, so the voters can vote on each candidate separately, were maybe none of the candidates would be accepted. 

In Netherlands, elections are called when the government loses the parliament's confidence, the governing coalition breaks down, the term of the House Of Representatives expires or when no governing coalition can be formed. Note the words "loses confidence". If we focus on this, and use accuracy, or the less useful but familiar measure "statistical Confidence Level", then a mathematician or statistician should be able to apply the concept of Confidence Level to an election result as a "necessary but insufficient measure", and see that almost all of these systems results do not pass the statistical significance test of a having a Z-Score of 2 or higher (See our Vote Z-Score Calculator) .

We can see from this principal that these voting systems used by governments worldwide are improper voting systems because "they do not use accuracy as a measure", and also, because "their voting violates the Vote Scope Limit".

It may be inconvenient for a parliament to vote in one thousand polls on one thousand different subjects, rather than vote one time in a single-poll-question that includes one thousand subjects, but if an accurate system is what you want, then this is what is required in effort.

Similarly, in a court trial, the Jury vote needs to be broken down to its smallest decomposable component to meet the Vote Scope Limit requirements, as some courts actually try to practice in criminal cases.