The impulse to develop a system of logic that relies on degrees of truth is one that many people have had over the history of philosophy and I can tell you that

The impulse to develop a system of logic that relies on degrees of truth is one that many people have had over the history of philosophy and I can tell you that it is highly problematic. I am struggling to find a succinct way to explain why this is but the following example might be work. 1. It is 50% true that Sally has red hair. 2. It is 50% true that Sally has brown hair. 3. It is 50% true that Sally has not red hair. (see 2.) You end up running into contradictions all over the place and having a non-binary system of logic makes it nearly impossible to develop any formal system of reasoning. I'm not completely clear on the second half of your comment but when you say "portion of people agree" I assume you are trying to use an empirical theory of truth. There are again many problems with this theory but I can think of an example that might illustrate. It's a toy example that I won't fully expand upon but it illustrates the point at hand. There is a box in a room that is painted yellow. A group of people is asked to state the color of the box but they are all colorblind and state that it is grey. The consensus about the color of the box is clearly wrong in this case. Some people will object to this example because the meaning of words is also clearly derived from their use. The epistemic theory of vagueness is not far off from what you are proposing and it is the theory that Williamson posits in his book. Essentially, there is a hard cutoff for all statements that are vague. It is either true that the collection of grains is a heap or it is not. An omniscient speaker could evaluate the truth of a statement about whether the collection of grains is a heap or not with definite certainty because only the omniscient speaker possesses all of the relevant information about the property of being a heap. In other words vagueness is a problem of inexact knowledge. Another example of inexact knowledge is if you were to look out over a stadium and state "there are 23,422 people here." Barring the possibility that you are a savant and actually counted all of the people, if you made that statement and it was true that 23,422 people were in the stadium it isn't also true that you knew that there were that many people. You lack the relevant information about how many people are in the stadium to safely make the claim that there are n number of people in the stadium just as you lack the relevant information about the property of being a heap to safely make the claim that you know it is true that a collection of n grains is a heap. This is a powerful theory which is not as easily defeated as others but keep in mind that it is not without weakness. Hopefully this at least exposes some of the concepts to you even if it's at a superficial level.