The meaning of majority: Is the majority right? (Tur 69)

With God’s help

Column 66 I addressed the question of whether the majority rules. The conclusion was that in a democracy it does, and I explained this by saying that the majority is a reasonable measure for determining public opinion as a whole. Against the Platonic proposal of the rule of philosophers, that is, giving excessive weight to wise people, I argued that in a democracy one does not seek a correct decision, but a decision that reflects the will of the public. The question of whether the majority is a good criterion for making a correct decision remains open, since following the majority in a democracy does not depend on it (one follows the majority whether the majority is right or not). As I promised there, I now come to a discussion of the second question: whether the majority is right.

As mentioned, Plato's assumption was that state decision-making should strive for truth, and in doing so he confronts the intuition that the majority is a measure of truth. His argument was that a few wise people come closer to the truth than many fools, and therefore recommends the rule of philosophers. Is democratic intuition indeed wrong? Are there really better algorithms than following the majority to reach the truth? We are talking about contexts in which the goal of the decision is truth, such as in some professional decision (judges, jurors, some scientific or strategic decision, etc.). In addition, at least for the sake of discussion, I will assume here that there is a type of wisdom or specific skills that are relevant to the decision in question.

What information do we have about the litigants?

The answer to this question is not simple, of course, and depends on the information we have about the disputants. I suppose we would agree that in a question that requires knowledge and skill (such as a scientific question), few experts will arrive at a better answer than a broad audience of laypeople.[1] And what if there is a disagreement among experts? In such a case, is the majority a measure of truth? The Education Book He claims that in this case too the answer is positive. In mitzvah eight (the mitzvah of "biasing after many", in the court of law) he writes:

And the choice of this majority according to the similitude is that both groups that are arguing know the wisdom of the Torah equally, which is not to say that a small group of scholars will not defeat a large group of ignorant people, even like the Exodus from Egypt, but in the wisdom of the Torah, or in the near future, we will be informed. That the majority of opinions will always agree on the truth more than the minority.. And whether they agree with the truth or not, according to the opinion of the listener, the law dictates that we should not deviate from the path of the majority. And what I am saying is that the choice of the majority is always in the two classes that share equally in the wisdom of the truth, because it is said everywhere except in the Sanhedrin, where we do not scrutinize whether they disagree or whether one class knows more, but we always do according to the words of the majority of them, and the reason is that they were considered bound by the Torah, and it is as if the Torah had commanded in an interpretation according to the majority of these, that you should do all your affairs, and moreover, they were all great sages.

First, it is important to understand that in the court of law, the goal is to reach as much halachic truth as possible (this is not a democratic majority based on rights, but a majority in a debate between experts trying to reach the correct answer). At the beginning of his remarks Education He claims that even among experts it is not always right to follow the majority. Even among professionals, a minority of wise people overcomes the less wise majority. But when wisdom is at a similar level, his claim is that the majority is a good measure of truth. This does not mean, of course, that the majority is always right or necessarily right, but that if we are looking for a uniform and a priori measure of truth, the majority is a better candidate than the minority.

And what about a situation where we have no information about the litigants? Or if we do not have clear indicators of their wisdom and intelligence in the field in question? For example, in disagreements in a court of law when we do not have a clear indicator to determine the degree of wisdom of the litigants (we are all peoples of countries, or postmodernists who do not believe in more or less wisdom), is it correct in such cases to follow the majority? Another example, when there are differences of opinion between military officers regarding the correct course of military action. In most cases, it is difficult to determine the degree of military wisdom of the litigants (one may have brilliant ideas that the others did not think of. But in the case where no one is convinced by the proposals of the other and does not see it as a brilliant solution to the problem, it is difficult to determine who is smarter and deserves to act as suggested). Is it correct in this case to follow the majority? Of course, even in cases like these, there is room to determine that in the absence of a clear way to approach the truth, we will adopt the majority as an alternative criterion. Not because it will necessarily bring us closer to the truth, but because in the absence of another criterion it is natural to adopt it (why? Like that! What other criterion do we have?!). But if we still want to maximize the chance of reaching the truth, is Rob the right algorithm?

This question will be clarified from a slightly different discussion.

Arguments from the distribution of opinions: religious-secular and right-left

In Dawkins' books, as well as on all sorts of atheist websites, you will find studies (in my opinion, it would be more accurate to call them surveys) that show that, on average, the educated tend toward atheism and believers are less educated.[2] The same is true for the right and the left. Although several explanations have been proposed for this that are not related to the question of which of the two sides is more correct, it is very common to present these data as an argument in favor of the left and secularism. If the wise and educated (I will not go into the question of the relationship between education and wisdom) support one position and the less educated and wise take another position, then the first position is probably correct. What is assumed here is that the educated are more accurate in their approach to the truth. On the face of it, this is very reasonable, isn't it?

Side note: Relevance of majority without discussion

Several halachic sources present a principle based on the understanding that there is no obligation to follow the majority except where the majority and the minority have agreed and agreed between them. For example, the Rashba writes in a reply (Chapter 5, Chapter 122) regarding a court of law, and also in another reply (Chapter 3, Chapter 126) in which he deals with the voting of elected officials (these things are also repeated in the Responsa Maharit Ha-Rita, Chapter 121, Chapter 123, and more). It is true that there was room to distinguish between voting on a halachic question and voting on a democratic question, since the reasoning deals primarily with the right of the minority to have its opinion heard. But even in halachic voting, where the truth is sought and not an expression of the right of the individual voter (see Column 66 And here at the beginning of my words), the same logic applies. If the minority and the majority did not discuss and agree among themselves and did not hear each other's arguments, then the majority's decision has no weight. This is also not an indication of the truth. It is possible that if they had heard the minority's arguments, they would have been convinced. Indeed, from this perspective, several rabbis wrote[3] In a dispute between different jurists on a halachic question, they do not follow the majority, since they did not discuss and agree with each other (unlike dayanim in the Book of Judges, about whom it is said "after many to incline"). Here is a clear example of "voting" whose goal is the truth, and yet they do not follow the majority if they did not sit down and discuss with the minority.

Even in surveys of the types discussed here, it must be taken into account that the parties do not really sit down and discuss with each other (there is certainly no real listening to the various arguments. On the contrary, there is usually complete mutual contempt). In such a case, it is difficult to decide in favor of the majority simply because it is a majority. Only when all the information, arguments, and justifications are exposed to everyone and yet there is a majority for one side does this majority have any weight.

But for the sake of discussion, let's assume that everyone has reached their conclusions after hearing and considering all the arguments. What does the majority mean in such a situation? Is it any indication of the truth?

Usually the minority is right.

My initial anarchist intuition is that in every argument, both sides are wrong unless proven otherwise. But even if the two opinions that are confirmed are the only possible ones (in which case it is not possible for both sides to be wrong) – then usually the minority is right. I even had a nice argument in favor of the matter. After all, it is likely that there is a pyramid of intelligence, meaning that in a normal group of people there are a few wise people and a lot more stupid people. So if there is a public debate on some subject that requires wisdom, it is reasonable to assume that the minority is the opinion of the wise and the majority is probably the majority of people (which is of course made up of the stupider people). Therefore, in every argument, the starting point should be that the minority is right.

The conclusion is that in debates about faith or right and left, if the minority among the sages advocates faith and religiosity, they are probably right. Bnei Moshe proposed a more complex model. He claims that according to his impression the distribution is that the bottom four deciles are right/religious, the next five are left/secular, and the top decile is again right/religious. In the following sections I will propose a model that will explain this proposal.

Two hidden assumptions

On second thought, my intuition is based on two assumptions, at least one of which is implausible: A. We assume here that the distribution is homogeneous (meaning that the minority consists of a minority of smart people and the majority consists of a majority of stupid people). Isn't it possible that the two parties are each made up of smart people and stupid people? B. The distribution of smart people is in the shape of a pyramid with a wide base and a narrow top.

The first assumption actually sounds quite reasonable to me. It is of course not necessary, but at least in the absence of other information I would be willing to adopt it. If it is a decision that requires wisdom, and we have a distribution of people along the axis of (this particular) wisdom, then it is likely that those with the same ability and intelligence will reach the same answer. Therefore, it is reasonable to conclude that the minority and the majority are segmented by intelligence. Ask, what about the distribution between right and left, religious and secular, or socialism and capitalism? First, it is possible that this is indeed the case in these disputes as well. Second, these are arguments that also depend on values and not just on facts and wisdom, and therefore it is less likely there to assume that the segmentation is precisely by intelligence.

But the second assumption is clearly problematic. Just as there is a minority who are very smart, there is also a small minority who are very stupid. The majority is somewhere in between these two extremes. In other words, the distribution of intelligence is not in the shape of a pyramid but something like a symmetrical Gaussian. Here is an example of a Gaussian distribution of scores on a test:

The vertical axis depicts the number of people who received the score indicated on the horizontal axis.[4] The average score is 70 (there are 400 people who received it. In the Gaussian case, the average score is also the score received in the highest number of cases), and around it there is a symmetrical distribution of scores in the group. Most test takers receive scores between 60 and 80 (one standard deviation to the right and left of the mean), and a few receive higher and lower scores. The more extreme the score, the smaller the number of those who received it. If we treat this graph as the distribution of intelligence among our debaters (we gave them an intelligence test and this is the distribution of the results), you can immediately see that there are a few smart people and a few stupid people, and even fewer very smart and very stupid people. The majority are in better or less middle places.

So, even if we adopt assumption A, that the distribution is homogeneous and segmented by intelligence, we will have to assume that the minority belongs to one of the extremes, and the majority is everything else. If we assume that in the military debate 30% of the officers propose course of action X and the remaining 70% propose Y, we still have two interpretative options: A. The minority are those who receive a score above 80 and the majority are all those who receive below that. B. The minority are those who receive below 60 and the majority are all those who receive above. So, even if we adopt assumption A, the question of whether the minority is right or the majority is right (i.e. whether to do X or Y) remains open, and this is because assumption B is incorrect. The conclusion is that while there is no reason to assume that the majority is right, on the other hand there is also no reason to assume that it is wrong. So half of our anarchist desire is in our hands. But don't worry, we are only halfway there.

Truncated Gaussian

Now think about a situation in which a discussion is held between students in a university biology department, for example. A reasonable assumption is that there are no complete idiots there, since they underwent reasonable screening when they were admitted to the studies (psychometric test and matriculation score). This means that our Gaussian is truncated from below. A reasonable model would assume that the composition of the class is described by the right part of the Gaussian (starting from a certain score and above). In such a situation, we have the few smart ones but not the few stupid ones. While it is not necessarily the case that the greatest smart people in the universe are in this class, it is clear that the distribution of intelligence there does not look like the population as a whole. The filtering is directional (upwards), and it breaks the symmetry. The result is similar to the distribution of the pyramid from which I emerged in the anarchist stage, and therefore for the purposes of the discussion we can assume that this is a Gaussian truncated from below. Even if this is a simplistic model, it is still clear that the distribution in such a situation is no longer symmetrical, and therefore the conclusion that in the case of a debate between students in the biology department, or in a debate between academics (assuming there is also filtering that skews the distribution from below), the conclusion is that the minority is right. Within a population that is sorted upwards, there is a lot of logic to the claim that the minority is right. In contrast, in a population that is sorted downwards, the majority is right.[5]

Application for Education-Faith Surveys

Now I will apply this to the claims regarding the superiority of the left and the secular among the educated, and you will see what a surprising result is obtained. The basic claim is not that all educated are secular leftists and all uneducated are religious rightists, but that among the educated, the majority is leftist-secular and among the uneducated, the majority is rightist-religious. In order to analyze these results and draw conclusions from them, we will first look at the educated group. This is described by a Gaussian truncated from below, and therefore in this case the minority is right (because in such a Gaussian, the minority is the smarter one). I will only mention that among the educated, the minority supports the right and faith. The conclusion is that analyzing the results among the educated is more correct in concluding in favor of the rightist-religious view. Now we will move on to look at the second group, that of the less educated. Here, the Gaussian is truncated from above, and therefore in such a group the majority is right (because the majority is on the smarter side). But here the majority is right-wing-religious, so the conclusion is once again that the right-wing-religious view is correct. In other words, it appears from both sides of the equation that these data lead to the right-wing religious conclusion, and not as one might think at first glance (perhaps the first view is left-wing-secular, i.e. less intelligent).

One can of course argue about several elements in this analysis, and there is no doubt that it contains a great deal of simplification (to the point of ridicule). I will certainly join those who laugh at such analyses, and in fact this is my very purpose in writing these things. And yet one thing is clear: drawing conclusions from the results of the surveys cited above (on the relationship between education and faith) is much more simplistic than the analysis I have done here. Therefore, this simplistic analysis suffices to show that the left-wing-secular conclusion certainly does not arise from, and is not even supported by, such data. In other words, if anyone at all tries to draw any conclusion from these data (as mentioned, not recommended), then at most the right-wing-religious conclusion can be drawn from them. We have therefore more or less returned to Bnei Moshe's argument cited above.

Note: Long after writing and publishing the column, in a lesson I gave on the subject of majority (see video lessons, P.T., majority, dated October 18, 2018), I received a comment from Eric Peshdetsky against the explanation I put forward regarding the fact that the minority is usually right. The comment is correct, and therefore I am correcting it here.

He argued that even if we accept the model of a talent pyramid, or a truncated Gaussian situation (i.e. when there are few smart people and many stupid people), the majority is still right. We are dealing with a binary question, which has a yes or no answer. Contrary to my assumption here, the stupid people do not answer the wrong answer but a random answer. Therefore, on average, half of them will answer correctly and half will not. On the other hand, among the smart people, the majority will answer correctly. Therefore, overall, there will be a majority for the correct answer. Of course, this can also be challenged, but it is clear that the basic model I proposed here is incorrect. Correct!

[1] Column 62 I touched a little on the wisdom of crowds, and explained why it is irrelevant to our kind of questions.

[2] See here andhere (around note 34) A more balanced account. Additional sources on evolution and creationism are given in the introduction to the book. God is playing In cubes And in note 2 there.

In such a discussion, it is important to distinguish between surveys that show that believers are less educated (or that atheists are more educated) and surveys that show that the less educated are believers (or that the more educated are atheists). The direction of the correlation has a different meaning for our purposes. In the discussion that follows, I will assume results that express the percentage of believers/atheists by level of education, and not vice versa.

[3] See Shch H.M. C. 25. S.C.T., and W.Natiyam (Novels) Name of the Skikh andUrim There is a C. K. and many more.

[4] The description is simplistic because I didn't give the resolution. Try to think about how many examinees there were in total and you'll see that there's no way to tell from the graph. But for our purposes here, it's enough.

[5] A question for thought: Is a Gaussian distribution of grades (with two tails in both directions) also expected in biology student classes? If so, does this contradict the description I gave here?