In Chapter 5, John Allen Paulos says that "Societal preferences are determined by a majority." If this is the case, how does innumeracy effect societal preferences? Give a specific example from the chapter to illustrate your point.
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Monday, March 16, 2009
Chapter 5
Posted by Mr. Wille at 1:29 PM
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26 comments:
Candy L.
I like the part about "Statistical Mistakes" in Chapter 5. The example I like the most is about the toothpaste. It's about a new toothpaste coming out say that they reduces cavities by 200 percent, that sounds very impressive. But the number 200 percent is very misleading, assume a toothpaste reduce 10 percent of the cavities, this new toothpaste can reduce 30 percent cavities, 30 percent is a 200 percent increase of 10 percent. But if they say they reduce 30 percent cavities, it's less impressive, and people will prefer to buy other toothpaste that says “reduce 150 percent cavities” other than "reduce 30 percent cavities", even though the second one actually works better. And that's why companies rather use misleading numbers than "real" numbers. Situation like this, a good question to ask will be "Percentage of what?". Let's use the example I just gave, if it's 200 percent of cavities other than 200 percent of what other toothpastes can do, it will be a totally different story, but people will never notice the difference if they are innumerate.
Keith M.
My favorite was the reference to the 1988 Democratic primary battles. The three people Gore, Jackson and Dukakis are competing. 1/3 of the electorate prefers D>G>J. Another 1/3 prefers G>J>D. The last 1/3 prefers J>D>G. Because of this, each can claim that 2/3 of the electorate prefers themselves over one other. If majority does have such a pull on societal preferences, then the outcome would be that people prefer D>G, G>J, and J>D. This, as Paulos explains, cannot be used to find societal preferences. This is because it is not transitive. (Transitive means that if A is better than B, and B is better than C, then A is better than C.) Look at the example about the candidate again.... Dukakis can beat Gore, and Gore can beat Jackson, but Dukakis cannot beat Jackson. This is actually a lot like Rock, Paper, Scissors. Rock > Scissors, Scissors > Paper ..... if you use the transitive prop. from here, you get the outcome Rock > Paper, which is not the case. If a person uses a situation that is not transitive and uses it to interpret societal preferences, that is a major example of innumeracy.
BrooksR
Statistics are a good way of showing the probability that any even will happen. If the number of times and the actual time a bus shows up at the stop is recorded, then the probability of arriving at the bus stop just when the bus is pulling in can be calculated. In this way, statistics can be used to help make the best decision, which is usually the purpose of analyzing statistics. In Innumeracy, Paulos gives a very succinct example as to when statistics can be used in an actual real-life situation. Suppose, for instance, that two females are making a drug transaction. They have little time to make the transaction so they grab each others bag and run right after they do so. It is easy for these drug dealers to be cheated out of what they want. D1 may have simply put newspaper shreddings in her bag, and D2 could have followed suit. This leaves both people without what they want. This is the individualist. The cooperative option, in which both drug traffickers provide exactly what was agreed upon, benefits both of them. That would most likely be the best decision in this case. Another example of real-life application occurs when two accomplices in crime are apprehended and placed each into their own separate interrogation rooms with the hope that out of anxiety, one of these two criminals will confess. They are told that if they confess and implicate their accomplice, they will receive a reduced jail sentence, while the other one will receive a heavier sentence. This is an instance in which some people would testify against the other and some people who would not. After thinking about probability, it is left to the criminals to decide on a whim.
Benjamin G.
Innumeracy affects societal preferences in many ways. One of the ways discussed in this chapter I found interesting was when Paulos talked about polls and their (in)accuracy. He talks about how many times a survey will talk about how a survey or poll will claim that "67% (or 75%) of those surveyed prefer tablet X," but that doesn't really tell you anything if you don't know the amount of people surveyed. If three people were surveyed, then saying 67% of people surveyed liked a certain product more has no impact. If I made an add saying that 90% of people liked a certain product, and the people surveyed were 9 of my friends and myself, it would hold no impact; there aren't enough people in the group, and they probably hold the same or similar interests. These kinds of things are continually being presented to the world, though, and people assume they're true and valid. This contributes to many people being innumerate, as well as believing everything they see with a statistic in it, no matter how little evidence they've seen.
Rondelle B
My favorite example was about the toothpaste and how different companies like to use misleading numbers. Big companies like to use bigger numbers to trick innumerate people into buying their product. The toothpaste factory stated that they reduce 200% more cavities than the leading brand. What they don't say is how much percent the leading brand reduces. Lets say the leading brand only reduces 5% of cavities. Then that way this new toothpaste allegedly only reduces 15% which is 200% more than 5%. Now people like big numbers so instead of sayin 15% they say 200% more. This just goes to show how the public forces itself to be innumerate.
I liked the part of how a philanthropist was giving away $10,000 to everyone in the room if they did not press the button, but only the select few that did would get $3,000 and the others would get none. THis basically means that if no one pressed the button, then each of them would be awarded $10,000 but if a person did, only they would get money. Now the safe bet would be to press the button because it gurantees you money. If you wait and somebody else presses the button, then they get the money and you leave with nothing. ou would prefer getting the $10,000 but your fear of not getting anything would probably make you press the button, even though it may not be best for the entire group and not better for you either seeing as how you were only rewarded less than 1/3 of what you were promised.
Jeffrey L.
I feel that innumeracy has a major impact on society whether you realize it or not. My favorite example in the book is the example about the two men who bet on a series of coin flips. The men agree that the first to win six such flips will be awarded 100$. The game is interrupted after only eight flips. One man leads 5 to 3 in the game. An individual would argue that he is to receive 5/8 of the award and the other was to receive 3/8. Actually, the possiblility of the first man going to win is 7 out of 8 so he should actually get 7/8s of the prize instead of the 5/8s. This just goes to show how innumeracy affects life everday.
Innumeracy takes a big toll on society. This is mostly, because peolple make descisions based on their interpretation of things. An innumerate person would probably something or not beleive what a numerate person might. Since your descision can affect other people in society knowing statistically whats happening can benefit a lot of people. My favorite example is the one about the philantropist who will give each of the 20 people in a room, who have not communicated, 10,000 if they don't press the red button in front of them. on the other hand if you press it you will recieve 3000 and the other will get nothing. the problem here is if you press it you get 3000 but if somebody else does then you get nothing. Your descision maight chnage if the stakes changed which is just a matter of statistics.
Nada G.
I like the example when there is a group of people in a room together brought by an eccentric philanthropist. They cannot communicate in any way with one another and each of them is given the choice of pressing a button or not. If nobody presses the button, everyone will get $10,000, however if at least one presses the button, they will receive $3,000 and everyone else will receive nothing, so the problem is should you press the button or not. This refers to the statement of John Paulos saying” Societal preferences are determined by a majority”; this group as a whole must decide what to do. Innumeracy plays a big role into this, because some innumerate people may come and mess it up. An innumerate person may just look at the big numbers for themselves and press the button, while the rest of the people are planning to benefit the whole. Because, innumerate people overlook some numbers, they also overlook the rest of society.
Tony L.
Being innumerate affects a great deal of your life. such as the example in chapter 5 about the toothpaste. it talks about a new toothpaste that reduces cavities by 200 percent. consumers automatically assumes that it will reduce your cavities by "alot" since the number 200 seems to be a great amount. but lets say the regular toothpaste reduces cavities by 10%, this new one reduces it by 200%, so then a inummerate person will know that it will reduce cavities by a bit more than 10%. many innumerate persons will believe that it will reduce cavities by 200%. companies use this strategy to convince consumers to buy their products.
My favorite example in the lsat chapter of INNUMERACY by John Allen Paulos is the example about the toothpaste. It talks about how some new kind of toothpaste can reduce cavities up to 200 percent. Most buyers will see this and think "wow thats good" because 200 is alot out of 100, (which is what percentages are out of). But if your previous toothpaste only reduces cavities by 3% then 200 percent of that is 9 percent, So the new toothpaste only really reduces cavities by 9% and that is not at all like 200 %. Alot of companies uses the Innumeracy of some people to sell products.
Nina A.
Trevor L.
Chapter 5 for the most part is about how human preference can be affected by how innumerate people are. John Allen Paulos wrote about many examples where people were given an individualist option and a cooperative option. From what I gathered, the individualist option is usually a more prime target. My favorite example was the example where two WOMEN are drug trafficking. Each woman will put down a paperbag with whatever they are supposed to give, and they will pick up the other bag. Since there is no interaction, the women have two choices; the individualist choice of putting ripped up newspaper or the cooperative choice where they put in whatever they are supposed to trade. Now, for woman A, the best option would be to put in the ripped up newspaper. If woman B puts in the money, then woman A gets her prize and woman B is duped. But if both women put in ripped up newspaper, then neither one of them were duped, but they got nowhere. Obviously, it is the same for woman B. This shows how innumerate these women were because obviously, the best answer would to have both of them be cooperative so that they each receive what they were meant to receive. That way, they can move on. If they have to go through meeting multiple times, they get nowhere and loose trust for each other each time.
Sergio G.
Innumeracy affects Societal Preferences in that, for example with toothpaste and the percentage of cavities removed, people tend to prefer bigger numbers.
People tend to believe that a toothpaste which reduces cavities by 200% will clear their mouths twice over, while that figure may mean that it reduces cavities by, say, 30%, compared to the original product, which would remove 10% of one's cavities, 30% reduction being a 200% addition to the 10% figure.
In that case, people would overlook toothpastes that claim to remove 80% of all cavities, for example, while looking at those that say they remove 200%, passing over the better toothpaste for the one with the bigger number, and better 'stats', if you will.
Aleksandar P
The majority of the content within chapter 5 is about social preferences and how innumerates may play a part in this. My favorite example within this chapter is where a coin is flipped 20 times. If the coin comes up heads all 20 times, you win a billion dollars, but if a tails comes up, then you must pay 100 dollars. Many people would not play because of the odds of winning are only 524,288 or 2^19. But through the use of math, one could figure out that if enough games were played, you would eventually win, and this payout would be greater than all the money you put in and you would get an average profit of $1800. but simply by seeing the 1 out of 524288 chance of winning, many people will nod their heads if asked to play.
*i personally would have played, even before seeing the math.*
Craig H.
In chapter 5 of Innumeracy John Allen Paulos discusses the effects of innumeracy in society. My favorite example of this the eccentric philanthropist that puts a group of 20 people in the room, with no way to communicate with one another a red button if no one preses the button everybody gets 10,000 if somebody press it, then the person who pressed it and everybody else who pressed gets 3,000 while the people who didn't get nothing. Innumeracy is present in this model of a very common societal dilemma because the majority of people would press the red button because they the its best possible outcome because somebody else might press it. They (meaning society) overlook the fact that if everybody cooperates together the outcome will be better than looking out for themselves. Another example that further proves my point is seen frequently in many shows like Law & Order, and is very helpful for police in getting a confession. If two who committed a major crime together get caught doing a minor crime they are put into separate rooms. They are both given the choice of either confessing and getting let free while implicating his partner or remain silent. They are three possible outcomes, if one testifies while the other remains silent, the second offender gets five years while the first gets let free. The second if they both confess and implicate each other they could get three years, while the last which is that they both remain silent they might each get only one year. This example clearly demonstrates the problem with society and innumeracy, which is evident in real life situations like the prison dilemma, and others like it. The innumerate society always tends to overlook that fact that if they work for benefit of the group and not the individual they can achieve a higher rate of success.
In today’s society majority rules and common ways of thinking or what mostly is accepted is what usually goes. Peoples views on the world when buying or anything to that topic is “what can i get the most of for the least price” or “which gives me more.” However numbers can be very misleading when looking at the value of something. That is why the toothpaste example is one of my favorites in Ch. 5 in John Allen Paulo’s book “Innumeracy.” When a toothpastes says it reduces cavities by 200% it seems really good since that’s a big number but in fact it maybe be 30% compared to the other toothpaste, which is 10%. That 30% doesn’t really look so good because it’s not that big of a number. That’s where the innumeracy comes in most people don’t look to see that 30% they only see that big 200. There might be another tooth paste with a greater value but you wont find it because you think you have a better one in your hand, but your wrong.
-Monika C.
Amanda Z.
In the last chapter of Innumeracy, Paulos examines the social effects of innumeracy and how these effects are harmful to the individual as well as to the society. There are several examples where individuals are pitted against society. In essence, one may choose to cooperate on behalf of society or choose not to cooperate on behalf of individualism. An example of this that can be found in the book is that of the two traffickers who must make a hurried transaction involving brown paper bags. Before the meeting, each person has the same option: to put in her bag the item of worth which the other wants (the cooperative option) or to fill it with shredded newspaper (the individualist option). If each person takes the cooperative route, then each will receive what she wants at a fair cost. However, if A fills her bag with shredded newspaper and B doesn’t, then A would get what she wanted at no cost and B would be duped. Therefore, regardless of what the other does, one would think that they would be better off if they took the individualist alternative and give her a bag full of newspaper. Person B, which would reason the same way, would cause both of them to exchange worthless bags of shredded newspaper.
Grissel G
My favorite example of innumeracy in society is that of the two female drug-traffickers who must make a brief hurried transaction and switch two paper bags without drawing attention. The plan is for each bag to contain what the other party wants, however they can put in shredded newspaper if they like. If one puts in shredded paper and the other puts in her bag what was asked of her, she will be the only one duped. If both use shredded paper, neither will be duped but they do not get what they want. if both do what is asked of them, both get what the want at a reasonable cost, which is described as the best option in the book. However, they are both more likely to reason that the individualist option (the shredded newspaper) is the best way to go because it is the best way to get out of being duped. If female A reason that she will put shredded newspaper into her bag and not the substance, she will either receive what she wanted or nothing, but either way she did not lose anything. Female B will likely reason the same way and neither will be left with anything but a bag of shredded newspaper.
Christian J
In chapter 5, I like the part about "Statistical Mistakes". Paulos gives an example regarding toothpaste statistics. He says that when a toothpaste company advertises that they get rid of 200 percent more plaque then the leading brand. The leading brand could get rid of only 10 percent of plaque but the other brand could get rid of 30 percent of plaque. That's because 30 is 200 percent of 10 so instead of getting 200 percent of plaque out of your mouth, your getting rid of only 30 percent. However, nobody would buy your product if you advertised that your product got rid of only 30 percent plaque. This also relates back to Pheunoscience
Bix K.W.
My favorite part was the one about statistical mistakes and my favorite example is the one about toothpaste. A toothpaste says it will reduce cavities by 200%. This is a trick of the numbers. If an old toothpaste reduces cavities by 10%, and the new one reduces them by 30%, then that is a 200% increase. The companies say that their toothpaste will reduce cavities by 200% instead of 30% because if they say 30%, consumers might buy another toothpaste which claims to reduce cavities by 150% even though the first one works much better. And so, companies make claims that their product can reduce cavities by 200% to manipulate the consumer
Damaris F.
In Chapter 5, John Allen Paulos says that "Societal preferences are determined by a majority." The harmful social effects of innumeracy is a conflict between society and the individual. An innumerate often does not realize that an apparently small decision one makes has a huge impact on society- which can be good or bad. Take the example of page 139, about a prisioner's dilemma. Two men are suspected of having committed a crime. They are separated, questioned, and have a choice: Either they stay silent or they confess the crime and implicate the other man. If one confesses and the other doesn't, the one who confesses will be let out while the one accused against will receive a five year term. If they stay silent, they each get only one year of prison. But if they both confess, they have to stay in prison for three years. You can either be cooperative-meaning take the decision that is mineful of society (partner) or take the individualist option (confess). I especially like this example because its a realistic everyday situation I never thought of in that way, not that I ever want to be in this particular crimeful situation. So someone who is innumerate will weigh out the probabilites that their partner will confess or stay silent, and probably stay silent. Meanwhile, the innumerate partner will chicken-out and take the individualistic choice (think only about himself) and tell on his partner (which is a bad choice). I personally think the cooperative choice (stay silent) is the best one, since the risks are smaller. And if your partner is loyal, even better. You'll both be silent and win!!
My favorite example is the one that uses the tooth paste as a direct reference to the misleading slogans that businesses us to draw in consumers. John Allen paulos stated that if a toothpaste were to decrease tooth decaying bacteria by 200 percent, that could only mean about 5 bacteria out of 20 originally. now the new number would be 10 out of 20. this is technically a 100 percent increase. however it is not very convincing to buyers to see that the product that they are about to but is only so effective. Instead the businesses show you a huge number that we take for granted and say is definitely of a high calliber. We forget that numbers can represent others numbers with copmletely different variables. i believe is a very intresting thought because i once to had the same concept as him. it has you thinking about what your items are truely worth in quality.
I like what John Allan Paulos says about the simulation made between Dukakis Gore and Jackson. if 1/3 of the electoral votes prefers dukakis to gore to jackson, the other 1/3 vote prefers gore to jackson to dukakis, adn the remaining votes jackson to dukakis to gore. Paulos calls this a "paradox". This is a paradox because for the 1st scenario, dukakis night say that he has 2/3 of the votes since he is prefered to gore who is prefered to jackson. He might use 1/3 (for him) + 1/3 (gore to jackson) and end up as 2/3. But this is not true, although an innumerate person might be able to see this as an actual fact. Seeing this, an innumerate person might vote for dukakis, or any other candidate who uses this sort of logic, because they are too blind to see the real statistics behind this.
-Sadichchha A.
John-Corey M.
This prompt suggests that all social preferences are decided by majority. However, this is not true. Take for example the common breast cancer statement that 1 out of 11 women will contract breast cancer. This data is false and a good example of immuneracy. Only the "minority" of women 85 years of age and older will it be that 1 out of 11 will contract breast cancer as said on page 162 chapter.
This is a social preference that we generally would think that 1 out of 11 will contract breast cancer, but, is not based on the "majority". At the approximate majority age of women, 40, the likeliness of contracting breast cancer is approximately 1 out of 1000, not 1 out of 11. So, in this case the social preference is based on the minority rather majority. Maybe the reason for this is when we as an American society think of cancer we think of the fact that it takes 100's of lives each year, so, we would want to think of it as the something harsh as contracting is more likely to happen more than 1 in a 1000 times. I guess that's just our social preference.
Chapter 5 was my favorite chapter because all the skepticism that had been building up inside me was released as I finally figured out the purpose behind John Allen Paulos' book. He's doing his part in the world by trying to prevent innumeracy, and to do that, he first has to tell us how it happens. Now that I know how, I know why, and I realized that Innumeracy was just another great read.
Evan Y.
My favorite example of societal preferences John Allen Paulos gives in this chapter is the accuracy or inaccuracy of statistics. Many people assume that because a statistic says something it is correct. This is however not the case very often and many surveys are biased. IF I claimed that 100% of people surveyed had a college degree, it would make it seem as though everybody went through college. However if I inform you that everybody surveyed is one of my school teachers the survey and statistic would be thrown out the window because those surveyed are in a particular field that requires a college degree. Many surveys aren't being looked into to discover their biases and flaws so they are still held to be true even when inaccurate This begins to spread beliefs in untrue things and helps to cause innumeracy.
PS. Spelling "innumeracy" is messing up my spelling inaccurate. .
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