1.2 Inductive Argument

In the last chapter, we learned that deductive arguments begin with a general major premise, continue with a more specific minor premise, and end with a conclusion that follows from both premises. In this chapter, we study inductive arguments, which begin with specific observations and end with general principles. They follow the same structure as deductive arguments, which mean they contain a major premise and at least one minor premise. However, you can never be completely certain about an inductive argument, since it is essentially probabilistic. And if you can be 100% certain, the argument becomes deductive!

Imagine that you are going to restaurant where you’ve never been. You decide to look at reviews submitted by people who have dined there before, and see if there are any patterns. After reading ten reviews, you find that seven rave about chicken dishes, four comment on the beef (two unfavorably), and the only person who mentions lamb found it overcooked. Your decision to order chicken is an example of inductive reasoning.

The data you collect from the reviews allows you to make a probabilistic statement that you are more likely to be satisfied with chicken than beef or lamb. The form of your argument is as follows:

Major premise: Data indicates that chicken provides satisfaction to the largest number of diners.

Minor premise 1: I want to maximize the probability of a satisfying meal.

Minor premise 2: My preferences are not that unusual and are likely shared by others.

Conclusion: I am more likely to be satisfied with a chicken dish than another main dish.

Note that the certainty inherent in a deductive argument is lacking in an inductive argument. This is because you have no specific knowledge of the facts underlying each person’s observations, and because past behavior does not determine future behavior. For example, the people who ate the chicken may be friends of the chef, and he invited them to try his chicken dishes. It also could be that those who were dissatisfied with the chicken didn’t write reviews. Maybe everyone who ate the lamb liked it (except the one person who found it overcooked), but they didn’t bother to write positive reviews. And it could be that the chef who cooked the chicken recently quit and his replacement specializes in cooking beef and lamb. There are many ways that the data could lead you to a false conclusion. However, with no better way to gain information about the restaurant, you rely on inductive reasoning.

Polling is a common example of generating a conclusion from a sample of responses. If we want to know what the public thinks about a particular issue–or what candidate is preferred–we select a sample from the total population, ask the members of the sample what they think, and then reach conclusions based on the data collected. What allows us to infer that a sample accurately reflects what the entire population believes? The first underlying assumption is that most human behavior follows what is known as a normal distribution, otherwise known as a bell curve. The foundation of many inductive arguments is that measurable human behavior reflects a normal distribution of responses. This means that 68.3% of responses fall within one standard deviation of the mean (or average) and 95.4% fall within two standard deviations of the mean. The normal distribution means that if the sample is randomly chosen, the characteristics of the population are likely to be reflected in the sample. Furthermore, as the size of a randomly-chosen sample increases, the more confidence there is that the characteristics of the sample accurately reflect the entire population.

If you surveyed the entire population, you would have an exact picture of the public’s preferences and you could formulate a deductive argument to express it. This is what happens in elections. However, the cost of getting this exact picture is very high, which is why almost all decisions are made using samples and inductive reasoning. This means that there is a probability of an incorrect result every time inductive reasoning is used. There is always a tradeoff between sampling more people and saving time for other things in your life. How many reviews do you read when you consider making a purchase? If you’re buying a car, probably several; if it’s a small purchase, maybe one or even none.

When sampling generates an incorrect representation of the population, it is often because the sample is not representative of the general population. This means the sample presents a skewed distribution that leads to unreliable conclusions. One of the most famous examples occurred in 1936, when the Literary Digest invited its readers to opine about who they thought would win the presidential election. The 2.4 million responses overwhelmingly predicted victory for Republican Alf Landon, but in the general election he lost to Democrat Franklin Roosevelt–in the greatest presidential landside of the 20th century. So what happened?

The readers of the Literary Digest were mostly wealthy Republicans, a small minority of the total population during the Great Depression. While these readers preferred Landon, the vast majority of voters preferred Roosevelt. Elections involve one of the few situations where all preferences are known, so the accuracy of the poll could be tested against reality, and it proved very embarrassing to the Literary Digest, which soon after went bankrupt.

Scientific polling has greatly improved since 1936, and pollsters now attempt to reflect those attributes of the population that are correlated with voting behavior. However, they still make errors when they fail to identify variables relevant to the choices people make. In 2004, President George W. Bush was informed on election day that the polls showed he would lose Florida, the state that would decide the election. However, he ended up winning Florida by a comfortable margin. What had happened was that while the pollsters were making sure their sample accurately represented the demographics of Florida voters, they failed to anticipate that Democrats were far more likely to disclose who they voted for than Republicans. This led to an incorrect prediction.^[1] Similarly, polls in advance of the 2016 and 2024 presidential elections failed to predict Donald Trump’s victory. Again, the reason seems to have been that more of his supporters chose not to disclose their support than those of his challengers.

Inductive arguments are needed because the cost of knowing exactly what the entire population believes is usually too high to be worth the expense. Statistical inference can often generate good conclusions, but can never be 100% infallible. We still need to rely on it because without inductive reasoning, all predictions would just be guesses.

Another type of inductive argument involves analogical reasoning. This is when an unusual situation arises and there is a need to predict what the consequences could be. For example, how will consumers react to tariffs that make the price of imports much higher? What will a country do if another country demands that it change its laws, or surrender its territory? In situations like this, there is no way to take a poll or conduct an experiment. Therefore, we look to the past to help us discern the future. If we find that threatening to impose tariffs will force other countries to change their behavior, does that mean we can accurately reason that a future threat will have the same result?

In order to understand whether analogies are accurate, we need to distinguish between correlation and causality. The former refers to the sequence of events; if we see one action closely follow another, it is tempting to conclude that the first caused the second. Suppose that a state increases the penalty for carrying a gun during the commission of a felony, and we see the number of felonies drop in the next year. It could be that the change in laws caused criminals to reduce their illegal behavior, in which case there is causation. Or maybe the economy improved, encouraging would-be criminals to get a job, so the first and second action are merely coincidental. Or it could be that hiring more police officers has deterred crime in general, so that the cause was not the change in laws but a change in resource allocation. Disentangling cause from coincidence is often difficult, but it is necessary in order to determine if an analogy accurately reflects a causal relationship or mere correlation.