Slippery slope

“Soon nobody will come in at all”

Manager: If we let people work from home on Fridays, next they’ll want Thursdays too. Then the office will be empty most of the week, the team will stop talking to each other, and within a year the department will fall apart.

Each step is asserted, not shown. Nothing is offered to suggest that one remote day leads to a second, and the manager, who sets the policy, would be the one deciding whether it does. Even if each of the four links were fairly likely, say 70%, the chance of all four happening would be about 24% (0.7 × 0.7 × 0.7 × 0.7), far from the certainty the argument implies. Remote Fridays may or may not be a good idea; this argument doesn’t show which.

Real mechanisms, overstated odds

“Don’t put off this oil change. Old oil breaks down, broken-down oil stops protecting the engine, the parts wear against each other, and then the engine seizes. You’ll be buying a new car.”

This one sounds respectable, because every link describes something that really happens to engines. The problem is the probability, not the mechanism. Driving a few hundred miles past one scheduled change makes each step only slightly more likely, and the chance of all of them, ending in a seized engine, is small. A slippery slope can be fallacious even when every step is possible: what matters is how likely each step is, given the one before.

“Where do we draw the line?”

A book club is deciding whether to give itself two months for an unusually long novel. One member objects: “If we make an exception for this book, then next time anyone finds a book slow they’ll want an extra month too, and we’ll have no reason to say no.”

This is the precedent form: allowing one case supposedly commits you to allowing the next. It can be a fair point, but here the claim that there is “no reason to say no” is false, because an obvious, principled line is available: “books over 600 pages get two months.” An exception that comes with a clear rule doesn’t set the precedent the argument fears.

Stripped down, the argument is a chain with a bad ending:

The shape isn’t the problem. A chain of “if” premises can be perfectly good reasoning when every link holds. The trouble is that in a real slippery slope the links are usually “probably”, not “always”, and probabilities along a chain multiply:

So a chain can be made of individually plausible steps and still be unlikely as a whole. The other half of the calculation is how bad the outcome is. Ulrike Hahn and Mike Oaksford, with Adam Corner, analyze the strength of slippery slope arguments in terms of both how probable the outcome is and how much it matters, so a modest chance of a very bad outcome can still be a good reason for caution.

Textbooks have long disagreed about what a slippery slope is. Trudy Govier found three quite different treatments in them, and Douglas Walton’s book-length study distinguishes four types:

• Causal: each step brings about the next. The Stanford Encyclopedia of Philosophy’s illustration: skipping college means no degree, no degree means no good job, and no good job means you won’t enjoy life. The weak links there are the second and third.
• Precedential: treating this case one way commits you to treating similar cases the same way, and those to others. It draws on the reasonable principle that like cases should be treated alike.
• Conceptual (Walton calls it the sorites type, after the ancient paradox of the heap): a vague word has no sharp boundary, so each small step seems to make no difference. One grain of sand doesn’t turn a non-heap into a heap, and one hair doesn’t make a bearded man beardless, yet enough steps take you from one to the other.
• Full: Walton’s fourth type, which combines features of the other three.

On Walton’s later analysis, what makes a slope slippery is a gray zone: a stretch with no clear place to stop, where the person taking the steps loses control over whether to go on.

Not the same error: the argument of the beard. “There’s no exact point where a hobby becomes a job, so there’s no real difference between them” uses the same vagueness, but to deny a distinction rather than to warn against a first step. A lack of a sharp line doesn’t mean there’s no difference between the ends.

Govier concluded that two of the types she identified need involve no logical error, and Walton argues that slippery slope arguments are a special kind of argument from negative consequences, which is often perfectly reasonable. A slippery slope holds up when:

• Each link has evidence behind it. Known causes, such as a drug that builds tolerance, or documented patterns of how similar decisions have played out, support the steps.
• The chain is short, or its links are close to certain. Two steps at 95% each leave a 90% chance of the whole chain.
• Stopping partway really is hard. If there’s no clear place to stop, or once started you can’t easily turn back, the warning is about losing control, not about an imagined cascade.
• The precedent really binds. Where fairness or rules require treating like cases alike, and no principled distinction is available, allowing one case does commit you to the next.
• The outcome is bad enough. A chain with a modest chance of ending in something severe can be a good reason for caution, as long as the argument says “might”, not “will”.

The test: what’s the evidence for each link, and what would stop the slide at each one?

Choosing a medication that won’t escalate

A doctor is choosing between two drugs for a months-long treatment. “Drug A works slightly better at first, but patients build up tolerance to it, so the dose has to keep rising, and past a certain point the dose becomes dangerous. We can’t switch drugs partway through. Drug B does the job adequately without that problem, so we’ll start with B.”

This is a genuine slippery slope, and a sound one. Walton builds on a case like it, which he quotes from Burgess (1993), as one of the few clearly reasonable slippery slopes in the literature. Each link is documented pharmacology rather than speculation (each link has evidence behind it), and the inability to switch mid-course means that once treatment starts, stopping partway really is hard.

“Then I’d have to do it for everyone”

A student asks for a week’s extension on an essay because they forgot the deadline. The teacher says: “If I give you a week for forgetting, I have to offer the same to anyone else who forgot, and then the deadline doesn’t mean anything.”

This has the precedent shape, but the precedent is real. A teacher is expected to treat students alike, and “I forgot” offers no principled way to tell this student’s case apart from the next one. The chain is also short and predictable. That’s the precedent really binds condition. Compare the book club example, where an obvious rule was available to stop the slide.

A slippery slope tells a story, and each step on its own sounds plausible. People rarely multiply the chances along a chain; if anything, adding vivid, connected detail tends to make a sequence feel more likely, not less, the same pull behind the Conjunction fallacy. Meanwhile the endpoint is usually alarming, which draws attention away from how the argument got there.

There’s also a reasonable instinct underneath. Corner, Hahn and Oaksford found that people judge slippery slope arguments stronger when the first and last steps are more similar: the more alike the two ends, the more likely they are to end up in the same category. The authors argue that this part of the argument may have an objective basis. Walton points out that the argument is also hard to assess in either direction: it reaches far into the future, its structure is complex, and it’s usually stated in a compressed form, with most of the middle steps left out.

• Ask for the missing steps. Many slippery slopes jump straight from the first step to the disaster. Filling in the middle shows which links are carrying the weight.
• Put a rough number on each link, and multiply. A chain that sounds inevitable often turns out to be unlikely, or the exercise shows one link is doing all the work.
• Look for a bright line. Walton identifies as one of the most important questions whether a clear stopping point can be drawn through the gray zone. Rules, limits and review points are often how real slopes are kept from becoming slippery.
• Check that it’s a slope at all. Walton notes that students often label any argument from negative consequences a slippery slope. “If we remove the railing, someone will fall down the stairs” is a single, direct consequence, not a chain. Calling it a slippery slope misdescribes it, can turn it into a Straw man of what was said, and unfairly puts the other person on the defensive.

The slippery slope is a matter of reasoning rather than an empirical effect, but psychologists have tested how people judge these arguments.

• Hahn and Oaksford (2007) proposed a Bayesian (probability-based) account in which classic fallacies, including the slippery slope and the Argument from ignorance, are argument forms whose strength depends on their content, and reported experiments testing whether people’s judgments track the factors that account predicts.
• Corner, Hahn and Oaksford (2011) ran three experiments. The first found a robust effect of probability on how strong people judged slippery slope arguments to be. The second (with a follow-up) found that when the start and end of a slope were similar enough to be classified in the same category, the argument was rated stronger. In the third, a correlational study, people’s confidence in their categorization judgments predicted how strong they found the argument. The authors conclude that an important part of many slippery slope arguments may have an objective basis in well-established theories of categorization.

These studies show what makes people find slippery slopes more or less convincing, and that those factors are often relevant ones. They don’t show that any particular slippery slope is sound.