Inspired by Konkvistador's comment

Posts titled "Rational ___-ing" or "A Rational Approach to ____" induce groans among a sizeable contingent here, myself included. However, inflationary use of "rational" and its transformation into an applause light is only one part of the problem. These posts tend to revolve around specific answers, rather than the process of how to find answers. I claim a post on "rational toothpaste buying" could be on-topic and useful, if correctly written to illustrate determining goals, assessing tradeoffs, and implementing the final conclusions. A post detailing the pros and cons of various toothpaste brands is for a dentistry or personal hygiene forum; a post about algorithms for how to determine the best brands or whether to do so at all is for a rationality forum. This post is my shot at showing what this would look like.

At one point or another, we've all asked ourselves, "what is the most rational toothpaste?" After all, despite the length of the sequences, I've yet to see Eliezer's endorsed personal hygiene products. What is an aspiring rationalist to do?

Step one is to throw out the question entirely. The most rational toothpaste does not exist, nor does the best toothpaste nor the optimal toothpaste. These adjectives are only applicable relative to particular goals, constraints, and contexts. Avoid the mistake of assuming optimality is a trait inherent to toothpaste, rather than a joint function of the toothpaste and who is using it. Similarly, the best programming language, the best footwear, the best way to write, and the best job are all under-specified.

Even before determining what you are looking for in toothpaste, take one more step back. Is optimizing your toothpaste worth the time and attention? First, there is the issue of whether improved dental care is worth it, and then, whether better toothpaste is the best means of improving your teeth.

While recognizing "optimal" varies across individuals, goals might be aligned closely enough that something can be identified as approximately optimal. The search costs of finding the perfect solution could outweigh going with an approximate solution. Toothpaste seems like a product where users have essentially the same needs or fall into a small number of categories, unlike the best place to reside, which depends on a large number of individual factors. As a result, toothpaste is probably already well optimized for you and picking anything up off the shelf of a supermarket should do fine, but a product you use everyday still deserves a few minutes of deliberate analysis.

One basic algorithm for tackling these issue:

What do you actually want to accomplish? Two approaches for determining goals: 1. (Bottom-up) List all the goals your current actions or the first proposed solution might fulfill. 2. (Top-down) List your basic values, major goals, mid-level goals, etc until you reach the relevant scope.
How much are you actually willing to spend in time and experimentation costs for improvements to these goals? Quickly estimate the value of information.
Generate actions that might suit each goal. Focus on quantity.
Gather information. Is there published research on the topic? Who might have good advice? Are there quick experiments that can be run?
Filter actions and form a plan.
Are you satisfied with implementing the conclusion reached? If you feel a hang-up, try optimizing specifically for that.¹

Following a bottom-up approach, why do I use toothpaste at all? Toothpaste can decrease risk of cavities, whiten teeth, improve bad breath, or make brushing more pleasant. A change I make could be relevant for at least five years. Beyond that point, I discount the future enough not to worry about it, with the chances of my conclusions becoming irrelevant or out of date included in the discount factor.

How much am I willing to spend for improvements in these areas? Remember that resources are fungible and can be converted into one another, so this represents the total value of time, attentions, and explicit money spent. For myself:

Avoiding a cavity is worth about $300, including the cost of a filling, time, discomfort, etc. I tend to have one and a half cavities a year, so a 1% reduction in cavities over five years is worth 1.5 x 5 x $300 x .01 = $22.5. I expect I might be able to uncover something with up to a 5% improvement, so more info would be worth around $120.
Whiter teeth and better breath are harder to quantify. For noticeable improvements on either front, I'll say I'd pay $10 a month. Over five years, that would be $600. Additional information about aesthetic improvements probably only has a 5-10% chance of finding something that has a noticeable effect and causing me to go through with it, so I should be willing to invest about $50 now.
If a change made brushing more pleasant and ensured I did it regularly, this would multiply the benefits I'm getting from improved health or aesthetics, but I expect this to be too small to account for.

WIth a five-minute estimate, I've learned I could be willing to spend up to $170 total for improved information about dental care. How should I cash that out? Valuing my time at $20 per hour, I could justify up to eight hours of research for a 5% reduction in cavities and a 5% chance of aesthetic improvement. Diminishing returns to researching a topic like this likely set in quickly though, so no need to go overboard.

What possible actions might I take to improve these goals? Here are the results of a few minutes generating as many options as possible.

For health, better toothpaste, more frequent dentist visits, switching to an electric toothbrush, different means of flossing, regular mouth wash, topical fluoride treatments, investing in a commitment device to ensure always brushing and flossing, eating fewer sugary foods.
For aesthetics, in addition to the above, whitening treatments by dentist or store-bought, drinking less coffee and tea, buy a tongue scraper, use gum or breath fresheners more often, use a whitening toothpaste.

How can I gather information about the relative effectiveness of these solutions? Since dentistry is fairly well studied, some quick searches on Google Scholar would be my best starting point. A search for "evidence based dentistry" turned up this site with multiple meta-studies. Other actions, like buying a tongue cleaner for $5 are just worth trying to see if they have an effect.

Fluoride

In adolescents, fluoride in toothpaste can reduce cavities by 23% at 1000 parts per million and 36% at 2500 ppm. The effects for adults are unclear. Since the typical US toothpaste has about 1000 ppm, a high fluoride toothpaste could be worth $2 more per tube for a 10% reduction (~4 tubes/year x 5 years x $2 = $40). Type of fluoride might also matter, with stannous fluoride about 30% more effective at reducing gingivitis than sodium fluoride, and reducing bad breath. Mouthwashes with fluoride have too little to make a difference.

At my last visit to the dentist, the hygenist recommended a topical fluoride varnish. I wondered whether it was simply an up-sell, an easy way to tack $35 on my bill. For this price, a treatment at each visit should reduce the risk over cavities in a year by about 10%. Hard to find good conclusions, but benefit and cost probably cancel out.

Whitening Products

For amount of stain reduction with whitening toothpastes, multiple studies show statistically significant improvements with special toothpastes, although the level of practical significance is unclear. In one study, a water rinse control was equally efficacious as one commercial whitening paste. Other commercial whitening products have some evidence in their favor, although likely suffer from publication bias. Hydrogen peroxide treatments might be more effective, although have increased risk of tooth sensitivity. A meta-analysis of whitening strips conducted over four years at one dental school showed lightness and yellowness improved each by 2 points over two weeks on a scale where participants varied up to 10 points at the baseline. Approximately 20% of the participants experienced irritation or sensitivity. At around $35 for a two-week treatment, experimentation might be worthwhile since if results aren't obvious, it's not worthwhile.

Electric toothbrushes

Using an electric toothbrush could be as beneficial for gingivitis and sensitivity over a manual toothbrush as regular toothbrushing is over baseline. Meta-studies (1) (2) identify this as specific to rotation-oscillation action, with improvements of 20% in gingivitis and plaque over manual. Rotating electric toothbrushes sell for $50 and up, with replacement heads around $7, so purchasing one looks straightforwardly worthwhile.

Tongue cleaning

Some positive effect. Over toothbrushing along, statistically significant and small. As noted above, for $5 and a small amount of effort each day as part of a routine, experimentation of my own is probably worthwhile.

In conclusion, even though I didn't expect changing toothpastes to make a difference, finding a high fluoride toothpaste might be worthwhile. I've heard about the advantages of electric toothbrushes before, but never seriously considered it. I plan on buying one soon. My flossing previously improved substantially with a flosser using detachable heads over floss alone. The tongue cleaner and whitening strips are low priority experiments, established as plausible.

Do I feel resistance to implementing the new plan? I'm actually rather relieved. Instead staring at the wall of toothpaste in the supermarket, unsure of what to choose like I often do, I feel like the issue is settled. Going through analysis like this often leaves me excited or relieved. Common pitfalls I find myself in are trying to reason without meaningful information or not acting on conclusions due to lack of motivation. Reasoning without good information is what I try to do when standing in the toothpaste aisle. Each box has its little claims, but I don't know how to process it well, and end up frustrated by the abundance of choice. Fruitless conclusions aren't an issue here, but are common with bigger decisions. Hidden emotions around an issue can mean that an optimal solution on paper isn't feasible. Investigating small resistances and optimizing specifically for that concern is a means of implementing Pareto improvements for all parts of yourself.

Thanks for Anna Salamon for pointing out the benefits of this step to me as part of her fungibility algorithm. ↩