Monthly Archives: January 2014

Specific Techniques for Inclusion

One lovely thing about having a bunch of rationalist friends is that if I whine about a problem, I get a bunch of specific ideas about how to fix it. Sometimes the whining has to be very specific, though.

What I Complained About

Some people don't feel comfortable on Less Wrong or in other rationalist communities. Apophemi wrote about why they don't identify with the rationalist community because some of the language and topics under discussion feel to them like personal threats. Less Wrong discussed the post here, though sadly I think a lot of people got mindkilled.

Apophemi's post was most directly a response to some stuff on Scott's blog, Slate Star Codex. Scott's response was basically that yes, there's a need for fora where particular groups of people can feel safe - but Less Wrong and the rationalist community are supposed to be a place that's safe for rationalists - where you won't get banned or ostracized or hated for bringing up an unpopular idea just because the evidence supports it. Implicitly Scott was modeling the discussion as considering two options: the status quo, or ban certain controversial topics entirely because they make some people uncomfortable.

Ben Kuhn then responded that Scott was ignoring the middle ground, and there are plenty of things rationalists can do to make the community feel more welcoming to people who are being excluded, without banning discussion of controversial topics.

Sounds reasonable enough. What's my problem with that? Not a single example.

It's easy enough to claim there's a middle ground - but there are reasons it might not be feasible in practice. For example, in some cases it really could be the existence of a discussion of the topic that's offensive, not the way people discuss it. (I think Apophemi feels this way about some things.) In others, there's very little gain from partial compliance. If right now 25% of Less Wronger commenters consistently and avoidably misgender people, and as a result of a campaign to educate people on how not to do this, half of them learn how to do it right, that's still 12.5% of commenters misgendering people - more than enough that it's still going to be a consistent low-level annoyance to people who don't identify with a traditional gender, or women who don't have obviously feminine pseuds, etc. So that's kind of a wasted effort.

So I whined about this, on Facebook. To my amazement and delight, I got some actual specific responses, from Robby and Ruthie. Since there was some overlap, I've tried to aggregate the discussion into a single list of ideas, plus my attempt to explain what these mean and why they might help. I combined ones that I think are basically the same idea, and dropped ones that are either about banning stuff (since the whole point was to find out whether there is in fact a feasible middle ground) or everyone refraining from bad behavior (I don't think that's a feasible solution unless we ban defectors, which also fails to satisfy the "middle ground" requirement).

Trigger Warnings

(Robby and Ruthie)

Some topics reliably make some people freak out. You might have had a very bad experience with something and find it difficult to discuss, or certain words might be associated with actual threats to your safety, in your experience. If you have enough self-knowledge to know that you will not be able to participate in those discussions rationally (or that you could, but the emotional cost is higher than you're willing to bear), then it would be helpful to have a handy warning that the article you're about to read contains a "trigger" that's relevant to you.

This concept can be useful outside of personal traumatic events too. There's a lot we don't know for sure about the human ancestral environment, but one thing that's pretty likely is that the part of the brain with social skills didn't evolve to deal with political groups with millions of members. Any political opinion favoring something that threatens you is going to feel like a meaningful threat to your well-being, to some extent, unless you unlearn this (if that's even possible). Since politics is the mind-killer, you're likely to have this response even if people are just discussing opinions that are often signs of affiliation with your group's political enemies. This is possible to unlearn, but it could be really helpful to know what kind of discussion you're going into, in advance.

For example, I'm Jewish by birth. When people start saying nice things about Hitler and the Nazis, it makes me feel sad, and a little threatened. If it's just a discussion of pretty uniforms or monetary policy,  and not really about killing Jews at all, then there's no reason at all to construe it as a direct threat to my safety - but it's still helpful for me to be able to steel myself for the inevitable emotional reaction in advance.

Content warnings have the advantage of being fairly unambiguous. Someone who believes in "human biodiversity" might not agree that their discussion about it is threatening to black people - but I bet they'd agree that the discussion involves making generalizations about people based on racial categories. Someone who wants to vent about bad experiences involving white men might not agree that they are calling me a bad person - but I bet they'd agree that they are sharing anecdotes that are not necessarily representative, about people in a certain demographic.

The other nice thing about this solution is that right now it basically hasn't been done at all on Less Wrong. It seems reasonably likely that if a few prominent posters modeled this behavior (or a few commenters consistently suggested the addition of trigger or other offensive content warnings at the top of certain posts), it would be widely adopted.

The downside is that some uses of trigger warnings, while widespread on the internet (so there may be an off-the-shelf solution), would require a technical implementation, which means someone actually has to modify the site's code. This limits the set of people who can implement that part, but it's not insurmountable.

I'm not really sure this one has any clear disadvantages, except that some people may find content warnings themselves offensive.

Add a tag system for common triggers, so people can at a glance see where an information-hazard topic or conversation thread has arisen, and navigate the site safely. This is a really easy and obvious solution to Apophemi and Scott's dispute, and it benefits both of them (since it can be used both to tag politics/SJ discussion and to tag e.g. rape discussions), so I'm amazed this proposal hasn't been the central object of discussion in the conversation so far.


Widely implemented. We can help people who acknowledge that they don't want to be around certain topics stay away from. It also gives those who want to be part of overly frank discussions a response to give to those who criticize them for being overly frank.


Make it Explicit That People From Underrepresented Groups are Welcome

(Robby and Ruthie)

The downside of this one is that for women, at least, it's kind of already been done. A few years ago there were a bunch of front-page posts on the topic of what if anything needed to change to make sure women weren't unnecessarily pushed away by Less Wrong. But apparently Eliezer's old post on the topic actually offended some women, who felt stereotyped and misunderstood by it. A post with the same goal that didn't cause those reactions might do better.

I don't feel like this is a very good summary so I'm going to quote Robby and Ruthie directly:

Express an interest in women joining the site. Make your immediate reaction to the idea of improved gender ratios 'oh cool that means we get more people, including people with importantly different skills and backgrounds', not 'why would we want more women on this site?' or a change of topic to e.g. censorship.

- Robby

If more women posted and commented they might move the overall tone of discourse in a direction more appealing for other women. Maybe not. You could do blinded studies (have women and men write anonymized posts about anything, ask women and men which they would upvote, downvote). Again, this would be hard to do well.

- Ruthie

Put in an extra effort to draw women researchers, academics, LW-post-writers, speakers, etc.


Recruit More Psychologists


I can't substantively improve on the original:

If LW is primarily a site about human rationality (as opposed to being primarily a site about Friendly Artificial Intelligence), then it should be dominated by psychologists, not by programmers. Psychologists are mostly women. Advertising to psych people would therefore simultaneously make this site better at human-rationality scholarship and empiricism, and better at gender equity.




An "Ombudsman" is someone who works for an institution, and whose primary responsibility is listening to people's complaints and working with the institution to resolve them. A dedicated person is important for two reasons. First, it can be easier to communicate a complaint to someone who wasn't directly involved in doing the thing you're complaining about. Second, the site/community leaders may not have the time, attention, willingness, or expertise to listen to or understand a particular kind of complaint - maybe their comparative advantage is in building new things, not listening to people's problems.

I have no idea how this would work, but it was suggested to help solve problems on the EA facebook group and seems to have traction at least as an idea there. If they implement it and are successful, LW could follow suit.


Write Rationalist-Friendly Explanations

It would be silly if rationalists weren't at least a little bit better about rationality than everyone else. Unfortunately, this means everyone else is a little bit worse, on average. Including feminists. That doesn't mean they're wrong, but it does mean that many popular explanations of feminist, antiracist, and social justice concepts may mix together some good points with some real howlers. These explanations may also come across as outright hostile to the typical Less Wrong demographic. So as a result, many rationalists will not read these things, or will read them and reject them as making no sense (and this is sometimes a correct judgment).

The problem is that some of these ideas are true or helpful even if someone didn't argue for them properly, and feminists or others on Less Wrong might have to explain the whole thing all over again every single time they want to have a productive discussion with a new person using a concept like sexism. This is a lot of extra work, and understandably frustrating. A carefully-argued account of some key relevant concepts would be extremely valuable, and might even be an appropriate addition to the Sequences. Brienne's post on gender bias is a great start, and there's probably lots of other great stuff out there hiding in between the ninety percent.

Build resources (FAQs, blog posts, etc.) educating LWers about e.g. gender bias and accumulation of advantage. Forcing women to re-argue things like 'is sexism a thing?' every time they want to treat it as a premise is exhausting and alienating.


Get Data

This one's a real head-slapper - Less Wrong is supposed to be all about this. There's a problem and we don't know how to solve it. How about we get more information about what's causing it? Find the people who would be contributing to or benefiting from the rationalist community if only they didn't feel pushed away or excluded by some things we do. (And the people who only just barely think it's worth it - they're probably similar to the people who just barely think it's not worth it.)

Collect and analyze more-than-anecdata on women and minority behavior around LW

The existing survey data may have a lot of insight. Adding more targeted questions to next year's survey could help more. It's hard to give surveys to the category of people who feel like they were turned away from LW, but if anyone can think of a good way to reach this group, we may be able to learn something from them.

Try to find out more about how people perceive different kinds of rhetoric

This would be hard, but I'd be really interested in the outcome. Some armchair theories about how friendly different kinds of people expect discourse to be strike me as plausible. If there are really differences, offense might be prevented by using different words to say the same things. If not, we could stop throwing this accusation around.


Go Meta


Less Wrong is supposed to be all about this one too. Some people consistently think other people are unreasonable and find it difficult to have a conversation with them - and vice versa. Maybe we should see if there are any patterns to this? Like the illusion of transparency, or taking offense being perceived as an attack on the offender's status.

One of my favorite patterns is when person A says that behavior X (described very abstractly) is horrible, and person B says how can you possibly expect people to refrain from behavior X. Naturally, they each decide that the other is a bad person, and also wrong on the internet. Then after much arguing, person A gives an example, and person B says "That's what you were talking about the whole time? People actually do that?! No wonder you're so upset about it!" Or person B gives an example of the behavior they think is reasonable, and person A says "I thought it went without saying that your example is okay. Why would you think anyone objected to that? It's perfectly reasonable!" It's kind of a combination of the illusion of transparency and generalizing from one example, where you try to make sense of the other person's abstract language by mapping it onto the most similar event you have personally experienced or heard about.

I bet there are lots of other patterns that, if we understood them better, we could build shortcuts around.

If well-intentioned people understood why conversations about gender so often become so frustrating before having a conversation about gender, it might lead to higher quality conversations about gender.


Taboo Unhelpful Words More


Rationalist Taboo is when, if you seem to disagree about what a word means, you stop using it and use more specific language instead. Sometimes this can dissolve a disagreement entirely. In other cases, it just keeps the conversation substantive, about things rather than definitions. I definitely recall reading discussions on Less Wrong and thinking, "somebody should suggest tabooing the word 'feminist' here" (or "sexist" or "racist"). Guess what? I'm somebody! I'll try to remember to do that next time; I think a few people committed to helping on this one could be super helpful.

Taboo words

Possibly on a per-conversation basis. "Feminist" is a pretty loaded word for me, and people say things like this which don't apply closely to me, and I feel threatened because I identify with the word.

Scott Alexander also suggested this in the same context in his response to Apophemi on his blog (a bit more than halfway down the page). It can improve the quality of discourse simply by forcing people to use relevant categories instead of easy ones.

Higher standards of justification for sensitive topics

A lot of plausible-but-badly-justified assertions about gender are thrown around, and not always subjected to much scrutiny. These can put harmful ideas in people's minds without at least giving us reason to believe that they're true, and they're slippery to argue against. Saying exactly what you mean and justifying it is probably the best way to defend against unreasonable accusations of sexism. If people accuse you of sexism, they'll at least be reasonable. I think taboo words can go a long way towards achieving this.


Build a Norm That You Can Safely Criticize and Be Criticized For "Offensive" Behavior


I have no idea how hard or easy this is. Less Wrong seems like it's already an unusually safe place to say "oops, I was wrong." But somehow people seem not to do a good job becoming more curious about certain things like sexism. If I understand correctly (her wording's a little telegraphic to me), Ruthie suggested a stock phrase for people correcting their own language, "let me try again." It would be nice to come up with a similarly friendly way to say that you think someone is talking in an unhelpful way, but don't intend to thereby lower their status - you just want to point it out so they will change their behavior to stop hurting you.

Better ways to call people out for bad behavior

Right now, talking about gender in almost any form is asking for a fight. I hold my tongue about a lot of minor things that bother me because calling people out causes people to get defensive instead of considering correcting myself. A strong community norm of taking criticism in certain form seriously could help us not quarrel about minor things. Someone I know suggested "let me try again" as a template for correcting offensive speech, and I like the idea a lot.

Successfully correcting when called out can also help build goodwill. If you are sometimes willing to change your rhetoric, I take you more seriously when you say it's important when you aren't.

Our only current mechanism is downvoting, but it's hard to tell why a thing has been downvoted.


A Call For Action

If you are at all involved or interested in the rationalist community: The next time you are tempted to spend your precious time or energy complaining about how the community excludes people, or complaining about how the people who feel excluded want complete control over what is talked about instead, consider spending that resource on advancing one of these projects instead, to make the problem actually go away.

Wall, Staircase, Hallway: Obstacles Are Scary

When I try to make long-term plans, my attention generally slides most easily towards plans that involve things that I have already done, or that I know how to do. It makes sense to focus on the things known to be easy first, but what doesn't make sense is the degree to which I am averse to obstacles.

Right now, I see obstacles at three levels:


At a distance, every obstacle or new challenge looks like an impassable wall. I can get around it, maybe under or over it, but it just doesn't make sense to go through it. When I think about going from my bedroom to my bathroom, punching me-sized holes in the walls between them and walking through just doesn't seem like a viable plan, so I don't think about it.

This makes sense for literal walls (usually), but not for obstacles like a task that requires a skill I don't have yet. When I make plans at this high level with any attention at all paid to feasibility, I end up excluding every possible plan that would involve learning a skill or otherwise doing or figuring out something new.

This is a problem.



Sometimes, if I focus in on one particular obstacle, it turns out to have a bunch of different parts, many of which are soluble, and only a few of which are actually hard, by which I mean they require attention or willpower. Then instead of a wall, it looks like a long, steep staircase. I know I can get up to the top, but it's work.



Finally, if I focus on the staircase, sometimes it's just a series of tasks, none of which requires much willpower in the moment, it's just sticking to it that requires willpower. If I can set up the series in a manageable way, then the staircase flattens to a hallway and doesn't feel like it's work at all, just another path I can take.


Obstacles are Scary

I don't seem to gradually see my obstacles with greater resolution as I think about them more. Instead, it feels like a discontinuous, sudden shift in perspective. Moreover, my brain seems to think that there really are three different kinds of things that can appear to be obstacles. If I look more closely at a wall and it turns out to be a staircase or a hallway, it doesn't feel like I just have a higher-resolution picture - it feels like I was objectively mistaken about what kind of obstacle this was.

I think this is because obstacles are scary. More precisely, plans that involve a route through an obstacle are scary. Making a commitment I don't know how to execute yet feels like making a promise I know I can't keep (because it would involve walking through a wall). I really, really don't like doing that. 

Making a commitment I know will be a lot of work feels like, well, a lot of work.

So if I realize that a wall is just a staircase, it feels like all the routes through that staircase have switched from lies into promises I can keep.

I'd like to be able to think about this differently. I'd like to be able to imagine obstacles probabilistically, with a certain chance I'll be able to figure it out - and to automatically think of "think about how to get past this obstacle" as a step in the plan, instead of either making "impossible" plans or avoiding opportunities for growth altogether. I suppose the next step is to find out whether anyone else has had success making this change.

Have you?

Don't Worry, Be Canny


My girlfriend is [...] triggered [...] by many discussions of charity – whenever ze hears about it, ze starts worrying ze is a bad person for not donating more money to charity, has a mental breakdown, and usually ends up shaking and crying for a little while.

I just wrote a post on giving efficiently.

I just wrote another asking people to give to CFAR.

And I'm pretty sure I mentioned both to the person in question.


Of course I put a disclaimer up front about how I'm not talking about how much to give, just how to use your existing charity budget better. But of course that doesn't matter unless it actually worked - which it likely didn't.

Of course I would have acted differently if I'd had more information up front - but I don't get extra points for ignorance; the expected consequence is just as bad.

I'm going to try and write an antidote to the INFINITE GUILT that can feel like the natural response to Peter Singer style arguments. It probably won't work, but I doubt it will hurt. (If it does, let me know. If there's bad news, I want to hear it!)


You Don't Have To Be a Good Person To Be a Good Person

What are you optimizing for, anyway, being a good person or helping people?

If you care about helping people, then you should think of yourself as a manager, with a team of one. You can't fire this person, or replace them, or transfer them to another department. All you can do is try to motivate them as best you can.

Are you going to try to work this person into the ground, use up 100% of their capacity every day, helping others? No! The mission of the firm is "helping people," but that's not necessarily your employee's personal motivation. If they burn out and lose motivation, you can't replace them - you have to build them back up again. Instead, you should try really, really hard to keep this person happy. This person, of course, being you.

If telling them they should try harder gets them motivated, then fine, do that. But if it doesn't - if it makes them curl up into a ball and be sad instead, then try something else. Ask them if they need to give up on some of the work. Ask them if there's anything they need that they aren't getting. Because if your one employee at the firm of You isn't happy to be there, you'd better figure out how to make that happen. That's your number one job as manager - because without you, you don't have anyone.

That doesn't make the firm any less committed to helping people. As your own manager, you are doing your best to make sure helping-people activities happen, as much and as effectively as possible. But that means treating yourself like a human being, with basic decency and respect for your own needs.


Alright, suppose you do care about "being good." Maybe you believe in virtue ethics or deontology or have some other values where you have an idea of what a good person is, independent of maximizing an utilitarian consequence.

The same result follows. You should take whatever action maximizes your "goodness," but again, you don't have perfect control over yourself. You're a manager with one permanent employee. There's no point in asking more than they can do, unless they like that (some people say they do) - look for the things that actually do motivate them, and make sure their needs get met. That's the only way to keep them motivated to work towards being a "good person" in the long term; all the burnout considerations still apply.


What Do You Mean By "You"?

There's not really just one you. You have lots of parts! The part that wants to help people is probably distinct from the part that wants to feel like a good person, which is in turn distinct from the part that has needs like physical well-being. You all have to come to some sort of negotiated agreement if you want to actually get anything done.

In my own life, it was a major breakthrough, for example, to realize that my desire to steer the world toward a better state - my desire to purchase "altruons" with actions or dollars - is distinct from my desire to feel good about getting things done and be validated for doing good work that makes a clear difference. Once I realized these were two very different desires, I could at least try to give each part some of what it wanted.

Pretending your political opponents don't exist is not a viable strategy in multiple-person politics. It's no better in single-person politics. You have three options:

1) Crush the opposition.

If exercising is a strong net positive for you, but part of you is whining "I'm tired, I don't wanna," you can just overpower it with willpower.

In politics, there are all sorts of fringe groups that pretty much get totally ignored. For example, legalization of cocaine doesn't seem to have gone anywhere in the US, even though I'm sure there are a few people who feel very, very strongly about it. No concessions whatsoever seem to have been made.

The advantages of this strategy are that you get what you think what you want, without giving up anything in exchange, and get practice using your willpower (which may get stronger with use).

The disadvantages are that you can't do it without a majority, that some parts of you don't get their needs met, and that if you're tired or distracted the government may be overturned by the part of yourself that has been disenfranchised.

2) Engage in "log-rolling."

Sometimes the part of you that's resisting may want something that's easy to give it. For example, I just finished the first draft of a short story. Prior to that I hadn't finished a work of fiction in at least ten years. I'd started plenty, of course, so clearly there was some internal resistance.

My strategy this time was to get used to writing anything at all, regularly, and "finishing" (i.e. giving up and publishing) things, whether I think they're good or not. Get used to writing at all, and worry about getting good once I've installed the habit of writing.

But I stalled out anyway when writing fiction. Eventually, instead of just fighting myself with willpower when I noticed that I was stalling, I engaged myself in dialogue:

"Why don't you want to keep writing?"

"I can't think of what to write next."

"You literally can't think of what to write? Or you don't like your ideas?"

"I don't like the ideas."

"Why not?"

"Because I think they're bad. I'm trying to write something good, like you asked, but all I have is bad ideas."

"Darn it, self, I didn't ask you to write something good. I asked you to write something at all. Go ahead and write the bad version. We'll worry about writing something good later."

"Oh, is that all you wanted? That's easy!"

And I happily went back to work and kept writing.

Sometimes the best you can do is give everyone just part of what they want, though. There are people who believe that the rich US should give much of its excess wealth to poor people. If you believe this, what's a better strategy? Start a magazine called "America Is Bad And It Should Feel Bad", or try to expand our guest-worker visa program? One, and only one, of these will increase the wealth of poor foreigners at all.

The advantage of this approach is that is probably maximizes your short-term happiness, more of your needs get met, and it saves willpower for things where this approach is not viable.

3) Lose.

If you can't crush the opposition, and you can't trade with them, then you lose. If you're losing, and you have spent five minutes thinking about it and can't think of either a viable way to win or an idea-generating method you expect to work, then give up. Stop expending willpower on it, accept the bad consequence, and get on with your life.

I'm a bad person? Okay, I'm a bad person, I'd still like to help people, though. What's for lunch?

The Bottom Line

KIRK: I wish I were on a long sea voyage somewhere. Not too much deck tennis, no frantic dancing, and no responsibility. Why me? I look around that Bridge, and I see the men waiting for me to make the next move. And Bones, what if I'm wrong?
MCCOY: Captain, I
KIRK: No, I don't really expect an answer.
MCCOY: But I've got one. Something I seldom say to a customer, Jim. In this galaxy, there's a mathematical probability of three million Earth-type planets. And in all of the universe, three million million galaxies like this. And in all of that, and perhaps more, only one of each of us. Don't destroy the one named Kirk.

Pay Today or Pay More Tomorrow

I am 27 years old. I recently bought a life insurance policy with a face value of $100,000. This policy will last my whole life - in other words, no matter when I die, the payout happens. It cost me roughly $10,000 in today's money. If this is surprising to you, or you think the insurance company got a bad deal, then read this.

Everyone makes choices about whether they'd rather have something now, or something else later. Almost no one understands the economic concepts that describes these tradeoffs. they're called "present value" and "discount rate."

I will start by describing some simple examples that use these concepts, without using the jargon. Then I will explain what these all have in common. I'm not going to explain how to use these in real-life situations, but if you're interested, please let me know in the comments and I'll write a follow-up post.

Return on Investment

I'll start with a simplified example, with made-up numbers. Abby has a bank account with a bunch of money in it earning 2% guaranteed interest per year. She also owns a bond that would pay out $1,000 if she cashes it out now, or $1,030 if she cashes it out in a year. Should she cash it out now, or a year later?

Let's say that in any case she wouldn't use the money until a year from now. Then if she cashes out the bond now, she can immediately deposit the money, and in a year, she'll have $1,020. But that's less than the $1,030 she'd get if she held onto the bond for a year.

On the other hand, suppose she wants to use the money right now. Then if she cashes out the bond now, she has an immediate $1,000 to spend. On the other hand, let's say she holds onto the bond, and withdraws $1,000 from her bank account. Then in a year, she has $1,020 less in her account than she would have, but an extra $1,030 from the bond, putting her $10 ahead of the first strategy. So in this case too she should hold onto the bond for another year.

It should be easy to see that if the bond only returned $1,010 in a year, Abby comes out ahead by cashing out now, again regardless of whether she wants to use the money now or later. Because the bond gives her a lower return on investment (1%) than her savings account does (2%).

Then suppose the bond pays out $1,030 in a year, but her bank account offers 4% interest this year. Then Abby also comes out ahead by cashing out now, because the bond's return (3%) is less than the interest she gets on her bank account.

Cost of Funds

Brian doesn't have any savings - he a student. But he has a good credit rating and is able to borrow at 5% interest per year, and is allowed to pay off his loans at any time.

He is deciding whether to rent a textbook for $100, or buy it for $150 and sell it back used to his school's bookstore in a year for $55.

If Brian rents his textbook, then after a year, he will owe $105, including interest, and have no textbook. On the other hand, if he buys his textbook, then after a year, he will owe $157.50. He can then sell his textbook back to the bookstore for $55, use that to pay down his debt, and owe only $102.50. So buying the textbook is a better deal.

Suppose instead Brian can only borrow at 10% interest. Then if Brian rents his textbook, after a year, he will owe $110. On the other hand, if he buys his textbook, then after a year, he will owe $165-$55=$110. So he should be indifferent between the two alternatives.

If Brian has to pay 15% interest, then if he rents his textbook, after a year he owes $115, but if he buys, then after a year he owes $125, so he comes out ahead by renting.

On the other hand, suppose at the 5% rate of interest, Brian can only collect $50 for his textbook after a year. Then instead of owing $102.50 at the end of a year, he'd owe $107.50, more than the $105 he'd owe if he rented, so in that case renting again becomes more advantageous.

Present Value

In each of the above examples, a future amount of money was related to a present amount of money, by either how much money you'd have if you used the current money in the best way available (either investing or paying off debt), or how much money you would have to have now, to produce the future money. The first is called the "future value" of money, and the second is called the "present value" of money.

When Abby is choosing between $1,000 now and $1,030 in a year, the "future value" of $1,000 is how much money she'd have at the end of a year if she put the money in her bank account yielding 2%. To get this, you multiply by (100%+2%=1.00+0.02=1.02): $1,000 * 1.02 = $1,020. This is less than the one-year future value of $1,030 in a year, which is of course $1,030.

The "present value" of the year-later $1,030 is the amount Abby would need today to produce that amount in a year. To calculate the value a year in the past, you simply do the opposite of what you did when calculating the value a year in the future: you simply divide by (100%+2%=102%=1.02), to get $1,030/1.02=$1009.80, more than the present value of $1,000 today (which is of course $1,000).

Another way to show this is algebraically:

Now let's look at the first example involving Brian. Brian is comparing making a single payment today, with making a payment today plus receiving a payment in a year.

Since Brian has to pay 5% interest on money he borrows, the future value of the textbook rental expense is how much Brian will owe in a year if he borrows the money, or $100*1.05=$105. The future value of the purchase price of the textbook is $150*1.05=$157.50, and the future value of the $55 Brian will receive for his textbook in a year is just $55. So the net future value of Brian's textbook expenses if he buys is $157.50-$55.00=$102.50, less than the $105 future value of the rental fee.

The present value of the renting option, $100 today, is of course $100. The present value of the textbook's price today is also the same as the price, $150. The present value of getting $55 in a year is the amount of debt he'd have to pay off now, to owe $55 less in a year: $55/1.05=$52.38. So the present value of the cost of buying and selling back later is $150-$52.38=$97.62, less than the $100 textbook rental fee. So the buying option costs less, in present value terms, as well.

The key here is that by converting each value, whether positive or negative, into the equivalent value for a single time period - whether the present or the future - we end up with numbers that can be directly added and subtracted to find out which amount is higher on net.

Discount Rate

You may have noticed that in Abby's case we were using the rate at which she could expect return on her savings to equate future and present amounts, but in Brian's case we looked at the interest rate he'd have to pay to borrow money. These might seem like quite different things, but in finance, there's little difference between spending saved money and borrowing money; in both cases money in the future is worth more than money in the present, and we assume a fixed conversion factor. Instead of calling it a cost of borrowing sometimes and an expected return on investment at other times, economics abstracts this into the more general term "discount rate", which is basically the extra share you can demand if you get your money in a year instead of today, or the share of your money you should expect to give up if you get your money today instead of a year from now.

This is related to the economic concept of "opportunity cost," which I will cover in a future post.

I will also cover how to deal with a series of future payments in a future post - and in the process show you that if you believe in discount rates, the future isn't as big a deal as it seems.

Which means, of course, that this is the first post in a series.