Life can be reduced to a number

I can never figure out whether you madmen who insist that things cannot be reduced to numbers are serious or not, so here you go. The short answer is that you can rank lives, thereby reducing them to ordinal numbers. The long answer is…

Imagine Alice, a girl just like you and me, being given the choice to live one of three different futures:

• a future in which she buys the winning lottery ticket
• a future in which she buys a losing lottery ticket
• a future in which she never participates in the lottery

Which should she choose?

Why, the one she thinks will lead to the best outcome, of course!

Obviously, which outcome is “best” depends on what she finds “good”. There are those who expect that winning the lottery will make them unhappy, and there are those for whom it seems to be the greatest good. This difference is not as irreconcilable as is commonly thought, but, in the interest of tackling controversial things one at a time, let’s assume that only Alice’s interests matter.

Alice just wants money. So she dislikes the future in which she buys a losing lottery ticket. She likes the future in which she never participates in the lottery, but not as much as she likes the future in which she buys the winning lottery ticket. For Alice, the options are ranked from worst to best like so:

1. the future in which she buys a losing lottery ticket
2. the future in which she never participates in the lottery
3. the future in which she buys the winning lottery ticket

Hold on… What is this that I see? Did your browser just assign numbers to these futures?

Indeed it did! How convenient! Now we can compare them by their numbers instead of by their wordy descriptions. Alice likes 3 better than 2, and 2 still better than 1. Each of these futures has effectively been reduced to a number. This shows that a future (which is not relevantly different from a life) can be reduced to a number.

Don’t roll your eyes and leave just yet. I will now address any objections I see myself and any objections which you bother to inform me of. If you feel your particular objection is not addressed, please post it in the comments. Feel free to start off your comment by saying this is “wrong on so many levels”; just be sure you point out at least one concrete problem.

There is more to life than money!

There is. This is just an example. In fact, it is an example in which it was assumed that only money matters.

But this kind of objection is valid. When you reduce things to numbers, you lose information. This is sort of the point. You need to make explicit what it is that you like, and base your reduction on that.

If Alice disliked the threat of being robbed, she would have to reduce differently. The future in which she wins the lottery might then no longer be the best option. She will have to trade off money and threat of robbery, and how she does this will depend on how important she finds both. (This importance can be reduced to a number.)

Actually, since a robbery would probably cost Alice money, this would already have to be taken into account in the original example in which she only cares about money. But that would be unnecessarily complicated for the purpose of the example.

There is more to life than good and bad!

Yes, there is. But if you want to measure how the goodnesses and badnesses of different options stack up to one another, then they are all you need to take into account. The reduction abstracts away the irrelevant stuff.

What if Alice’s conception of good and bad changes over time?

This is a solved problem of mathematics: you just integrate with respect to time.

What if two futures reduce to the same number?

Then they are equally desirable and therefore, just like the numbers, effectively equivalent.

As an example, Alice might have had a fourth option of a future in which she participates in multiple lotteries and breaks even in the end. If money is all she cares about, then this future and the one in which she does not participate at all are equally good.

Shouldn’t the future in which she loses money reduce to a negative number?

It doesn’t matter. Alice has to choose from the three options given. She can’t not choose.

In real life, you don’t always know all options beforehand, and you don’t want to have to do the ranking all over again when a new option reveals itself. You want to reduce each option to a useful number independent of what the other options are. Then when a new option becomes apparent, you can just reduce it to a number and compare that number to the numbers you already have.

These numbers aren’t useful beyond this pathetic example.

Correct. Most Alices care about much more than money alone, and most Alices don’t get to choose their futures. Additionally, most Alices’ desires change over time.

Let’s say you are shopping for a car. You want it to have a high mileage, low maintenance costs, and lots of cargo space. The first thing to realize is that these properties are already reductions to numbers.

Your mileage may vary, but the advertised mileage is still a fairly reliable indicator of how much the car will cost to drive. Advertised mileages may invariably be higher than actual mileages, but this does not matter much if all of the cars are off by roughly the same amount. (Although you should take this into account if you also have the option not to buy a car.)

The cargo space is reduced to a measure of volume. The space may not be one contiguous space as you’d like, but rather a bunch of inaccessible nooks and crannies that you’ll never be able to fit your drumkit into. A better number to go by might be a weighted sum of the volume and some measure of fragmentation.

The low maintenance cost is an expected cost. It is the sum, over everything that could go wrong, of the probability of this going wrong times the cost of this going wrong. Let’s say you’re looking at a particular car which you are planning to drive for the next five years. You are 90% certain that you will have to change the oil ten times, which will cost you $300 in total. You are 10% certain that the exhaust will fall out from under the car during this period, which your uncle will weld back together again for you for $50. You are 30% certain that that crack in the windshield will spread to the point where it needs replacing, which will cost you $500. If this were all that you expected to go wrong, the expected maintenance cost for the next five years would be 0.1*50 + 0.3*500 + 0.9*300 = $425.

You are not actually directly interested in these three properties. They are measured in different units and represent incompatible quantities. You are interested in what they are worth to you. Mileage may be worth 1 goodness unit per mile per gallon, whereas maintenance costs may score -2 goodness units per dollar per year. This is not always simply linear: an increase in cargo space may be worth less to you if you already have lots of cargo space.

Eventually, you will be able to sum the car’s worth on each of these properties, thus reducing it to a useful number.

That does not sound very practical.

You don’t have to be so precise and explicit about it. Your head already works roughly in this way, except that it is influenced by biases and irrelevancies (such as the color of the car). If you learn to correct for this, you will probably do better than you are doing now.

That said, being more explicit about what you are interested in can help prevent you from making bad decisions. If one of the cars you’re looking at reduces to a low score even though you really like the car, something is wrong. Whatever it is that makes you prefer the car, you apparently did not properly account for it. You need to examine what it is.

If it turns out that you find mileage more important than you thought, or that you also want power windows (the worst thing since sliced bread), go ahead and reevaluate the options.

If it turns out that you prefer the car because it smells better, you might want to disregard your gut feel and go with the cold, hard numbers instead. Baking an apple pie inside of a car is a well-known car salesman’s trick.

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