Average = Total/N

An argument against vegetarianism that I’ve encountered a few times is that any individual’s consumption decisions will have no effect on the actual production of meat, and so are ineffective. In particular, this argument was made recently at Bad Conscience.

This argument cannot be right.

We know that production decisions are based, ultimately, on sales and hence on demand. The proponents of this argument accept this, by granting that if everyone stopped eating meat, there would be no meat production (or barely any).

How sensitive are production decisions to demand? Either they are precisely sensitive – they can pick up the signal from each individual purchase and respond to it – or they are crudely sensitive – they use approximate, gross, indicators, perhaps involving hundreds of individual purchases as a single data-point.

If the former, then each vegetarian is directly responsible for preventing the manufacture and destruction of all the animals they would otherwise eat in their life – which is a large number.

The anti-vegetarian argument focuses on saying that this is not the case – markets are not this precisely sensitive, and if (as is implied) vegetarians think they are, then vegetarians are idiots.

But even if markets aren’t precisely sensitive, they must have some sensitivity – crude, rough, sensitivity. But the sensitivity still governs the same effects – does meat get produced, and if so how much. This means the same total effect is divided up among the consumers, just divided more roughly and unevenly.

This means that some purchases will have no effect – but only because other purchases have more effect, disproportionate effect. And since we can’t tell which our purchases will be, each one still on average has their proportionate effect of preventing a large number of individuals killings.


This is just maths. Let me do some tables.

Suppose there are 10 people, who each year eat a total of 100 ducks. The ducks are killed only to feed these people. 0 duck-eaters: 0 ducks killed. 10 duck-eaters: 100 duck killed. This is (analogous to) what everybody accepts – the two extreme points. The incomplete table looks like this →:

In a sensitive system, each individual could reduce the number of killings by 10. There would be this table ←:

Now suppose – as the anti-vegetarian argument asserts – that this isn’t the case. In fact, when the first of these ten people go vegetarian, it makes no difference to how many ducks are killed. Suppose the same holds for the second and third people as well. This gives our incomplete third table↓:

See how you still have the gap between 0 ducks killed and 100 ducks killed? That change has to occur at some point, wherever the change comes. For instance, the table might look like this ←:

Here, vegetarians 1-3 make no difference, as do the 5th, 7th, and 9th. But the 4th vegetarian saves 40 lives, and the 6th, 8th, and 10th save 20 each. So most vegetarians have no effect – but the average effect is the mean of 40, 20, 20 20, 0, 0, 0, 0, 0, and 0. Which =10. That is, the vegetarians have exactly the same average effect as in the sensitive system.

At risk of belabouring the point, suppose a different, very ‘rough’ system, with systematic irrationalities, as here →:

Here, two vegetarians have no effect at all, and three (the 3rd, 5th, ad 7th) actually increase the number of ducks killed. But what’s the average number of ducks saved per vegetarian?

Mean of 0, 0, -10, 29, -19, 50, -12, 42, 13, 7 = 10!

Noticing a pattern? It’s always 10! That’s because if everyone being vegetarian eliminates all meat production, which everyone in this dispute accepts, then the average effect of being vegetarian must always be the total meat production divided by the number of people who need to go veggie (in this example, 100/10).

Now, sometimes we shouldn’t act based on averages. For instance, if the 7th person in the last system knows how the system works, and knows that the last two people are definitely not going to become vegetarian, then they shouldn’t go vegetarian because they know they’ll cause an increase in killings (by whatever mechanism).

But that’s because they know the details of where they are in the system. Typically, consumers don’t. This is analogous to voting: my one vote could have no effect, or it might be a crucial decider that has a disproportionate effect, and I can’t know in advance. In this situation, I have to act based on what the average expected result is.

Of course, it might be that the people who use this argument against vegetarianism know where the critical points come. But that implies they know when, where, and how to have maximum, exaggerated effect on meat-production. They should tell us.

One last time: if N people doing x would produce total result R, the average effect of doing x is R/N. For vegetarianism, that means a dozen or more killings prevented per year.

The maths is simple: reality is complex, but when we can’t trace out the complexities we must act on whatever simple maths is available.

I’m aware that I’m starting to sound like Paul in his post: my argument is just so obvious, so evidently true, that I can’t understand how anybody could fail to accept it. Just as he feels about his opposite argument. One of us is wrong, despite our shared confidence. All I can say to this is that the one who’s right is probably me, because I’ve got tables.

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6 Responses to Average = Total/N

  1. Paul Sagar says:

    Luke, I’m afraid I can’t take your argument as being much more than sophistry. Are you being serious?

    “The maths is simple: reality is complex, but when we can’t trace out the complexities we must act on whatever simple maths is available.”

    Well actually the simple maths says: whatever the average number is, it’s a brute fact that *just my* consumer choice will not change it one way or the other. That’s the nasty nature of the Sorites situation we find ourselves in. Saying “but won’t somebody think of the averages!” doesn’t change anything.

    But notice also how you cheat: you fall back on saying that we *don’t know* what our individual impact will be – before picking an unfortunate analogy with voting. Because actually we *do know* (as with mass-democratic voting in eg a safe seat, which is the relevant analogy here) that our individual impact will be…nil. Pulling out simplified averages from a simplified table about ducks changes nothing.

    You can be vegetarian.m and that’s fine…but it’s an integrity issue about you, not the fate of any animals *you* save.

    • lukeroelofs says:

      “it’s a brute fact that *just my* consumer choice will not change it one way or the other”
      This is not true.

      “Because actually we *do know* (as with mass-democratic voting in eg a safe seat, which is the relevant analogy here) that our individual impact will be…nil.”
      This is also not true.

      To be a safe seat means to be a seat where it is known in advance that one candidate will get a large number of votes, each vote being cast by an individual, hence some individual votes have an impact. Each voter is an individual and no votes come from anything which is not an individual.

      “That’s the nasty nature of the Sorites situation we find ourselves in.”
      You know that the point of a Sorites paradox is that there *is* a change? And how the claim that there is a change, and yet no individual step makes *any* difference…that leads to a paradox? Because it can’t actually be true?

  2. Nakul says:

    Paul’s comments have gotten too long so I’ll post here instead. I’m atrociously bad at reasoning of this particular sort; hence my incompetence at microeconomics. But Paul, I take all your other points about integrity playing a big role in these arguments. But when you say, ‘any individual considering going vegetarian must face the truth that the vast majority of others won’t follow suit’, I’d propose a little qualification. Because the ‘vast majority’ don’t _need_ to follow suit to make a moral difference, do they? Just enough to get us pull us out of the Sorites bog. I’m not the best vegetarian myself, but I haven’t abandoned the aspiration. So how about these alternative arguments about individual moral motivation? They’re meant to be jointly reinforcing and motivating, but not necessarily compatible with each other.

    Crude argument:
    P1. Me giving up meat is a necessary (but not sufficient) condition for any animals to be saved.
    P2. The strains of giving up meat are not of comparable moral importance compared to that of the (infinitesimally small) contribution of doing so, modulo non-moral personal prerogatives.
    P3. I should do what contributes (in whatever small way) to animals being saved as long as nothing of comparable moral importance is compromised by my doing so. (NB: ‘moral importance can be glossed in a consequentialist sense, but not necessarily. See below)
    C. I should give up meat (or reduce my consumption thereof, modulo above).

    Some supplementary arguments:
    (1) In giving up meat, I make it easier for others with similar inclinations to do so. (Cf. Jerry Cohen on egalitarian ethoi)
    (2) In giving up meat, I express a moral disapprobation for the meat industry and a certain paradigm of treating animals; not to express such disapprobation would be incompatible with my deepest sentiments/attitudes about the moral worth of animals.
    (3) In giving up meat, I form a disposition that, *over the course of a lifetime rather than in any one instance*, has significant moral consequences. E.g. saving individual animals, providing the tipping point for close friends and family, forming the casting vote when making a catering decision for hundreds of people. These considerations weigh more heavily on you the more famous you are.
    (4) Unless you’re a Kantian who believes respect is only owed to rational beings, there might be argument against the eating of meat based on respect owed to the bodies of sentient beings. I have a friend who is a vegetarian on these grounds alone. I’m not sure what I think of these argument myself, but it gets us away from facts about meat production: something counts morally against *eating* meat, whatever be the rights and wrongs of the meat industry.

    • X says:

      I’m vegan primarily for your fourth supplementary reason. I see using the bodies of animals killed for human pleasure as food, clothing, etc. as itself exploitative and lacking in respect for animals, whether or not it’s effective as a boycott.

      It seems to me that the facts of meat production (and dairy production, which might well involve more suffering than meat) are added ethical factors. I’d oppose raising animals to exploit and kill them even in the most fluffy family farm scenario you can think of, but if the animals are suffering in the worst of industrialized factory farms, then that cruelty is another consideration that makes it ethically wrong.

  3. Salient says:

    This calculation does not take into account waste.

    If I stop eating meat, the effect of this consumption change is within margin of error in change in waste, so it will not be noticed by the market.

    • lukeroelofs says:

      I don’t see how that affects my argument. How many people would have to stop for the change to be ‘noticed’? 10? 50? Then logically some result must follow upon one or more of those people’s action (given some arbitrarily specified order in which they do it). You don’t get a positive change from adding up lots of zeroes, that being the point of the sorites paradox.

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