The Tipping Point

Richard Chappell offers this solution to the "causal impotence" problem (see also Alastair Norcross here):
A common justification for buying meat is that one's individual consumer choices won't make any difference: the supermarket buys steaks by the crate, and so isn't sensitive to such tiny changes in demand. It'd take (say) a hundred boycotters to make a difference. But there's a subtle fallacy here. It might typically take 100 boycotters to ensure that one less crate of 100 steaks is bought. But one of those hundred individual choices must have made the difference between the store choosing to buy X crates or X-1. We just don't know which one -- where the tipping point lies -- whether we just need to decrease demand by 1 more steak, or 36, or 99, before the store will respond. So, in the absence of any further information, any individual consumer should see their personal steak boycott as having a 1/100 chance of reducing the store's purchasing by 100 steaks. (And so on up the supply chain.) That's an expected impact of (ta-da) one steak. The "chunkiness" of the market's sensitivity thus makes no difference. Your lessened chance of making an individual impact is exactly counterbalanced by the higher steaks payoff if you happen to succeed in influencing an entire 'chunk' of demand.

The point generalizes to many other 'chunky' impacts, e.g. life-saving charities, or situations where each of many individuals has an equal chance of making the decisive difference for all of them. For a slightly different case, Derek Parfit made a similar argument in defense of voting: even if your individual vote only has a 1 in a million chance of making the difference between electing Inferior and Superior, it's worth it if the election of Superior would raise average welfare by more than what it cost you to vote. (The structure of this situation is different from the sort of consumer 'chunking' discussed previously, but hopefully the similarity I'm highlighting is clear enough.)

P.S. Technically, the consumer impacts aren't quite so straightforward as all this. For example, reducing demand might lower prices, causing some others on the margin to buy slightly more meat than they otherwise would have. But this presumably won't completely counteract the good done by one's own abstinence -- so we're not in "moral dupe" territory yet. Anyway, my point here is just that chunking doesn't undermine the expected efficacy of our individual decisions. Other things might, but evaluating other objections is a job for another day.
I hope nobody can find an objection because I make much the same argument in my book.


Alex Chernavsky said...

Philosophy professor Keith Burgess-Jackson puts it a different way:


I’ve always thought of morality in terms of personal integrity—of having high standards and striving mightily to live up to them. Morality, in this view, is more a matter of what one rules out as unthinkable than of what one decides or does. Do I want to participate in an institution that uses animals as resources—that confines them, deprives them of social lives, frustrates their urges, alters their diets and bodies, and eventually kills them in the prime of their lives? It’s a matter of not getting one’s hands dirty, of not collaborating with evil. Perhaps other people can do these things, I say, but I can’t. I want no part of such a cruel institution. There will be no blood on my hands. [...] Your actions reflect your moral values and what sort of person you are. Stand up for something. Say “These things go on, but they do not go on through me!” You’ll feel good about yourself; I guarantee it.


(I should point out that I don't agree with everything Burgess-Jackson writes, but I like this quote.)

Jean Kazez said...

I would very much like to think that I am contributing to saving chickens when I don't eat chicken, but if I couldn't convince myself of that, there is also KB-J's type of reason for not eating chicken, which is compelling as well. (FYI--he and I were graduate students together at Arizona. His blog is very useful.)

Tom said...

I've never understood this argument--and I mean that only sort of in the "actually, I think I do understand it and I see that it is a bad argument" sense of "never understood." I've argued with Alastair about it and he's stuck to his guns and he's smarter than I am--so that makes me think there is something I'm still missing. Let's see what you think.

It seems to me that, in your store/steak example, I should think that there a 1/100 chance that my not buying the steak will result in the store's reducing its order of steaks by 100 only if I know that somebody's not buying steak will result in that. That is, I need to know not only how many boycotters it will take to effect change in steaks bought by the store but also that fewer steaks *will be* bought.

The case seems to me analogous to this: Suppose 100 coins are distributed evenly among 100 people who are told that exactly one coin is made of pure gold--and that's all they are told. Then each has a 1/100 chance of having the gold coin. But if they are told instead that one of the coins *might be* gold, then they don't know if they have 1/100 chance of having a gold coin or not. In fact, no one knows if there is any chance that the coin he or she holds is gold. It depends on what the chances are that one of the coins in the first place.

It seems to me that argument about steaks/boycotting is more like the second gold coin case than the first. In fact, I think it's probably worse than the second case. Because, at least where I live, I have no good reason to think that my buying less meat today will contribute to the store's buying less meat in bulk tomorrow--since they'll only do that if (say) 99 others don't buy meat on or around the day I boycott it. And I have no good reason to think there are 99 others planning to boycott. In fact, I think I have pretty good reason to think that there *won't* be 99 others who boycott. So I should judge the odds of my boycotting effecting change to be really, really low--way, WAY lower than 1/100.

Caveat: I don't mean to say that there is no good reason for me to boycott buying steak at the grocery store--I think there is (e.g., other things being equal, we shouldn't take part in immoral institutions). I just, um, don't understand this particular argument.

Jean Kazez said...

I think Alastair is responding to an argument that says it's impossible for one person's vegetarian choice to save any animals because of the way the giant meat market is insensitive to small fluctuations in demand.

His argument is that possibly, right now, if I don't buy a chicken then I have a 1 in 10,000 chance of saving 10,000 chickens. I can't know if that's true because I don't know how many other chicken-decliners there are. I also can't know if I'm the lucky person who lowers demand to "the tipping point." So there's a lot that I can't know. Nevertheless, I shouldn't get really depressed and think it's impossible for me to have an impact. It's possible!

Your point seems to bear on the difficulty of knowing what the odds are. Doesn't it? Am I reading you right? But he's not saying we can know the odds. The bare possibility of being effective is his whole point (I gather).

Tom said...


Yeah, my point does concern the difficulty of knowing the odds. But you quote Chappell as saying:

"It might typically take 100 boycotters to ensure that one less crate of 100 steaks is bought. But one of those hundred individual choices must have made the difference between the store choosing to buy X crates or X-1. We just don't know which one -- where the tipping point lies -- whether we just need to decrease demand by 1 more steak, or 36, or 99, before the store will respond. So, in the absence of any further information, any individual consumer should see their personal steak boycott as having a 1/100 chance of reducing the store's purchasing by 100 steaks."

I'd say that in the absence of further information you have no idea at all what the odds are that your boycott will result in the store cutting its steak buy by 100.

I take it that it is always epistemically possible that there will be a sudden, wholly unexpected uptick in vegetarianism in my neighborhood over the course of the next couple of days, but that isn't sufficient to rationally motivate action since it is also epistemically possible that, somehow, my personal boycott will set off some weird chain of events that will lead the store to order an extra 100 steaks.

I still think I must be missing something...

Jean Kazez said...

Alright, Richard has made the odds seem knowable. Alastair openly admits he has no idea what the odds really are, though he says vegetarianism is on the rise. Being very clear-eyed about this, we do have to admit that chicken-eating is also on the rise. Also, it might not exactly be a possibility of lowering the number killed, but of preventing a sharper increase. The main thing is--vegetarians don't have to resign themselves to definite causal impotence. It's at least possible they're having a good impact despite the huge meat market. You say it's also possible they're having a negative impact, but isn't that a much more remote possibility?

Richard Y Chappell said...

Tom - let me illustrate the core idea with an oversimplified toy example. Suppose a store orders as many steaks for next month as were sold last month, rounded up to the nearest hundred. (This last element is the 'chunky' aspect of the situation.) Now suppose that last month I intentionally bought one less steak than usual. This made a difference (worth 100 steaks) if and only if the number actually sold that month is a multiple of a hundred. There's a 1/100 chance of this.

Maybe you're thinking that the market is insensitive in other respects besides mere 'chunkiness'. I only mean to be addressing objections based on this particular feature.

Jean Kazez said...

Nice way to put it, Richard.

I think Alastair is also just trying to explain how one individual, making one purchase, can possibly make any difference GIVEN that the meat market doesn't respond directly to individual purchases. Chunkiness--that's it!

s. wallerstein said...

Strange to say, I agree with the quote that Alex sends. Thank you.
I don't think that one is ever a "moral dupe" if one does the right thing.

Unknown said...

I think what Tom is getting at is the idea that there is a critical mass required for market influence.

Lets take Richard's example, and assume that steaks are ordered in lots of 100. In a city where there are a large number of vegetarians who will choose not to buy steak there is a 1/100 chance of making a 100-steak difference to supermarket purchasing.

In that setting there is no need to know or to calculate the odds to know that in terms of expected value it is worth refraining from purchasing a steak.

But if our purchaser is the sole vegetarian in a community of meat eaters the argument potentially loses its force. There is a very low chance of there being enough non-steak-purchasing to reach the threshold. It doesn't help that there might be more than 100 vegetarians spread throughout other communities. They need to reach the chunk threshold in this community.
Nor does it matter that the lonely vegetarian fails to purchase steaks on 100 consecutive occasions during his weekly shop - as long as the purchasing order has a short feedback cycle.

However, there is still a way of rescuing the purchasing argument for the lonely vegetarian. While others in town do not alter their steak purchases to avoid animal suffering - they do for other reasons. They buy more when they are entertaining, less when the bank account is low, or they are on a diet, more people may move into/out of town, buy from a different store. The reason that the supermarket has its 100steak feedback cycle is because orders can vary over time. So then it doesn't matter that there is a very low chance of there being 100 vegetarians this week visiting the supermarket. There is a small chance (1/100) that the steak purchases this week will be close to the magic threshold and that the vegetarian's non-purchase will make the difference.

This is the difference between being a vegetarian shopper and being a voter for the Monster Raving Looney Party. While there is no chance that 50% of the population will also vote for your favourite extreme minor party, there is a significant chance that the influence of other purchases (by non-vegetarians) will make your shop count.

Alex Chernavsky said...

I wanted to clarify something. I agree with the sentiments expressed in Burgess-Jackson's quote, but my primary reason for being vegan is to help facilitate, even if in some small way, the eventual end of animal exploitation. I don't think the two reasons are mutually exclusive. And the KBJ quote is good for answering people who believe that their actions won't make any difference one way or the other.

Faust said...

Reminds me of the arguments people present when they don't want to vote.

s. wallerstein said...

At the risk of agreeing with you again, Alex, there is another reason for doing the right thing in spite of the odds: the power of the right example. Sometimes people see you doing the right thing and are convinced to follow your example; sometimes, not. Any case, someone always has to take the first step.

Jean Kazez said...

Dom, That's an extremely useful point you make. It really seems to rescue the possibility of causal efficacy from the worry about how many vegetarians there are. That's a very natural worry, so it's great to have a new way to think about it.

Anonymous said...

@Tom: the actual probability doesn't matter. As we say in science: the factor will "cancel out".

So if you they buy in lots of X, then you have a probability of 1/X of stopping them to by X, so your actual contribution is "worth" X * 1/X = 1.

you see that the actual value of X doesn't matter.

The equivalent for your coins example would be: you distribute 100 coins, each worth $1. Whoever gets the only coin with the special sign on the back will win all the other coins.

How much would you be willing to pay to participate in this game? you have a 1/100 probability of gaining $100, so the "just" price to participate should be $1, exactly the value of the coin. Repeat the experiment with 1000 coins, and the result will not change.


Tom said...

Gio: I can certainly see that, in your coin example, the number of coins doesn't matter and so the odds of my winning are irrelevant. As long as the payout increase is proportionate to the increase in the number of coins, the "value" of my participation remains the same.

Again, it might be that I'm remarkably dense on this point, but I don't see how this shows my objection to the original argument is wrong.

Consider this analogy:

Suppose Smith tells 100 of us that if and only if, simultaneously, we each put the whole of the sole of one of our feet on a relatively small tile, he will randomly select one of us for a prize of $100. The problem, we can plainly see, is that the tile is too small; it's just not possible to do as we are asked. The probability of success in performing the task is zero and so the probability that anyone will get $100 is zero.

Still, if 100 of us do as asked, someone would get $100. Now it seems to me in this case my "participation" has no value at all and the reason for this is that the probability of the desired outcome coming to pass is zero. Now if we make it not zero, but a suitably low number between 0 and 1, then if the value of my participation is anything like the expected utility of my participation, shouldn't we deem that value to be low too? Again, I might well be just showing my ignorance in these matters but I can't see how this isn't right.

So I don't see why the steak/store example is different in principle from the above tile example--except that it isn't impossible for my failing to buy meat to turn out to have consequences. But we just have no idea what the likelihood of that is (or so it seems to me), and so we aren't in a position to know the causal value my action will have (if any) even if we know that if 100 of us boycott steaks, the store will order 100 fewer.

Thanks for the discussion.

Jean Kazez said...

Tom, I think Dom (above 3:52) both appreciates and responds to your worry very well. Don't you think?

Tom said...

Sorry for the delay. Yeah, somehow I missed Dom's response until you pointed it out. And it does seem right.

Actually, I think things are even better than this chunkiness argument suggests. Why should we suppose that if we aren't the 100th boycotter then our actions are causally impotent? If thousands of us each put a single piece of straw on a camel's back until, eventually, the placement of a single straw causes the back to break, it is surely wrong to think that only the last straw was causally potent. That's just not the way causation works. The back was caused to break by the cumulative weight. So why shouldn't we say the same thing about the efficacy of the other 99 boycotters?

Again, maybe I'm missing something.


Unknown said...

Hi again Tom,

you might find this classic chapter by Derek Parfit on mistakes in moral mathematics interesting and helpful

Parfit describes different ways of thinking about collective and contributing actions, and the ways in which these theories go wrong.


Jean Kazez said...

I should probably read Parfit before saying this...

but if the 100th boycotter triggers a result, I wouldn't say the others are causally impotent. To be the 100th, there must have been an 85th and a 23rd, etc, etc. The 100th stands on the shoulders of the previous boycotters. So in fact the earlier boycotters are just as important as each piece of straw that broke the camel's back. I think!

Anonymous said...

@Tom: sorry for the delay. I'm not sure I really get your sole/tile example, but it seems to me that there is a little confusion about what "impossible" means, in the same sense that the concept "zero" (impossible = zero probability) is sometimes confusing in calculus (as is "zero times infinity" is sometimes zero, sometimes infinity, sometimes a fixed number, sometimes undeterminate)

I can easily imagine situations where our lonely vegetarian will really not impact the production of meat. To consider the basic case with round number: one town of 49 meat eaters, and 1 vegetarian. Each buy their food once a week. Meat eaters always buy one steak. Vegetarian always buy 1 portion of soy products. Store buys in lots of 100, and buys one every week. Meat cannot be kept in store for more than a week. So every week 51 steaks are thrown away. If the vegetarian also becomes a meat eater, the store will throw away 50 steaks per week.

So actual conditions do matter. We can also have a more realistic scenario where the store has a safety margin to avoid running out of meat, and even if managers think (from extrapolation of previous market demand and historical seasonal variations) that they will sell 100 steaks, the decide to order 120 (so a 20% safety margin). I think in many industries it is normal to have these extra capacities built into the systems (but I'm not an expert of supermarkets ...). In such a case we could assume a "bell shaped" normal (gaussian) distribution of demand around the average of 100, and so the probability of selling the 121st steak is a lot smaller than that of selling the 101st one.

I think in this non-linear scenario the "moral" impact of the vegetarian choice is a lot smaller than the "moral harm" involved in the production of one steak. But as in the "straw that breaks the camel back" responsibility has a lot to do with the knowledge about the effects (or the probability distribution of such effects).

If the camel back breaks at the 100th straw, and the person that put the first straw estimates that there is a one in a million probability that other 99 people will put straws on the poor camel, then (I think, and am I NOT an expert on this) I think he (the first man) is responsible for the millionth part of the harm caused to the animal.

Of course we shifted the problem up one level, and we should know see if his estimation was fair, if he didn't bother checking how many people wanted to put straws, and he was really negligent in his reasearch.

I will read Parfit one day ... it's been in my "TOREAD" list for a long time.