First published 25 August 2017. Last updated 11 June 2018.
This post is part of the “I Used to Believe” series, introduced here.
Contents
My History With the Topic
I can’t recall ever being against vegetarianism. For that matter, I can’t recall thinking about vegetarianism at all until around age 13.
I had a close vegetarian friend in high school, and I remember talking to him about it. I would say things like, “I respect that. I think it’s morally right. But it would be hard for me to do it at home, because I don’t think my parents would support it. Maybe someday.” I hadn’t developed an explicit ethical framework by that time, so my ideas about the moral rightness of vegetarianism were by no means well thought-out. But it seemed like common sense to me that the animals we ate were not less deserving of consideration than the ones we kept as pets, and all the arguments I’d heard in favor of meat eating sounded obviously wrong.
I ended up going vegetarian for a month in high school after eating too much cheap Korean barbecue one night. I did it with a friend who’d also been at the dinner, and it definitely had the character of “let’s see if we can do it for a month.” I don’t remember if I ever expected or wanted it to last long. And it didn’t, because I pretty much ate quesadillas and PB&J all month.
In college, after studying philosophy a little and clarifying my ethical foundations a bit, I got more interested in the problem of factory farming, and just how severe the situation was. But any time someone asked me, “If it’s so evil, then why aren’t you vegetarian?” I oh-so-cleverly explained that individual vegetarians don’t make much of a difference, because the supply chain for meat is made up of large bulk purchases. “If the grocery is buying packs of chicken by the hundreds, clearly they won’t order a hundred fewer on my account!” So the argument went.
I ended up going vegetarian in college anyway, shortly after my roommate did. He also believed it didn’t have much direct impact, and cites signaling value as motivating the change. I valued signaling too, but also still had some sense of “let’s see if I can do it,” and increasingly had a sense of just wanting to be on the right side of history, or to not be a hypocrite, even if it didn’t have real direct impact. So for the first couple months of my vegetarianism, I continued to think that I was making a near-negligible direct impact, but I wanted to put my money where my mouth was anyway.
I did some light Googling on several occasions to see if any work had been done on exactly how little impact individual vegetarians make, depending on which kinds of supply chains they participate in and so forth. I found nothing interesting in the first couple months. My roommate and I talked about how fun it might be to publish some primary research on the topic. The headline “Two vegetarian Harvard undergrads prove vegetarianism doesn’t matter” would surely get some attention!
Finally, a lucky combination of Google search terms turned up Brian Tomasik’s article on the topic. He made exactly the argument I needed to hear: “it is true that any given individual is unlikely to make a difference through meat-consumption choices, but there’s a small chance that he makes a huge difference, and the expected value works out such that avoiding eating one chicken or fish roughly translates to one less chicken or fish raised and killed.” My first reaction, having never heard of Brian before, was something like, “This is too good to be true, right? There must be some lurking mistake.” But of course, there isn’t one. I had just been flat wrong for a long time.
Analysis
This is a frustrating case. Frustrating because I never figured it out myself, and frustrating because it took me so long to find the answer even when actively searching for it. I could have very easily gone years without hearing anyone make Brian’s expected value argument, perhaps falling out of vegetarianism in the meantime because I persisted in thinking it didn’t matter much.
I think part of the problem was that there are relatively few people who have a combination of traits which leads them to ask or answer this particular question. Most vegetarians are “right for the wrong reasons” in some sense: they believe individual vegetarianism matters, but they do so on an intuitive, common-sense level. They’ve never thought about bulk purchases, they’ve never heard the expected value argument, etc. Most omnivores, on the other hand, are “wrong for the wrong reasons”: they reject vegetarianism because they’re confused about basic ethics, or they’re speciesists, or they’re lazy, or whatever. We’re left with a relatively small group of people like me, who needed to hear the expected value argument, and another relatively small group of people like Brian, who were prepared to make it.
I’ll try to make clearer here why I was insensitive to all the arguments I heard before Brian’s. Basically, in other domains, statements like “one person can’t do much, but together we can do great things” are actually dodgy. At best, they’re imprecise, and at worst, they rely on hidden unjustifiable assumptions. As a result, I was disinclined to take them seriously in general.
Take, for example, the case of voting for president. People who express skepticism about the value of a single vote often hear “what if everyone thought that way?” or “your vote may be small, but they add up” or “every vote counts”. These are bad arguments. “What if everyone thought that way” invokes a useless assumption, because there’s obviously no causal link between your thinking that way and everyone else thinking that way. (A much weaker version of this argument can be salvaged: if you talk a lot about the worthlessness of voting, then you may actually cause others not to vote, which is bad. But this argument doesn’t apply to just abstaining from voting yourself, as long as you keep quiet about it.) The other two responses are just obfuscation. Of course they add up and they all count – that doesn’t change the fact that your individual vote, which is the only one you can directly influence, is actually small. (See the appendix for more on voting.)
So what distinguishes these bad arguments about voting from the good argument about vegetarianism? It’s hard to tell without invoking the actual math. The value of a single vote for president equals (the probability of that vote being decisive) times (the value of that candidate winning instead of the other). The probability of your vote being decisive is really small, something like 1 in 60 million according to Nate Silver. So the expected value of the vote ends up being pretty small too.
I always thought the case of vegetarianism was similar, but I didn’t think about it hard enough. I thought that an individual purchasing decision was like an individual vote – that on average, it would get totally lost in the bigger picture. This is wrong because the probability of your purchasing decision being decisive is actually negatively correlated with the value it has if it is decisive! I.e. if your local grocery store buys 100 chickens at a time, then when you abstain from buying 1 chicken, you have a 1 in 100 chance of saving 100 chickens, so on average you will save 1 chicken. If instead they buy 1000 chickens at a time, you have a 1 in 1000 chance of saving 1000 chickens, so you still save 1 chicken! And so on. In general: (1 / n) * n = 1. (In practice, we also have to consider elasticity effects, but we can ignore them for now.)
So now the key difference should be clear: the same correlation is not present in the voting case. If your vote has a 1 in 1000 chance of being decisive, then it’s simply worth 1/1000*(comparative value of candidate), because there’s no outcome where you elect 1000 presidents!
The major problem for me was that people tend to use the same vague language to talk about the voting and vegetarianism cases, when in fact there is a different underlying mathematical reality to be revealed. A year ago, I could have heard (and did hear) “small actions add up” till the cows come home (heh) and not be convinced at all.
This problem concerns me, because I know there are people out there right now who are where I was a year ago. They’re on board with collective vegetarianism for all the usual reasons, but they are tepid about individual vegetarianism because of the “bulk purchasing loophole.” My roommate would sometimes make a particularly strong version of this case, saying, “I would vote to ban meat production today, but in the meantime, there’s no point in me changing my diet.” These loophole people may be a relatively small group of potential converts to vegetarianism, but they ought to be a productive one. If they really fit the description, it will take all of five minutes to disabuse them of their mistake, as Brian did for me. How do we find them? Your guess is as good as mine. For now, I’ll just keep shouting these words into the void.
Appendix: Thoughts on Voting
To clarify, I do think voting in important elections is still a good idea! We can do some rough math to see this. Suppose your vote has a 1 in 60 million chance of being decisive, as referenced above. The reason this makes sense, by the way, is that your candidate only needs to win by 1 vote – so if they win by 2 votes, or 3 votes, or 4 votes… (or if they lose), then your vote wasn’t actually needed, and has 0 “marginal” value in terms of helping your candidate win. It may seem weird at first to think only about this marginal value. It may seem selfish, because you’re assuming others will vote, but you’re not holding up your end of the deal. But really, you only control your individual vote, so it actually is valid to just assume that everyone else is going to vote a certain way regardless of your action – sort of like you’re the last one to turn in your ballot. If everyone else voted before you, and you knew that your candidate had already won by a million ballots, it wouldn’t be worth your trouble to drive to the polling place! So your vote is only decisive – only *really* counts – if your candidate wins by exactly 1 vote. This obviously doesn’t happen often, hence the 1 in 60 million figure. There are other factors to consider too, but that’s the gist of it.
Now, add up all the ways that your candidate is better than their opponent (and, of course, subtract any ways that they’re worse). Put a dollar value on this cumulative difference, just to make it easier to think about. Suppose your candidate is on balance superior to their opponent by the equivalent of 1 billion dollars. This means your vote has an expected value of 1 billion divided by 60 million = around $16.67. Not bad at all, especially if voting only takes you a half hour or so! You can also add to this whatever value you personally get from voting (education, satisfaction, etc.) and whatever your voting/talking about it does to encourage others to vote. I know thinking of it in terms of money sounds weird, but it’s the best way we have of agreeing on specific values – even for seemingly intangible things like human and other animal suffering!
So yes, voting is often quite worthwhile (although it does technically depend on factors like where you live, how likely your candidate is to win without your vote, how much better your candidate is than their opponent, and the “opportunity cost” of your time spent voting). The example isn’t really meant to say that voting doesn’t matter. It’s just a useful way of parsing out two different mathematical phenomena that often get lumped together when we talk about things with non-mathematical language.
Evan Sandhoefner 
This is a great post. I don’t really understand the problematics of bulk purchases but everytime someone tells me ‘you can’t change anything anyway’, I just smile and reply: ‘The lower the demand, the lower the offer.’ Isn’t that one of the essential rules in Economics? And if we’re vegans or vegetarians, it’s one more person who doesn’t support this industry. One person cannot do much, that is true. But if all of these individual vegans/vegetarians unite, as we are uniting today, we can make a huge difference. Every big changes have always started in the heads of a few individuals. Our aim is to show by example so that others can join as well. 🙂
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Thanks for reading! Glad you enjoyed (: Your comment is useful, because I was having trouble being absolutely clear in my writing.
The arguments you make here are basically true, but they wouldn’t have worked on me a year ago in the way that Brian’s expected value argument did. To me, it would have felt like you and I were ships passing in the night. This is because in other domains, statements like “one person can’t do much, but together we can do great things” are actually dodgy. At best, they’re imprecise, and at worst, they rely on hidden unjustifiable assumptions. As a result, I was disinclined to take them seriously in general.
Without getting too far into the weeds, here’s an example: the case of voting for president. People who express skepticism about the value of a single vote often hear “what if everyone thought that way?” or “your vote may be small, but they add up” or “every vote counts”. These are bad arguments. “What if everyone thought that way” invokes a useless assumption, because there’s obviously no causal link between your thinking that way and everyone else thinking that way. (A much weaker version of this argument can be salvaged: if you talk a lot about the worthlessness of voting, then you may actually cause others not to vote, which is bad. But this argument doesn’t apply to just abstaining from voting yourself, as long as you keep quiet about it.) The other two responses are just obfuscation. Of course they add up and they all count – that doesn’t change the fact that your individual vote, which is the only one you can directly influence, is actually small.
So what distinguishes these bad arguments about voting from the good argument about vegetarianism? It’s hard to tell without invoking the actual math. Thankfully, the math is simple – beautifully simple, actually, if you ask me. The value of a single vote for president equals (the probability of that vote being decisive) times (the value of that candidate winning instead of the other). The probability of your vote being decisive is really small, something like 1 in 60 million according to http://www.stat.columbia.edu/~gelman/research/published/probdecisive2.pdf . So the expected value of the vote ends up being pretty small too.
I always thought the case of vegetarianism was similar, but I didn’t think about it hard enough. I thought that an individual purchasing decision was like an individual vote – that on average, it would get totally lost in the bigger picture. This is wrong because the probability of your purchasing decision being decisive is actually negatively correlated with the value if it is decisive! I.e. if your local grocery store buys 100 chickens at a time, then when you abstain from buying 1 chicken, you have a 1 in 100 chance of saving 100 chickens, so on average you will save 1 chicken. If instead they buy 1000 chickens at a time, you have a 1 in 1000 chance of saving 1000 chickens, so you still save 1 chicken! And so on. (1/n)*n=1.
So now the key difference should be clear. The same correlation is not present in the voting case. If your vote has a 1 in 1000 chance of being decisive, then it’s simply worth 1/1000*(comparative value of candidate), because there’s no outcome where you elect 1000 presidents! This is just (1/n)*1=(1/n).
Please let me know if this makes sense, because if you do run into people like [me a year ago] in the future, you can say “small actions add up” till the cows come home (heh) and you won’t convince them.
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Wow, you’re very clever. I mean this honestly. I’ll have to read this at least five more times in order to properly understand it, haha.
But even when it comes to voting, I realise that your argument is very strong and makes sense, but I still very much agree with one quote I’ve seen on some badges of Amnesty International: Indifference kills.
Even when our individual vote cannot change much, it can still change more than doing nothing. That’s correct, isn’t it? It’s always better to get up and go voting or to stop for a moment anf change the way we eat than doing absolutely nothing and being indifferent to the world.
Anyway, thank you for your comment, I will try to use this tactics if my ‘spiritual blahblahs’ don’t work, haha.
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Yes, to clarify, I do think voting in important elections is still a good idea! We can do some rough math to see this. Suppose your vote has a 1 in 60 million chance of being decisive, as referenced above. The reason this makes sense, by the way, is that your candidate only needs to win by 1 vote – so if they win by 2 votes, or 3 votes, or 4 votes… (or if they lose), then your vote wasn’t actually needed, and has 0 “marginal” value in terms of helping your candidate win. It may seem weird at first to think only about this marginal value. It may seem selfish, because you’re assuming others will vote, but you’re not holding up your end of the deal. But really, you only control your individual vote, so it actually is valid to just assume that everyone else is going to vote a certain way regardless of your action – sort of like you’re the last one to turn in your ballot. If everyone else voted before you, and you knew that your candidate had already won by a million ballots, it wouldn’t be worth your trouble to drive to the polling place! So your vote is only decisive – only *really* counts – if your candidate wins by exactly 1 vote. This obviously doesn’t happen often, hence the 1 in 60 million figure. There are other factors to consider too, but that’s the gist of it.
Now, add up all the ways that your candidate is better than their opponent (and, of course, subtract any ways that they’re worse). Put a dollar value on this cumulative difference, just to make it easier to think about. Suppose your candidate is on balance superior to their opponent by the equivalent of 1 billion dollars. This means your vote has an expected value of 1 billion divided by 60 million = around $16.67. Not bad at all, especially if voting only takes you a half hour or so! You can also add to this whatever value you personally get from voting (education, satisfaction, etc.) and whatever your voting/talking about it does to encourage others to vote. I know thinking of it in terms of money sounds weird, but it’s the best way we have of agreeing on specific values – even for seemingly intangible things like human and other animal suffering!
So yes, voting is often quite worthwhile (although it does technically depend on factors like where you live, how likely your candidate is to win without your vote, how much better your candidate is than their opponent, and the “opportunity cost” of your time spent voting). The example isn’t really meant to say that voting doesn’t matter. It’s just a useful way of parsing out two different mathematical phenomena that often get lumped together when we talk about things with non-mathematical language.
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Thank you, this is some real good math, haha.
Now I get it. 🙂
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What an informative post. Would love your permission to republish over on Learning from Dogs.
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Please do – I’d be honored!
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Thank you!!
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Thanks for following my blog.
I have been vegetarian most of my life, the ova lacto variety. I am now much more ovo vegetarian and unlikely to become vegan until I can no longer buy eggs laid by hens who I know will live out their natural days. However, my own vegetarianism came not from ethical conviction, but from the fact that I disliked meat. I don’t think you can ignore the fact that many vegetarians are naturally inclined towards a meat free, fish free diet. The ethics follow. I remember the day as a pre-teen that I picked up a flyer about factory farming and was horrified. It was a pivotal moment.
On the whole, although meat eating is an anathema to me, I do believe people should have the choice. The caveat is that all animals reared for meat must be reared in a quality environment, that their deaths must be as pain free and as stress free as possible, that they must have free access to the outside and live lives free from cruelty.
I own a cat; a carnivore. It is an issue to me that much of the meat and fish that goes into pet food is from factory farmed animals. I believe we should be campaigning for ethical rearing of animals for all markets. We will not stop everyone from eating meat, many people (including some of my own close friends and relatives) love it. So therefore educating the public about how meat is produced, the ethics of meat eating, needs to focus on animal welfare and quality product.
As to whether individuals can make a difference; of course they can. Margaret Mead said: Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it’s the only thing that ever has.
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Hi Evan,
I really enjoyed this part!!! Very insightful! It was one of the ‘ah ha!’ moments.
“I always thought the case of vegetarianism was similar, but I didn’t think about it hard enough. I thought that an individual purchasing decision was like an individual vote – that on average, it would get totally lost in the bigger picture. This is wrong because the probability of your purchasing decision being decisive is actually negatively correlated with the value if it is decisive! I.e. if your local grocery store buys 100 chickens at a time, then when you abstain from buying 1 chicken, you have a 1 in 100 chance of saving 100 chickens, so on average you will save 1 chicken. If instead they buy 1000 chickens at a time, you have a 1 in 1000 chance of saving 1000 chickens, so you still save 1 chicken! And so on. In general: (1 / n) * n = 1.”
Joanne
Veggie for two years a.k.a saved many chickens.
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Thanks Joanne! Glad you enjoyed it (:
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I’m glad you found my article helpful. 🙂
> If your vote has a 1 in 1000 chance of being decisive, then it’s simply worth 1/1000*(comparative value of candidate), because there’s no outcome where you elect 1000 presidents!
A single president for a population 1000 times larger may have roughly 1000 times as much impact. For example, suppose you measure political impact by changes to budget allocation. If the country’s population is N, the tax revenue and thus government spending will be proportional to N. If the probability of changing the election is proportional to 1/N, we’re back to something similar as in the meat case. (That said, I agree that voting can in principle be different, because of the winner-take-all nature of it. For example, if current polls predict one candidate getting 99% of the vote, then the probability that your vote for the apparent loser will make a difference is probably much less than 1/N.)
> Suppose your candidate is on balance superior to their opponent by the equivalent of 1 billion dollars.
I would guess the difference in value between candidates is often vastly bigger. 🙂 US federal discretionary spending is over $1 trillion each year, so even, say, a 1% improvement in that would be worth $40 billion over 4 years. There are also big-picture things like the 2003 Iraq war, which some estimate has already cost $2 trillion — money that has been worse than wasted in terms of its impacts. It seems pretty likely that Al Gore wouldn’t have gone into Iraq, so the entire trillions of dollars could have been prevented by a different result in the 2000 election.
Of course, money that you personally spend on optimal charities may be much more valuable than money spent in various ways by the federal government, so these numbers should be shrunk to account for that.
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Good points, Brian, thanks!
> A single president for a population 1000 times larger may have roughly 1000 times as much impact.
This is true. I was thinking about it within a given country, where population size is relatively stable between elections. This seems like the most relevant framing for the typical individual voter. In this case, the value of the ballot is proportional to the closeness of the race and to the candidate value gap. It also seems plausible (conjecture alert) that the closeness of the race is negatively correlated with the size of the candidate value gap. Insofar as that’s true, there is less variance in the value of a ballot between elections (within a country) than the candidate value gaps alone would seem to suggest.
> I would guess the difference in value between candidates is often vastly bigger.
Maybe. I didn’t think hard about that number, since my main intention was to illustrate a contrast with the vegetarianism case in terms of the mechanisms, not in terms of the absolute values. I’m not a political expert at all, but I think my estimates of these value gaps would tend to have really wide confidence intervals, possibly crossing the zero line in many cases.
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