Monday, January 11, 2010

Voting, Vegetarianism, and Other Chunky Impacts

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.


  1. > 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.)

    Whoa whoa, hold on. I'm not sure the argument survives the transfer.

    Let's imagine an ideal supermarket, one that isn't bound by shipping constraints.

    If a consumer buys 1 steak, instantly a pneumatic tube system (or something) whisks a fresh steak from the warehouse and orders are sent to the farmer, who then butchers a teeny-tiny cow to make 1 steak to replace the consumer's purchase. In this case, the consumer's choice directly impacts the total number of teeny-tiny deaths: it will be _n_ if she refrains from buying, and _n+1_ if she buys. Her choice determines 100% of the result, and all is as it should be.

    No problem. The inefficiency in purchasing means the effect of our choice is uncertain and probabilistic, but the system still will try to converge on producing & delivering the exact amount of steaks demanded. A perfect system would adjust immediately, an imperfect one will take time and its accuracy will be limited by its 'resolution' of quantities.

    But let's consider an election of some candidate. The voter votes and his vote is instantly tallied up and recorded, and alas, his favored candidate loses by a margin of 6%, and so his disfavored choice gets 100% of the result (viz. power).

    Would an ideal election result in the favored candidate getting 47% of the power, and the disfavored getting 53% of the power? (It's funny imagining how this would work; maybe they roll carefully weighted dice every day to decide who will be president.) If we imagine elections held over the centuries where the population is static at 47% preferring one candidate/party/platform and 53% the other, would we expect to see 47% of the victories go to the weaker side and 54% to the stronger side?

    Of course not. Elections are winner-take-all; the stronger side will win every time if their preferences never change. The whole point of an election is to be 'chunky'. It is specifically intended & designed to run roughshod over fine differences. A president has all the constitutional powers regardless of whether he had 50% or 90% a vote. There is no continuum of outcomes in an election which one can hope, in one's ignorance, to influence. And so there is nothing for the system to home in on, no tipping point other than 50%; we are not ignorant of the effect, but quite aware of whether our vote will matter or not.

  2. Gwern, I don't understand your objection. There is a tipping point, namely 50%. Prior to voting, you can't be sure how close to the tipping point we are. Maybe there's a one in a million chance that your vote will make the decisive difference. Since the outcome is 'chunky', the payoff in this rare case is massive (affecting millions of people), which counterbalances the low probability when we consider the "expected value" calculation.

  3. I'm probably oversimplifying this, but I can't get past the fact that in either case, you should do what you believe to be right (whether that is not purchasing meat or voting for a particular candidate). Why should others' actions play into your decision-making in these cases at all?

  4. Richard, I think Gwern is correct. It's true that if there were complete uncertainty as to whether your vote tipped your candidate over the 50% mark, then the expected value of your vote is high. But in the real world we usually have a decent idea of just how various candidates will poll, and can sometimes predict with accuracy that our vote will not change the outcome. Then the expected value of the vote is indeed low.

    Think of an extreme case where you vote for a total no-hoper candidate (e.g. No matter how good their policies are, the expected value of your vote is zero. In less extreme cases the expected value won't be zero, but it still might be extremely low.

  5. 6p010

    Some 'right' actions come at a personal cost, from anything as trivial as lost time, to wasted effort or compromising your lifestyle. At any rate, most people make practical decisions with a hope of achieving something. In some situations, this requires an idea of how others will act, with or against you. Richard's arguing why it may still be worth acting even with incomplete knowledge of how others will help or hinder the outcome.

  6. Richard,

    I'm afraid I haven't really grasped the argument, but that's my fault, as I haven't read through it thoroughly, and will do. But doesn't it ignore the nagging question that normally stops people taking risks viz. is probability truly enough of a factor to justify the fact that if I fail, I fail 100%? I'd rather know that even with a 70% chance of success, should I fall into the 30% failure zone, my failure won't be a 100% failure.

    Also (I think others above may touch on this), surely even if my boycott results in a reduction in demand, it simply means there's less meat, not no meat? All that happens, I think, would be me doing without meat, with no overall disincentive for Supermarket Corp to keep on selling it.

    Maybe there's something to be said for 6p010's view about doing the right thing. Seems to me that the real fallacy people make with that argument is in treating a virtue question as a means-end question.

  7. I think I am getting stuck on the individual scenarios...

    For voting, I can see how predicted outcomes may affect decision making if the question is 1 whether)to vote for a candidate you most agree with but has little chance of winning versus voting for a candidate you agree with less but has a better chance of beating out a candidate you agree with even less (read: is voting third party a wasted vote) or 2) whether or not to actually go to the polls (which, in my opinion, just sounds lazy!)

    For the meat buying scenario, again this is dependent on other factors. Why are you even considering avoiding or decreasing meat purchasing? If you think eating meat is altogether immoral, then to be consistent with your beliefs you should not purchase meat, regardless of what others choose to do. If you think we need to reduce the consumption of meat (say, to reduce negative environmental effects), I can at least see how someone might argue that if no one else is going to do it, then I'm not going to either.

    Dickie's comment about confusing a virtue question as a means-end question makes sense to me, but I also disagree with the logic that one consumer's choice does not have any impact. After all, we would never get to one million consumers making a certain choice is dependent upon each consumer with in that one million making that decision. If I'm making any sense...

    Sarah (not trying to be anonymous; Typepad has just been showing up as my letter/number ID for some reason...)

  8. Sarah,

    You raised the point that if one thinks eating meat is wrong, that should be decisive of the matter, regardless of what others will do in support. I don't think I disagree with that -- I said it myself, but I've now noticed there seem to be two separate kinds of people in this scenario:
    1) The ones who say, "This practice is wrong so I will not take part in this practice"
    2) The ones who say , "This practice is wrong and I want it ended/reduced"

    Both kinds of resolutions are morally justified, but the latter is probably just more ambitious than the former. I'd say in some cases, the latter is the only one worth having.

    One might use foxhunting as an analogy. The fact that I've never participated in a foxhunt preserves the moral maxim "gratuitous killing of animals is morally unacceptable" [or whatever]. Therefore I will not do it.

    But that doesn't do enough to respond to the fact that fuxhunting is (or was) a widespread activity. And if you consider it a morally unacceptable practice, it's not a morally satisfactory result to merely succeed in keeping yourself out of it. The only morally acceptable outcome to such a person would probably be to see the practice ended or reduced. He or she says "X practice must be ended".

    I think in some cases, the individual contribution is only made morally effective by its contribution to the outcome. Otherwise it's about as effective as flogging the sea.

  9. Alex - sure, there are possible cases where the chance of swaying the outcome is too low to be worth it. I'm merely pointing out that the crude objection fails. That is, the mere fact that big numbers are involved, and hence that one's vote is extremely unlikely to affect the outcome, doesn't suffice to show that it isn't worth it (as a matter of expected utility).

    Sarah - I'm assuming a consequentialist framework here. (The alternative strikes me as a kind of moral fetishism.) There's nothing intrinsically wrong with eating meat. It's merely wrong if it causes more suffering (e.g. of factory-farmed animals). Conversely, it's only worth becoming a vegetarian (on ethical grounds) if such efforts will actually make a difference to what I care about, namely preventing suffering (and generally making the world a better place).

    Dickie - less meat, and hence less suffering, is at least a step in the right direction. It would be absurd to pass up a chance to improve the world, just because the result still falls short of utopia.

    On your probability point, are you suggesting that it's rational for people to ignore these high-stakes low probabilities? Or are you just making a psychological observation, that many people find it difficult to make wise choices when probabilities are involved? (I'd agree with the latter, but it isn't my concern here.)

  10. Oh no, I was just reminded of "Shoot for the moon. Even if you miss, you'll land among the stars." Ha sorry about that.

    Your response did help me better understand the point you are making. Another way a decision-maker could look at this (and in my opinion, should) is that every "chunk" is made up of individuals. Maybe an individual's decision not to consume a given produce could even influence others' decisions.

  11. You say: "But one of those hundred individual choices must have made the difference between the store choosing to buy X crates or X-1," but I am not sure that is correct.

    Suppose we had a list of each person who bought steak that included the time of purchase, so that the list is ordered from earliest purchaser to latest. Now, if the list is exactly long enough to get the store to order N crates, it doesn't seem right to assess the final person on the list as wholly responsible for the additional crate (in whatever sense you mean when you say "one of those [...] choices must have made the difference." If the last two people on the list swapped places in line right before making their purchases, it doesn't seem like they have traded any status with respect to which of them (if either) makes a difference.

    Supposing that the number of crates ordered is a simple function of the number of steaks purchased, the number of steaks purchased is a function of a set of individual shopper choices. It seems as though everyone on the steak-buying list is in the same boat; each of them is such that if they had not purchased the steak (and everyone else made the same purchases), one fewer crate of steaks would be ordered. So I think it is not the case that some individual shopper can be assessed as having made the difference.

    This doesn't do anything to challenge the larger point about not knowing whether we are in a situation where if we purchase, some threshold for ordering more crates will be crossed, and if we don't purchase, no such threshold will be crossed.

    Of course, I'm not sure that the point holds up if the number of crates is something other than a simple function of the number of steaks purchased (for instance, if the calculation of how many crates to purchase involves multi-month trends, or the like, the exact number of steaks purchased is further removed from having an impact. Additionally, this argument is less effective for people shopping at large chain grocery stores (where we might expect the size of their bulk orders to be substantially higher, thus increasing the distance between thresholds, and diminishing the expected impact of any individual decision).

  12. "it is not the case that some individual shopper can be assessed as having made the difference."

    Right, I didn't mean to suggest that, but I can see that my wording was unclear. By "one of those hundred individual choices" I really meant one of the hundred increments between having n or n+1 fewer steaks bought.

    I'm not sure I follow your last point. If my argument is right that (simple) chunking doesn't affect expected utility, then having larger rather than smaller chunks also makes no difference. The diminished probability of making an impact is precisely counterbalanced by the increased payoff in the lucky case.

  13. I see how the counterbalancing is supposed to work if you have a 1/100 chance of increasing the steak purchase by 100 steaks.

    Which translates to the situation where the function from number of steak purchases to number of steak crates is to divide by 100 and round up (i.e. order the smallest number of crates that is at least sufficient for the demand).

    Suppose that the function is different though. For instance, suppose that the store will calculates how many crates to purchase based on the previous two weeks of data. So that if N steaks were purchased this week, and N' steaks were purchased last week, the store will order the smallest number of crates to guarantee that at least (N+N')/2 steaks can be purchased this week. In other words, if, last week 240 steaks were sold, and this week 320 steaks are sold, the order for next week will only be 3 crates (since that is an average of 280 steaks sold). Now, my choice whether or not to purchase a steak this week has something like a 1 in 200 chance of effecting the number of crates bought next week by 100. Or in your terms, an expected impact of 1/2 a steak.

    I think, as I phrased it, my last point in the above post was not well put. You are right that if the size of the crates is 100,000, and the function is still "the smallest number of crates that meets last weeks demand" the point will hold equally well. My thinking was that large chains undoubtedly (in part because they are working with higher volumes) are more likely to employ a process that is based on more information (such as historical trends, community demographics, etc.) If the calculation of how many crates to purchase depends on more than just how many steaks were purchased in the last round, it is possible for such functions to decrease the expected impact of an individual decision. And while the system I described is probably not a good system, it is entirely possible that the best estimate of next week's steak demand relies on information other than this week's steak demand.

  14. Richard, I'm not sure whether the uncertainty as to whether or not your vote is decisive, or whether your purchase is decisive is a relevant consideration. Actions with regard to chunky situations are best defended with reference to institution and supporting them

    Don't we have an obligation to contribute to practices/institutions that do good?

    i.e. even though your individual action will neither support nor destroy the institution, since we desire that those institutions exist, and that if not-supporting those institutions were a universal law of nature, the institutions would not exist, we have a wide duty to support those institutions.

  15. Lewis - "Now, my choice whether or not to purchase a steak this week has something like a 1 in 200 chance of effecting the number of crates bought next week by 100"

    Plus another 1/200 chance of effecting an impact of 100 the next week, right? So even this slightly more complex system still looks like it offers us a total expected impact of one.

    Murali - as previously noted, I'm assuming a consequentialist framework here. For the record, I disagree with you: I don't think we're obligated to perform some action that's useless in the actual circumstances, just because in some different circumstance (where everyone magically behaves the same way you do) it would be worth acting that way. But it'd take us too far astray to debate this here.

  16. as previously noted, I'm assuming a consequentialist framework here


  17. The problem is that the systems for measuring your preferences (whether markets for beef or election votes) simply are not sensitive enough to register an individual. It's not that your vote/purchasing decision has a tiny impact. It has literally no impact because it disappears in the measurement error.

    Russell Hardin has a very depressing book out on this: How do you know?: the economics of ordinary knowledge

  18. There is some number n of additional actions that would have a noticeable impact X. For this to be possible, the system must be sensitive to some individual changes, e.g. the change between having n-1 people and the tipping point of the nth. All else equal, any given individual has equal (1/n) chance of being the tipping point with massive impact X. Each individual's expected impact is thus (X/n), just as was expected to begin with. Measurement insensitivity makes no difference.

    What's wrong the above reasoning? I don't rely on the idea that every individual's slight impact is measured. Rather, the idea is that every individual has a slight chance of triggering the measurement of the whole chunk. And the expected value is the same either way.

  19. Richard, thank you for the concise refutation of the Chunky Fallacy

    Unfortunately, I believe you erred in the postscript by claiming that consumption will affect production by less than 1:1 due to changes in prices. I believe that is correct in the short term, but most relevantly, incorrect in the long term. I lay out my reasoning in this post:

    1. FYI I made another attempt to argue that the effect will actually be about 1:1:


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