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6 Responses

  1. A.J. Sutter says:

    1. Thanks for the shout-out. I disagree with one of your fundamental premises, though: I, for one, love oatmeal raisin cookies (as long as they don’t have that sticky brittleness that comes from too much granulated sugar in the recipe). Sorry that I live too far way to free-ride on your cookie events.

    2. Please help me to understand the tax advisor point: does it make a difference what kind of tax advice you’re talking about? For example, compare some advice about the permissibility of a home office deduction or some other bread-and-butter thing like that, with advice about some fancy new tax shelter that hasn’t yet been prosecuted, and is designed for the wealthier sort of client. In the first case, won’t the adviser’s opinion (which may be oral, rather than written) be based on how many times his clients have gotten into trouble when audited? Whereas in the second case, the basis for the probability estimate may be much more “out there,” or based on more distant analogies? Not that this means the home office probability estimate is frequentist, since each tax return presumably is unique in some way; but at least in that situation there’s some experience that can be used for estimating the “prior probabilities,” even if the advisor has never heard of Bayes. Doesn’t this reduce uncertainty for the home office types?

    3. So does this suggest that the ultra-are-you-thinking-what-she’s-thinking-what-you’re-thinking (the “fog of tax”?) approach of lawmakers should be reserved for big-ticket deductions that might be taken by wealthier taxpayers? BTW, which taxpayers are the ones who are most uncertainty-averse — the wealthier ones or home-office types? If lawmakers should reserve their subtle thinking for the big-ticket tax shelters, but (a) the folks who use shelters are more dice-rolling, or (b) their advisers more prone to look for loopholes in ambiguous rules, does this defeat the enhanced compliance result you desire (or assume that lawmakers desire)? Aren’t most ambiguities likely eventually to get resolved in the course of a cat-and-mouse game between wealthy taxpayers and lawmakers?

  2. billb says:

    [citation need], given that I love oatmeal raisin cookies.

    Also, why is it better to have high uncertainty about a dubious tax proposition than high certainty? If a tax dodge has 99.9% chance of being disallowed by a court, and tax lawyers are 99.9% certain about this, isn’t that more helpful to taxpayers who can then be advised quite accurately not to do it?

    Aren’t high levels of uncertainty likely to stop people in their tracks and thus inhibit high numbers of both legit and illegitimate transactions thereby reducing efficiency?

  3. Matthew BCL says:

    Yeah, not to pile on, but lately my wife’s been making a big deal about how oatmeal cookies are her favorite. I think she likes how they’re more like food than a lot of cookies are – yet they’re still a sweet treat! Perhaps that article should be titled “Oatmeal Cookies: All Things to All People?”

  4. AEW says:

    I don’t understand how the distinction between risk and uncertainty relates to subjective and frequency interpretations of probability. Say I have two dice, one with dollar signs on 4 sides, and one with dollar signs on two sides. I put one in each hand (behind my back) and let you choose a hand. I take that die and say “I’m going to roll this, and if a dollar sign comes up, you win a dollar.” What are the odds that you win a dollar? You could say that the probability is either 1/3 or 2/3, you don’t know. Or you could say the probability is 0.5. Does this count as uncertainty? It’s true that to say that the probability is 0.5 is subjective in the sense that someone who peeked behind my back would have a different belief of the probability. But it’s fully consistent with a frequentist interpretation of probability in that if we repeated the process ad infinitum, the frequency would approach 50%.

    It’s empirically true that people seem to have a psychological aversion to more complicated ways of obtaining an outcome. They seem to prefer a coin flip to the process above. But I don’t see how this is logically related to the philosophical interpretation of probabilities. Am I misunderstanding uncertainty?

  5. A.J. Sutter says:

    AEW, your dice analogy might be clouding the issue for you. A condition of “risk” requires that you know the chances of an event happening, and frequentists have particular criteria for such knowledge. In theory (though see below), rolling dice is the kind of repeatable event that can meet these criteria. But many events involving human activities aren’t properly analogized to rolling dice, pulling marbles from an urn, watching beta decays of atoms, etc. They don’t occur often enough to know the frequentist, long-run probabilities. Even batting averages don’t make the cut. There might be a good argument to consider one individual’s at-bats as repetitions of an identical event, one of the preconditions for using a frequentist approach. But even in this case, a player’s batting average doesn’t necessarily stabilize the more at bats he or she has; it may have a plateau at some times, but generally it has ups and, especially ultimately, downs.

    Suppose you know the resolution of hundreds or thousands of tax shelter cases, and let’s say that the number of cases, had they been dice rolls, might be of a number that we’d agree would be sufficient to establish the frequentist probabilities for dice. Is it really plausible that all these cases, involving different taxpayers, in different tax years, with different judges, counsel, etc., are so similar that your could consider them repetitions of an identical event, for purposes of establishing long-run frequencies of outcomes? Of course, you could *treat* them all as identical events, and compute such a number, but your methodology would be debatable. As I understand Sarah’s point, if they’re not repetitions of an identical event, then the frequentist approach doesn’t apply, which means that you can’t *know* the probabilities of outcomes a priori, which means you aren’t in a “risk” situation.

    Actually, even dice rolls can be “uncertain”. In your example, there are a number of assumptions implicit in saying that the frequency would approach 50% if your $-dice rolls were repeated ad infinitum. For one thing, you might always put the same die into the same hand, and the player might have the strategy of always picking the same hand. For another, in a frequentist world, you’d have to have already rolled those dice an awful lot of times to know a priori that they are fair. If you haven’t done that, then even with a randomized game-playing strategy it’s too early to know what the limiting frequency would be. Of course, maybe you’ve looked at the dice and they seem balanced and symmetrical. But then you don’t really know the probabilities of rolling a ‘$’ or not; you just assume or trust that, based on their appearance, the dice are fair. (I suppose in theory it might be possible to establish a frequentist probability as to symmetrical and balanced dice being fair, but that would involve collecting data on an awful lot of rolls of an awful lot of dice. You couldn’t rely on statistical inference; since that mathematical framework already assumes the frequentist view, your reasoning would be circular.)

    If even dice rolls have to overcome so many hurdles before being classed as “risk,” then the distinction between risk and uncertainty doesn’t seem to have much practical value. Maybe its value is more a polemical one. From the litle bit I’ve read of Knight, it appears that his point was that the economics of the day ignored judgments made under uncertainty, even though most business decisions — even about insurance — are made in that condition. He seemed to be protesting the purist, theoretical view of economics. From the little bit I’ve read of Sarah’s article, she seems to be pulling in some connotations of “subjectivism” that go beyond mathematicians’ use of the term, to talk about the ways IRS can collect more money by messing with your, or your tax adviser’s, head. In each case, I think the goal is to get people more focused on (relatively) practical reality, rather than in the theoretical realms where “risk”, as they define it, seems to be confined. Sarah, have I misunderstood your point?

  6. Sarah Lawsky says:

    AJ Sutter: That is a great reply to AEW’s comment. You have certainly not misunderstood my point. I think AEW’s dice example is really interesting, too, and will put up a post shortly discussing it.