Not everyone was convinced by my contention in yesterday’s post that the mismatch theory of loopholes is wrong, to put it mildly. Their reservations are understandable. More detail is needed to make the claim convincing, more detail than a blog post allows.
More importantly, however, it is hard to be convinced of the wrongness of a plausible theory, like the mismatch theory, whatever its defects, if one doesn’t have a plausible alternative. In this post, I will try to offer you one.
It has often been suggested that the prohibition on sex discrimination was added to the Civil Rights Act of 1964 as a devious attempt to kill the Act. Supposedly its sponsors calculated that there would be a majority to support the amendment regarding sex discrimination, but that once the amended bill went up for a vote, a majority would find it too repellent and the entire Civil Rights Act would go down in flames.
Whether this is what really happened is controversial. But what is not controversial is that killer amendments are often a successful strategy for derailing a bill that is about to be passed. There is something deeply paradoxical about this. If a majority of legislators support the amendment, why would a majority then not support the amended bill?
What we have here is a particularly interesting version of Condorcet’s voting paradox, first discovered in the late 18th century (actually by a colleague of Condorcet’s, Borda, and then misattributed to the former), which says that it will sometimes happen that as between three alternatives, a majority might support A over B, a majority might support B over C, but that it will then not necessarily be the case that a majority will also support A over C. The very reverse might happen: A majority might support C over A. Not because anyone has changed his mind about anything, but just because majority voting can do funny things. (For a simple demonstration, just look up “voting paradox” in Wikipedia.)
The killer amendment is an illustration of this. When it works, it works because three things are true at the same time, though it is hard to believe that they could be: (1) A majority supports a proposed new bill over the status quo. (2)A majority supports the amended proposed bill over the unamended proposed bill. And (3) A majority supports the status quo over the amended new bill.
Which alternative comes out on top, thus depends on the sequence with which votes are taken. If the process starts by having legislators compare the proposed bill with the amended bill, and voting on it, and concludes by having them compare the amended bill with the status quo, and voting on it, then the status quo will prevail. Under the usual rules of parliamentary procedure, the legislators will never get an opportunity to compare the status quo with the unamended bill, and vote on that.
Modern voting theory, starting with Arrow’s famous impossibility theorem, established that the possibility of such manipulative killer amendments afflicts all half-way plausible voting systems.
What makes the killer amendment interesting in the context of thinking about loopholes is that it is one more counterexample to the mismatch theory of loopholes I discussed yesterday. Killer amendments smack of loophole exploitation but they clearly are not to be explained by the mismatch theory. The killer amendment strategy obviously doesn’t involve exploiting the divergence between the spirit and the letter of the pertinent voting rules.
But the relevance of killer amendments to loopholes goes way beyond this. That’s because it was understood from early on that the insights of voting theory are relevant not merely to voting, but to decision-making more generally, even if it is individual rather than collective decision-making.
Most individual decision-making is of the type decision theorists like to call multi-criterial. What decision theorists soon realized, after voting theory came on the scene, is that when you are synthesizing a multiplicity of criteria into a final decision, you are doing something very similar to synthesizing the preferences of a multiplicity of voters into a final selection among various alternatives.
To be painfully explicit about it, suppose you are trying to decide which of several cars you should buy. You rank the cars along a variety of relevant dimensions: price, safety, looks, and so forth. In the end, you have to somehow aggregate these various rankings into a master ranking that dictates which car you will actually buy. By whatever means you do this (and whether you do it informally and through your gut, or by actually using some kind of algorithm), what you are doing is going to be closely analogous to that of aggregating the preferences of several voters into a master ranking in the way that voting rules usually do. Your decision making mechanism is therefore subject to a version of the various paradoxes of voting theory, such as Condorcet’s voting paradox, Arrow’s impossibility theorem and so on.
What several legal scholars came to realize—chief among them Bruce Chapman and Matthew Spitzer—is that this makes for an interesting and hitherto unexplored connection between voting theory and the law. Legal decision making can be thought of as a kind of multi-criterial decision-making, and therefore the various paradoxes of voting theory might be helpful in explaining certain paradoxes of legal decision-making.
What is most interesting for my purposes here is that one can use this perspective to explain loopholes, in a way that is very different and more satisfactory than the mismatch theory. If we think of legal doctrines as being structurally very similar to voting rules, then should they not be vulnerable in some way to analogues to the killer amendment?
And so they are. Loopholes it turns out are the exact analogue of the killer amendment in the context of multi-criterial decision-making. Looked at in the right sort of way one can think of each of the tricks I described in yesterday’s post as being a kind of killer amendment. And just as all voting rules are inevitably vulnerable to killer amendments, all laws, so long as they involve the application of a multiplicity of criteria, which is true of virtually all laws, are bound to be vulnerable to loophole exploitation. Wishing loopholes away is a bit like wanting every child of Lake Wobegon to be above average. As a matter of logic, it can’t be done.
Perhaps the most important implication this has for lawyers is that they really need not feel bad about exploiting loopholes, no worse anyway than a parliamentarian who makes use of a killer amendment.
But perhaps you in fact think the parliamentarian ought to feel bad about using a killer amendment? Once you think about the matter a bit more, it is hard to see that what the parliamentarian did as the least bit objectionable. To be sure, he did derail a bill that had majority support. But did the bill he derailed in fact deserve to pass? To be sure, a majority supports it as against the status quo. But there is another bill, the amended bill, that yet another majority would prefer, and then there is another majority that would prefer the status quo over that one. Given that, what makes the proposed bill anymore expressive of the legislature’s “true” wishes than these other alternatives?
If you are interested in seeing the analogy between loopholes and killer amendments shown to be an exact rather than merely a loose analogy, and in understanding why Arrow’s famous impossibility theorem actually guarantees the ubiquity of loopholes in law, you will find an explanation of it in Why the Law Is So Perverse.
GF23 says:
Look, I’m interested to see where you’re going with this whole loophole topic and I love me some voting theory, but…
This claim isn’t correct. It’s certainly true that some methods of aggregating will be nontransitive (i.e. vulnerable to voting paradoxes), you seem to be arguing that any method of aggregating will be similarly vulnerable. This is equivalent to saying you can’t come up with a full ordering on a multidimensional space, which is false.
As a concrete counterexample: Assume you have 5 dimensions for a car (price, safety, looks, MPG, top speed). Each dimension is ranked from 1 to 10, and your aggregation function is simply the sum of the 5 rankings. (highest sum wins).
November 1, 2011, 1:22 amCar C1 (1,8,9,4,9) (sum 31) is going to be preferred to car C2 (7,4,2,6,4) (sum 23) (in other words, C1 > C2). There is no car C3 such that C2 > C3 and C3 > C1, giving a loop of preferences. There’s no set of cars C3, C4, … CN such that C2 > C3, C3 > C4, …, and CN > C1.
There’s no possibility at all for preference loops given such a rating system.
EMB says:
This isn’t exactly true in practice; for example, approval voting gets around this problem: you could present the legislators with all three options (in this case, status quo, amended bill, and unamended bill) and take a vote of how many people approve of each, and whichever option gets the most votes becomes law (handle ties somehow).
This gets around Arrow’s Theorem because the input is different: on the one hand, the voters are providing less information about their ordering on the preferences, but on the other hand they provide more information on the strength of their preferences.
Of course, the game theory is rather complicated in deciding how to vote in this system, and there may be other better systems, but the point is that Arrow’s Theorem in no way suggests that the practical problem of designing a better voting system is impossible.
(I know though that you’re trying to explain why our current political system produces loopholes, and the question of how one might design a better system isn’t actually relevant to that.)
November 1, 2011, 1:41 amduffy pratt says:
Sidney Morgenbesser was having lunch in a diner with a guy who was insisting on explaining Condorcet. The waitress came by and asked what they would like for dessert. Morgenbesser asked what kind of pie they had. “Apple and Blueberry,” said the waitress. Morgenbesser ordered the apple. A few minutes later the waitress came back and said, “I just noticed, we also have cherry pie.” Morgenbesser replied, “In that case, I’ll have the blueberry.”
November 1, 2011, 2:13 amEMB says:
I like this joke, but it’s not really about Condorcet, but rather about the “independence of irrelevant alternatives” hypothesis from Arrow’s Theorem.
November 1, 2011, 2:55 amRicardo says:
I’m not sure about this one. Arrow’s impossibility theorem states that it is impossible to construct a group decision rule that respects unanimity (if everyone prefers X to Y, then the group prefers X to Y), independence of irrelevant alternatives (if someone prefers Z to X or X to Z, that alone doesn’t change the group’s decision between X and Y) and the “no dictator” condition at the same time.
But if I’m an individual deciding something using multiple criteria, I’m the “dictator” so to speak and my preferences can be transitive, complete and satisfy independence of irrelevant alternatives without any problem.
It’s been a while since I’ve studied this stuff but I don’t immediately see the connection between Arrow’s theorem and legal decision making, at least if the laws get to be made by a dictator.
November 1, 2011, 3:24 amAndrew MacKie-Mason says:
Ricardo — I’m not trained or well-read in this, but I think the point is that in the car-decision scenario we aren’t viewing the individual’s preference a singular thing, but as a collection of preferences along different axes. So there’s no “you” to be a dictator: it’s a question of whether your preference for big cars will be the dictator, or your preference for blue cars.
November 1, 2011, 3:49 amAndrew MacKie-Mason says:
I meant to add — thanks for this post! It raises some interesting relationships between game/voting theory and law that I hadn’t thought about before, and I’m interested in learning more about them.
November 1, 2011, 3:50 amlo78689pg9 says:
I think it is easier to understand if you consider the minority that does not want a bill passed. If a minority doesn’t like A and a (different) minority doesn’t like B neither A or B will pass. However if those minorities when combined constitute a majority, then a bill containing both A and B will not pass if.
Considered this way, it seems to me that a killer amendment is not entirely ethical. You could get an equivalent result if those who were were anti A and anti B agreed formed an agreement to support each other’s side in separate votes on A and B. It doesn’t really reflect the majority opinions on A and B.
This also reminds me of studying probability theory in math where some problems are easier to calculate if you consider the probability something won’t happen rather than the probability it will happen.
November 1, 2011, 5:13 amlo78689pg9 says:
oops: “neither A or B will pass” should have been: “both A and B will pass in separate votes”
November 1, 2011, 5:15 amNoah says:
Follow the money.
November 1, 2011, 6:16 amBrett Bellmore says:
Sounds to me like this account of “killer” amendments ignores the importance of pretext in legislative voting. That is to say that it is frequently the case that some of a bill’s “supporters” only support it because they see a need to be seen as supporting it, and are looking for an excuse to “regretfully” vote against the bill. Killer amendments provide this excuse.
While paradoxical voting preferences are possible, never neglect bad faith as an explanation for real world voting patters in legislatures. It might be less interesting from the perspective of theory, but it tends to explain things better.
November 1, 2011, 7:00 amtrash says:
Like others, I do not immediately see the comparison between legal decision-making and legislative decision-making, but the analysis of “killer amendments” is fascinating. I note that you, as I, seem to have no ethical dilemma with the use of such amendments as a parliamentary procedure. I suspect neither of us, if in a parliament or discussing one, would have any ethical problem describing the use of such amendments by the opposition as evil skullduggery, however, while defending our own use of them.
I have not read your book, but I imagine that in it, you elaborate more on the use of loopholes in parliamentary procedure. These are often, in my opinion, the mirror image of the killer amendment. After all, while a killer amendment is often inserted to prevent passage of a bill (and if it is passed anyway the result is possibly perverse), often a loophole is inserted to peel away opponents of the bill, but sometimes the loophole itself prevents passage of the bill by instead vitiating support for it (a result that also may be perverse).
The problem with actually implementing things like approval voting and Borda count voting in parliamentary systems, and other similar things is that they are mainly tailored to selection of candidates for office, who are generally quite finite, while potential legislative enactments are effectively infinite. There is no system that is immune from gamesmanship. It is arguable that those best suited for gamesmanship are also best suited to draft laws in the first place, but I don’t think the actual results of this thinking bear this out.
I have no (fundamental) ethical problem with either creating or exploiting loopholes, or the use of killer amendments in parliamentary procedure. I think a judicial equivalent to the killer amendment, however, might be the “parade of horribles,” in which an advocate argues that by adopting a certain position, a court, often an appeals court, will also adopt all sorts of ghastly results. This may force the court to limit the scope of its holding to exclude the horrible results, or at least explain why its reasoning precludes those results or, if the advocate actually succeeds, to rule the other way if there is no way to disconnect its ruling from the horribles.
Of course, just as the “killer amendment” may end up passed into law, a “parade of horribles” could end up being the actual result of its ruling, especially if the court does not find the parade all that horrible.
November 1, 2011, 7:14 amLou Gots says:
The best recent example of a “killer amendment” was the poison pill the NRA put in the failed DISCLOSE Act. The NRA’s explanation of its conduct: http://www.nraila.org/News/Read/NewsReleases.aspx?ID=13920
The bill had been a gun aimed at the head of the NRA’s issue advocacy operations, so it had been strenuously opposed by the Association’s members and supporters. A carved-out “loophole” was supposed to induce the NRA to stifle its opposition, but it made the bill unacceptable generally, and down it went.
It was a masterpiece of parliamentary maneuver. If you would see how the game is played, watch us dumb, redneck yahoos with the shotguns handing in the rear windows of our pickup trucks.
Not only did the NRA dispose the day, we showed our power to the world. If applicants to my gun club ask why we require that our members belong to the NRA, I tell them about the failed DISCLOSE bill, and about the role of the NRA in the Citizens United case.
November 1, 2011, 7:39 amIpso Fatso says:
There is another variation of the “killer amendment” offered by interested parties that we get with potential or newly passed legislation, it is the “We know the SC will rule against it” doctrine.
This happened with McCain-Feingold passed by Congress in 2002 and signed into law by George Bush. Any number of conservatives were convinced that the law would never pass SC review, much to their surprise and our loss (IMO)–it did.
November 1, 2011, 8:03 amParadox says:
The idea here is that, in a multi-criteria setup, if you determine beforehand what the weighting system for the criteria is, then the set of your rankings per criterion is mathematically identical to a weighted voting system in which Person A votes based solely on Criterion A, Person B solely on Criterion B, and so on. Thus Arrow and Condorcet apply.
As a heavy-handed example, suppose you’re buying a car, and you decide that you’re going to base your final decision on three criteria: safety, economy/reliability, and fun. You decide that you’re going to give 20% weight to safety, 35% to reliability, and 45% to fun. You then go out and rank each tested car according to each of the three criteria, and calculate the winner. This is identical to saying Person S has 20% weight and votes solely on safety, Person R has 35% and reliability, and Person F has 45% and fun.
Arrow breaks down here when you change the rules after the vote has taken place, and use your own “dictator power” (in quotes because it has a different meaning than the mathematical one in Arrow) to pick how you bloody well feel. (Maybe this was what you were saying in the first place?)
November 1, 2011, 9:00 amMichael says:
Leo,
With groups, strategic decisionmaking is a concern. But with individual decisionmaking, there is no danger that the criteria will act strategically; the single decisionmaker should be able to report honest valuation of preferences. Meanwhile, Arrow’s Theorem depends on ordinal preferences, rather than cardinal preferences. There may be good reasons for focusing on ordinal preferences in evaluating a legislature, where binary choices must be made at discrete points in time, and where strategic decisionmaking is possible. But in the individual context with no concern of strategic decisionmaking, do we still face a variant of the Impossibility Theorem? Can’t we just cardinalize our accurately reported weights and straightforwardly optimize the individual utility function?
November 1, 2011, 9:32 amSnaphappy says:
Brett Bellmore has it. When you describe “using” a killer amendment, you mean proposing an amendment because you do not want the bill to pass. When you say that a majority “prefers” the amended bill, that majority is made up of people who genuinely support the amended bill and people who only support the amendment because the oppose the bill in any form. And likewise the people who oppose the amendment also include people who would really support the amended bill, but realize that it’s unlikely to pass in that form. All this is to say that I think there’s plenty missing in this analysis.
And the analogy to loopholes is not satisfying at all. Your examples of “loopholes” yesterday were not legal doctrines, they were statutes — bankruptcy and immigration. I have no idea what you mean that those supposed “loopholes” are like killer amendments. Do you mean that the idea of asylum was introduced to kill some immigration bill, or that a given state’s homestead exemption to bankruptcy was intended to kill that state’s bankruptcy law? That is nonsensical. Or perhaps you mean that God put “letting a gentile turn on the lights” in to the commandments in order to kill the “Keep holy the Sabbath” commandment? Also, you still haven’t defined “loophole,” which would be useful here.
All in all, I’m becoming less likely to buy your book, your daily plugs notwithstanding, because I imagine its more of the same quallity analysis I’ve seen here.
November 1, 2011, 9:38 amRobert says:
That’s what I was trying to convey in the previous thread, thanks.
November 1, 2011, 9:54 amsilverpie says:
I just looked up Arrow’s theorem, and can explain how the car scenario gets around it. Arrow’s theorem assumes that the information on voting is limited to having each voter rank the choices. Our car buyer has introduced what is called “cardinal utility,” or in other terms, the strength of his preferences. This fails in voting scenarios because it requires comparing the strengths of preferences across individuals (which is not workable–the technical term is “interpersonal comparison of utility”), but a single person deciding on multiple criteria can certainly do so.
November 1, 2011, 10:17 ambyomtov says:
GF23,
Your car example seems to depend on the use of an actual numerical score for each attribute. If you are working just with preferences I think life gets harder.
November 1, 2011, 10:21 amDebrah says:
This is all endlessly fascinating and I find Professor Katz’s posts riveting in the requisite multi-layered complexity — mille-feuilles (“one thousand leaves”) — of an educational overseer most interested in the activity of scholarship.
Unfortunately, this elaborate exercise also reveals — by accident or by design — the ever-present lack of probity inside the law profession.
At its very core.
November 1, 2011, 10:28 amAF says:
I still don’t know what Professor Katz means by “loophole.” I’m reasonably confident that under some definitions of loophole — those analogous to a 0% tax rate on taxpayers making exactly $250,000 because the statute only provides tax rates for people making over or under $250,000 — loopholes can indeed be explained by the mismatch theory. If telling clients to take advantage of an explicit statutory safe harbor is considered a loophole, I’d agree that’s not a question of mismatch, but I wouldn’t agree that’s a loophole.
November 1, 2011, 10:44 amParadox says:
November 1, 2011, 11:02 amParadox says:
November 1, 2011, 11:02 amAnthony J. Lawrence says:
Agreed. It seems that his definition is incredibly broad as compared to our former intuitive sense. When broadened in such a way, his observations regarding voting theory and legal doctrines may have some salience, irrespective of traditional “loopholes” and the mismatch theory.
Based on what I’m reading, though, I’m not seeing a reason to set-up the mismatch theory in this way only to try to knock it down. All of these examples, as per the broadened definition of loopholes, appear to be describing somewhat different phenomena.
The killer amendment does not in any way strike me as a “loophole.”
November 1, 2011, 11:34 amyankee says:
At least in the context of the tax code, “loophole” is commonly used as a simple pejorative. A few months ago there was a debate over whether or not to eliminate the “corporate jet loophole,” which allowed private planes to be depreciated faster than other capital goods. This wasn’t a drafting accident: it was put there on purpose at the behest of industry lobbyists. That didn’t stop critics from calling it a “loophole.” I’d say this is pretty common: if you want to criticize a provision of the tax code, you call it a “loophole.”
On the other hand, nobody would ever refer to the mortgage interest “loophole,” because that deduction, unlike favorable treatment for private jets, is very popular.
November 1, 2011, 11:43 amBL1Y says:
I agree, this doesn’t really have the loophole feeling to it.
I would say that introducing a killer amendment is an abuse of the amendment process, similar to voters crossing party lines in a primary to make sure that the opposing party ends up nominating a weaker candidate, but is that really a loophole?
From Wikipedia:
I suppose this does fit that definition, but when I think of a loophole, I’m picturing circumvention of a more strict or sophisticated set of rules. A broad rule, such as saying you can introduce whatever amendment you want isn’t so much a loophole as just a hole.
November 1, 2011, 11:46 amyankee says:
It depends what properties you want your ordering to satisfy. You can impose an arbitrary ordering on any set, and if you accept the Axiom of Choice you can impose a well-ordering on any set. But no ordering of the complex numbers will satisfy the properties of an ordered field.
November 1, 2011, 11:52 amBL1Y says:
Similar to the killer amendment, you can circumvent the new SEC rules for nomination of board members by minority shareholders.
Minority shareholders get a certain number of nomination slots (combined among all minority shareholders, not slots for each person), and they’re designed to facilitate bringing in challengers to the current board membership. But, it’s easy to circumvent. Certainly a number of minority shareholders are just fine with the current board, and they can either put up a killer nominee, whom no one would vote for, or a clone nominee, who will vote the same way as the current board (George Wallace is on the board, so you nominate Lurleen).
Going a bit off topic now, but a fix to this ‘loophole’ is to require anyone who nominates someone to either vote for that person, or not vote at all. This doesn’t hurt anyone who nominates a candidate in earnest, but discourages killer/clone candidates, because now you cannot vote for your real top choice; at best you’re now splitting votes between George and Lurleen, which may result in neither getting enough.
I don’t know if that fix can carry over to legislation though. Perhaps a rule that if you propose an amendment and it passes, you are prohibited from voting Nay? Only Aye or abstain? That may be heavy handed and hurt people who propose amendments in earnest, but it would seem to discourage killer amendments.
November 1, 2011, 11:54 amToby says:
What If you liked A, but would like it better if B (and made that amendment) but then amendment C came along and now you hate the whole thing. This would merely lead to a whole new way of gaming, i.e., get those guys locked in with a broad-based Amendment B, and then we propose the C that we want, safe in the knowledge that those guys cannot attack because they voted for the overall…
Seems like this would just create new problems.
November 1, 2011, 12:12 pmBL1Y says:
Toby: Right, that’s why I thought it was a bit heavy handed in regards to people proposing in earnest.
There’d also be a situation where I Really Hate the proposal, propose an amendment that improves it, though I still Kinda Hate it. For instance, the federal government proposes a 2% national sales tax. I hate it, but think it’s going to pass, so I add an amendment that would make food products exempt. I’m adding the amendment because I genuinely think that would make the law better, but I’m still opposed to the law even with the amendment. I should be allowed to vote against the law.
Perhaps a system where you can vote Aye, Nay, or Aye But For This Amendment? If a majority votes Aye But For, it passes without the killer amendment. If some smaller amount, say 1/3, votes Aye But For (and there’s not a majority straight Aye votes), then the bill is put up for another vote immediately, with the killer amendment removed.
November 1, 2011, 12:37 pmAnthony J. Lawrence says:
In the last post, Katz said:
Here, he says that “loopholes” are a product of multi-criterial decision- making, i.e., if I understand correctly, that there is no way to reflect the underlying purpose perfectly (either because it doesn’t/can’t exist or because, paradoxically, there isn’t one), hence there will always be “loopholes.” But the more I look at it, I’m not seeing this explanation as substantially different from the mismatch theory. We’ll always disagree on the underlying purpose of the rule as long as the rule is in any way beyond extreme simplicity or basic complexity and arrived at by multi-criterial decision-making. How one characterizes the purpose(s), determines whether one sees the loophole as a loophole.
Take the recurring originalism debates, for example. Underlying purpose or original intent/understanding is at the core what makes any perceived deviation from it illegitimate or loophole-ish.
Look at Laura’s immigration example from the last thread: Was her daughter’s date abusing the immigration system or simply using it?
What is the purpose of football? We had a large amount of answers for this seemingly simple question back in those threads.
What is the purpose of a legislature? What is our theory of democratic legitimacy? Parliamentarian procedure? All these antecedent questions inform our view on whether or not the killer amendment is dastardly and loophole-ish.
Again, my point is that I’m increasingly seeing the observations on so-called loopholes as a complex explanation of the mismatch theory rather than a refutation of it.
November 1, 2011, 12:55 pmRobert says:
>30 yrs. ago I worked briefly for a Chi. market research co., Market Facts, whose president was a mathematician who’d worked out an algorithm for turning ordinal data (order of preferences) into cardinal data (strength of preferences). I’ve got his paper somewhere.
November 1, 2011, 1:01 pmMark N. says:
Arrow’s theorem does show that any voting system must permit some loophole, though, if you agree with Arrow’s statement of the desiderata for a loophole-free voting system, which he proved impossible to satisfy. Better systems than our current system, sure, but no loophole-free ones (unless you disagree with what he defines as loophole-free).
November 1, 2011, 1:06 pmyankee says:
I think this is wrong on two levels.
First, Arrow’s theorem isn’t about voting systems, it’s about the aggregation of total orderings into another total ordering. This describes only a very narrow class of voting systems. There are a bunch of theorems that show that no voting system satisfies every desirable criterion, but Arrow’s theorem isn’t one of them.
Second, I don’t think failure to adhere to Arrow’s criteria is in any sense a “loophole.”
November 1, 2011, 1:20 pmarch1 says:
“all laws, so long as they involve the application of a multiplicity of criteria, which is true of virtually all laws, are bound to be vulnerable to loophole exploitation.”
Leo, I can well believe that a proof of this won’t fit in a blog, but a concrete example should fit with room to spare, and greatly assist our understanding of your terminology and of the assertion itself.
Can you describe an “underlying intent” involving (say) two criteria for which a loophole-free law can’t be crafted? (Of course if the assertion’s true, this should be easy-peasy; any example will do:-).
November 1, 2011, 1:43 pmGF23 says:
Yeah, the well-ordering (assuming AC) was what I was thinking of.
And agree on the ordered field point, but I don’t think we necessarily need to bring in fields for decisionmaking. I’m not sure, when I’m trying to buy a car, that I care about whether a Roadster plus a Boxster is greater than a Countach squared.
I was trying to show a counterexample to the argument that any method of aggregating will be vulnerable to intransitivity, not a counterexample to Arrow’s theorem. I agree with you that it’s not a counterexample to the latter.
November 1, 2011, 2:45 pmParadox says:
I’m generally aware of the topics you’ve raised; I did quite a bit of work on them while pursuing my doctorate.
However, I’m not aware of the ability to impose an ordering (not necessarily a well-ordering) on any set; I’m inclined to doubt it, remembering the construction of a well-ordering given the Axiom of Choice. If you have a citation for this, it would be appreciated, since it’s pretty interesting to me otherwise.
Meanwhile, the acceptance or rejection of the Axiom of Choice is at best highly problematic. Most mathematicians, at least, won’t accept proofs which involve that Axiom, and it’s not precisely correct to make mathematical statements without explicitly sating that you’re accepting the Axiom.
November 1, 2011, 2:56 pmyankee says:
For decision-making I think an “ordinary” ordering is more than sufficient–there’s no need to drag the Axiom of Choice into it!. We don’t even need an ordering, just a way of selecting one option from a set of options. But there’s no voting system that satisfies every “desirable” criterion: see this chart from Wikipedia for a comparison.
November 1, 2011, 3:01 pmAssistant Village Idiot says:
I think the simplest cases are being conveniently left out. There are sometimes laws, or preferences, or decisions, which are favored by an overwhelming majority. Attempts to get around that are what people usually mean when they think of loopholes or technicalities. We don’t want them, and we are quite justified in that. That situations exist at the margin which can be gamed, and this is possibly even unavoidable under any system, doesn’t change that. That gaming can also be called exploiting a loophole, and a critic could well say “See, you like loopholes just fine sometimes. Get over your loophole prejudice.” That would seem to be largely a semantic discussion at that point, whether one things that all gaming is a loophole and unethical or only some of it.
But some of it is clearly unethical. We don’t want to appoint frogs as hog reeves (or hogs as frog reeves), and any attempt to get under the radar of our statute forbidding animals from serving as town officers is unethical. Pointing out that the police use dogs is irrelevant, an attempt to abuse reason in the service of something unreasonable. Some things that people call loopholes or technicalities are in fact sometimes reasonable. That does not mean they are always reasonable, nor that no abuse is possible.
All systems will have gray areas. Yes. What of it? That does not mean that all decisions are gray. (Tangentially, whenever someone tells you there is no black-and-white, he is always trying to get you to choose a darker shade of gray.)
I am finding the posts interesting, but not persuasive.
November 1, 2011, 3:11 pmyankee says:
I’m afraid I don’t have a citation. It may depend on how “ordering” is defined. If indifference is allowed (i.e. a >= b and b >= a, but a != b), then any set can be trivially “ordered” by saying a >= b for all a, b.
November 1, 2011, 3:20 pmrfhirsch says:
A clearer statement of the car example is this:
Our family visits a car dealer looking for a sedan to hold all five of us comfortably. Among the several sedans at the dealership we unanimously vote to buy the blue one. Then one of us notices a car with a ten-speaker sound system. We unanimously vote in favor of this feature (the amendment). However, none of the blue sedans has this option. So we unanimously (again) vote not to buy at this dealer.
November 1, 2011, 3:54 pmPrometheeFeu says:
If you want to take such an aggregation method outside of a single individuals, you need to assume two things:
November 1, 2011, 4:42 pm1) cardinal utility
2) meaningfulness of inter-personal utility comparisons
Both of these assumptions then allow such aggregation. However, such assumptions are generally rejected in favor of preference orderings. Then, even if you get these assumptions, you next need to measure utility. That is as far as we know impossible. At best you can ask someone whether they prefer option A to option B which means you are back to ordinal preferences and non-transitive aggregation.
yankee says:
Generally rejected by economists, you mean. The rest of us are not obligated to accept that principle. Of course, that doesn’t mean we can turn individual utility into specific numbers rather than using a rough-and-ready comparison, but since we don’t know individuals’ preference orderings in the first place, ordinal preferences are not actually any more useful. (Also people do not typically have well-defined preferences as defined by economists.)
If we’re dealing with actual voting systems rather than abstract preference relations, we can ask people to assign cardinal values. Of course such systems are vulnerable to gaming, but so are other voting systems.
(The simplest way to vote with cardinal numbers is range voting, in which voters assign a numerical value to each alternative and the winner is the one with the highest sum. However, it turns out that the optimal strategy is to give each option either the highest possible score or the lowest possible score, making it equivalent to approval voting.)
November 1, 2011, 5:04 pmDale Sheldon-Hess says:
For a treatment of this that directly addresses voting in the United States, I recommend “Gaming the Vote” by William Poundstone (2006). He covers Arrow, Borda, Condorcet, and settles on approval voting (that, or range voting, which is just approval w/ more than 2 levels).
Even though there is no precise mathematical way to adjudicate interpersonal comparisons of utility, in practice (or at least in vast simulation) it works out significantly better than any rank-order based system.
November 1, 2011, 5:08 pmAndrew MacKie-Mason says:
Inter-personal comparison of utility is a very suspicious idea. It’s true that we don’t *have* to accept it, but it would take a pretty compelling argument to make it seem plausible. What does it even mean for me to want something “the same amount” as you do?
November 1, 2011, 5:09 pmMike s. says:
This is complete nonsense. Arrows theorem holds, fundamentally, because the different voters may rank the choices in different orders in an arbitrary way, so there is no voting scheme satisfying all the criteria. But a single person making a decision based on multiple criteria will still, unless he is insane, rank his choices in a transitive way no matter how many criteria he considers. This is fundamentally different from the case of the killer amendment where the majority favoring each of the possible approaches does not consist of the same people.
Also, approval voting schemes do not avoid Arrows paradox.
Finally, it doesn’t pass the giggle test. Does any one really believe that the reason one can get asylum by deliberately inviting persecution is anything other than that the legislature really didn’t think anyone would do that just to get a green card?
There are many kinds of loophole. Some occur because the legislature either didn’t consider them or didn’t find a good way to write a tighter law. Others occur because at least some fraction of the legislature considers them good features rather than loopholes. Still others because corrupt legislators put them in for connected parties to exploit. Trying to make a general theory is a mistaken notion from the get go.
November 1, 2011, 5:36 pmAnonymous Coward says:
The primary criteria used by legislators when deciding how to vote on a bill or amendment, killer or otherwise, is:
How will this vote affect my re-election?
November 1, 2011, 5:40 pmyankee says:
It’s not that they “avoid” Arrow’s theorem so much as that Arrow’s theorem doesn’t apply. Arrow is about attempts to map a set of complete orderings to another complete ordering: approval voting maps sets of acceptable options to a single winner (though it can be used to generate a total ordering if you want). I’m not sure if a modified version of Arrow can be used on approval voting.
November 1, 2011, 5:51 pmLee Moore says:
A bit like yesterday, I am not managing to go very far with the good Professor, because he always starts by smacking me round the face with a wet fish. Surely it is obvious that not everybody who votes for something is in favor of it ? Do not libertarians grit their teeth and vote Republican from time to time ? And socialists Democrat ? Hence the paradox of voting isn’t a paradox at all. Some of those voting for a killer amendment will actually favor what the amendment proposes, but will judge that the amended proposal will still pass. Others who vote for it will oppose what it proposes, but will judge that the amended proposal will fail to win a majority. Different perceptions of how future votes might go are quite sufficient to explain what is going on. Moreover, even if all legislators had perfect knowledge of how everyone would vote on the amended proposal, that still wouldn’t necessarily prevent some true believers in the amendment joining the wannabee killers in voting for it, and knowingly dooming it, and the original proposal. Because they may have other motives for voting besides getting things into legislation. They may want to make a statement. They may be unable to vote against their conscience. And so on. If they were to vote down the amendment, even though they agreed with it, they would be voting against what they believe for tactical reasons. Which is the precise mirror of voting in favor of things you oppose, for tactical reasons.
November 1, 2011, 7:59 pmDan Lavatan says:
I don’t think there are any theorems that show you can’t satisfy any desirable criterion. Once you abandon determinism, it should be fairly easy to come up with a reasonable system. After all, like isn’t deterministic.
November 1, 2011, 9:33 pmKirk Parker says:
EMB
And… the notion “majority” disappears from this formulation. I hope the absence of your pointing this out is unintentional.
Also, I’ll join AF in calling for a better definition of “loophole”. The example of a 0% tax rate seems to show a complete accident (which could even be the result of a typo, cf. the “Adulterer’s Bible”), but too often in common usage “loophole” merely means “complying with the law by behaving in a manner I wish were also banned.”
November 2, 2011, 10:31 amOvercoming Bias : More Random Hypocrisy says:
[...] Katz has a new book that also explains legal hypocrisy as mainly accidental. He says that when we make decisions based [...]
November 6, 2011, 8:57 am