Subject: RISKS DIGEST 12.31 REPLY-TO: risks@csl.sri.com RISKS-LIST: RISKS-FORUM Digest Thursday 12 September 1991 Volume 12 : Issue 31 FORUM ON RISKS TO THE PUBLIC IN COMPUTERS AND RELATED SYSTEMS ACM Committee on Computers and Public Policy, Peter G. Neumann, moderator Contents: Re: Export controls on workstations (Neil W Rickert, Brinton Cooper, Haakon Styri) "Checkless society" (Daniel B Dobkin) Re: Multinational Character sets (Dik T. Winter, Robert Ullmann, Hugh Davies) Re: +&*#$ (Mike Morris) Re: M16 and James Fallows' "Two Weapons" (Jon Jacky, Tom Faller) Junk Mail -- In memoriam, Dave Sharp (Peter Mellor) Risks of assumptions? (R. Cage) The seriousness of statistics mistakes (Jeremy Grodberg) Risk Assessment: a specific experience (Justine Roberts) Re: risk analysis (Victor Yodaiken) Averages and distributions (Jerry Leichter) The RISKS Forum is moderated. Contributions should be relevant, sound, in good taste, objective, coherent, concise, and nonrepetitious. Diversity is welcome. CONTRIBUTIONS to RISKS@CSL.SRI.COM, with relevant, substantive "Subject:" line. Others ignored! REQUESTS to RISKS-Request@CSL.SRI.COM. For vol i issue j, type "FTP CRVAX.SRI.COMlogin anonymousAnyNonNullPW CD RISKS:GET RISKS-i.j" (where i=1 to 12, j always TWO digits). Vol i summaries in j=00; "dir risks-*.*" gives directory; "bye" logs out. The COLON in "CD RISKS:" is essential. "CRVAX.SRI.COM" = "128.18.10.1". =CarriageReturn; FTPs may differ; UNIX prompts for username, password. ALL CONTRIBUTIONS CONSIDERED AS PERSONAL COMMENTS; USUAL DISCLAIMERS APPLY. Relevant contributions may appear in the RISKS section of regular issues of ACM SIGSOFT's SOFTWARE ENGINEERING NOTES, unless you state otherwise. ---------------------------------------------------------------------- Date: Wed, 11 Sep 91 13:09:29 -0500 From: Neil W Rickert Subject: Re: Export controls on workstations (Markoff, RISKS-12.30) This proposal should properly be referred to as the "full employment for people in Singapore, Taiwan, Hong Kong and Japan" bill. Neil W. Rickert, Computer Science, Northern Illinois Univ., DeKalb, IL 60115 +1-815-753-6940 ------------------------------ Date: Wed, 11 Sep 91 16:40:24 EDT From: Brinton Cooper Subject: Export controls on workstations (Markoff, RISKS-12.30) The real absurdity here is the chauvinistic attitude in DoD that US-made computer workstations are the only "inexpensive but powerful" products on the world market or that such US-made products are even cost-competitive. The net result of such export controls may be one more nail in the coffin of US-based manufacturing and is likely to do absolutely nothing to thwart terrorism. The computer-based RISK here is based upon permitting morons to make decisions about computers. _Brint ------------------------------ Date: Thu, 12 Sep 91 12:23:59 BST From: Yu No Hoo Subject: Re: Export controls on workstations (Markoff, RISKS-12.30) Why not? The european computer industry probably need something like this to get a comeback. To have DoD creating a niche in the market sounds like a nice thing to me. The end result for the DoD paper pushers will probably be *less* control. Haakon Styri styri@cs.hw.ac.uk ------------------------------ Date: Thu, 12 Sep 91 10:30:28 EDT From: Daniel B Dobkin Subject: "Checkless society" The 11Sep91 New York Times carried an article on the first business page about the growing use of imaging systems by banks: instead of returning cancelled checks to the customer, they return scanned images (sometimes as many as eighteen on a page). This form of confirmation has been familiar to American Express customers for some time now. To be sure, the technology offers some advantages: for example, the images can be reduced, or they can be enlarged for sight-impaired customers; they are reproduced on standard cut-sheet paper, which can be drilled for use in a ring binder. (The banks' marketing people see even more advantages: offering free binders to new customers, printing on drilled paper, printing marketing messages between the checks; the list goes on and on.) Many banks offer reduced fees to customers who choose this option; indeed, the article reports that further fee reductions are offered to customers who don't want any checks (scanned images or otherwise) returned to them at all. If a cancelled check becomes necessary (as proof of payment, in case of a dispute with a credit card company, etc.), the bank will provide an image free of charge. There was some discussion here lately of the ease with which bogus checks can be created by use of relatively cheap technology (laser printers and desktop publishing software). It seems that as the imaging technology gains more public acceptance, and as the banks push it more aggressively to reduce the costs of check processing, that there is a further RISK: if the scanned images are acceptable proof of payment, can the use of the same cheap technology to create bogus records be far behind? \dbd ------------------------------ Date: 12 Sep 91 01:55:00 GMT From: dik@cwi.nl (Dik T. Winter) Subject: Re: National characters on car plates Torsten Lif writes about the possible risk because Finnish car plates from the A*land Islands (to follow his spelling) have a national character, and wonders what problems that might give in other countries. I think the problem is moot in this case, as there are (as far as I know) no duplicates in Finland, whether you leave off the ring or not. There is however a serious risk for people from Yugoslavia. One of their national characters is S with hajek (an upside down circumflex). There are indeed cars where the single distinction between two number plates is that hajek. E.g. cars from Sarajevo always start with the letters SA, while cars from Sabac also start with SA, but there the S has a hajek. By the way, in Torsten Lif's own country (Sweden) until recently no national characters were used on car plates (A ring, A diaeresis and O diaeresis). With the introduction of vanity plates these are allowed, which again might result in confusion. dik t. winter, cwi, amsterdam, nederland dik@cwi.nl ------------------------------ Date: 11 Sep 91 14:11:16 EDT From: Robert Ullmann Subject: re: Universal Character Set What Hugh Davies and Kim Greer write on character sets (RISKS 12.30) was mostly correct, but is now out of date. An ISO working group is working on a new version of DIS10646 (to eventually be IS10646) a multi-byte code set that attempts to be comprehensive, and will be extensible. The Unicode Consortium and the ISO WG have agreed to merge their efforts, to create one (draft) standard. (The previous DIS10646 failed in the balloting for, among other things, not addressing Unicode: several NO votes, including the U.S., stated that having two different codes, 10646 and Unicode, was not acceptable). One of the proposed representations of the code set is "upward compatible" with ASCII-7, and useable in mail (with 8-bit support). (Send a message to ISO-Char-Subscribe@List.Prime.COM to subscribe to a demonstration list.) Two other points: there is a (set of) 8 bit sets defined by IS8859, which "solve" the substitute character problems that Davies laments (created by ECMA-35). 8859 is used by (among other things) Xwindows and Postscript version 2. (Of course, lots of people still use ECMA-35) The ASCII/EBCDIC problem is "solved": SHARE (the IBM users group) has defined an invertible (reversible) mapping table, used by BITNET to Internet gateways. (I will supply a copy to anyone who wants it) Robert Ullmann, Prime Computer, Inc. +1 508 620 2800 x1736 ------------------------------ Date: Thu, 12 Sep 1991 02:21:37 PDT From: hugh_davies.wgc1@rx.xerox.com Subject: Re: Multinational Character sets Firstly, an apology, related to the topic under discussion. In my last posting, I used a dagger character to reference the footnote on the XCCS. I am writing this on a Xerox 6085 workstation, which uses the XCCS character set, and I forgot that the dagger would not be translated correctly by our mail gateway, so a string of weird characters appeared in the digest. A case in point, as if we needed one. Secondly, klg@george.mc.duke.edu (Kim Greer) writes; > Perhaps we have overlooked the risk of forgetting the origin of words and >what an acronym *originally* meant. "ASCII", as we all remember, stands for >American Standard Code for Information Interchange, the key word being >"American". Would it not be stretching things a bit to expect >non-"American" language nuances (like umlauts) to automatically fit in? This would be entirely true, except that American computer manufacturers cheerfully exported their computers all over the world, without making any changes for the local language. It was ASCII or nothing. (Or EBCDIC or nothing!). They also didn't (and in most cases, I suspect still don't) translate their manuals into the local language. You don't read (American) English? Tough. Perhaps this should be considered as another RISK that I hadn't considered? What happens when a standard is applied well outside it's original area? In the case of ASCII, the shambles we have today. The fact that the 'A' in ASCII stands for "American" is irrelevant today. I suspect there are far more ASCII based computers outside America than inside it, and it's about time that we all realised that it is quite simply not good enough to expect a customer to learn a foreign language in order to use a product. You might also like to think about the fact that the majority of the people in the world don't speak English anyway. Does *your* computer "do" Pin-Yin and Cyrillic? (Mine does!) Incidentally, the designers of ASCII wrought better than we might think. The ESCAPE character is supposedly intended to allow a system to insert non-ASCII characters (to "escape" from the ASCII set). Pity it's never used that way. Hugh Davies, Rank Xerox, Multinational Customer & Service Education- Europe, Welwyn Garden City, Herts. England. ------------------------------ Date: Thu, 12 Sep 1991 08:26:10 GMT From: morris@grian.cps.altadena.ca.us (Mike Morris) Subject: Re: +&*#$ (Moore, RISKS-12.21) >... the computer (in Topeka, KS) would not accept a license number of WA0DVD This is true in California - which has a 7-character plate format. My amateur radio callsign has 6 characters (note that ham calls can be from 4 to 6 characters). _Almost_ all the dispatchers know that a plate of less that 7 characters includes a trailing space by default. If you run my callsign plate on the state DMV (Dept of Motor Vehicles) computer as WA6ILQ or WA6ILQ it comes up just fine. If you run it as WA6ILQ, or WA6ILQ, or any other combination, it comes up with "Record not on file". This has caused me serious problems. Once I was pulled over by a cop who was as fascinated as I was when my plate wouldn't come up and we spent some time with his patrol car terminal discovering this quirk. You can imagine the reaction I get now when I tell the cops "Tell the dispatcher to run it as 'WA6ILQ'". And it works. Mike Morris WA6ILQ PO Box 1130 Arcadia, CA. 91077 818-447-7052 evenings ------------------------------ Date: Wed, 11 Sep 1991 12:02:29 -0700 (PDT) From: JON@GAFFER.RAD.WASHINGTON.EDU (Jon Jacky) Subject: Source for Fallows' "Two Weapons" "Two Weapons" (about the M16 and F16) is a chapter in James Fallows' book, NATIONAL DEFENSE, Vintage Books, 1982. I think the hardcover edition was from Random House, 1981, but I'm not sure. Much of Fallows' book is a critique of technically complex weapons systems, which many RISKS readers would find interesting. Another excerpt from the book, describing Fallows' boyhood visit to a SAGE installation, appeared in RISKS a few years ago. - Jon Jacky, University of Washington, Seattle jon@gaffer.rad.washington.edu ------------------------------ Date: Thu, 12 Sep 91 09:10:10 CDT From: tomfal@tr6.wes.army.mil (Tom Faller) Subject: Re: M16 and James Fallows James Fallows article "Two Weapons" is actually a chapter of his book "National Defense". The book discusses the perceptions used if forming a national defense policy, shows where these conflict with reality, and how the average person mistakenly perceives military life and its tools, and discusses trends in future military policy. The book just went through a revised edition, I believe. Other good books on this subject include James Dunnigan's "How to Make War", and a book called "The Great Rifle Debate", by an author whose name I forget, but who does an excellent job of showing how the military armorers mind works. The tie-in with computers is that most of these books include examples of sloppy war-gaming, over-reliance on favorable models, and a "if it's got more electronics, it's got to be better" attitude. A little-discussed fact is brought out; our own electronic Maginot Line, electronic, "smart", warfare. One thing nobody wants to admit too loudly is that we may be back to rifle-based warfare real soon if attacked with a nuclear weapon, due to the Electro-Magnetic Pulse (EMP) given off by a nuclear explosion. There are estimates that one good nuke, exploded in near-space over Kansas could fry most of the missile controls, computers, radios, phone switches, smart weapons, late-model automobile engine electronics, and other items this country depends on, nearly coast-to-coast. Nobody's really sure how serious this is, although a lot of testing and "hardening" goes on. And it's a losing game trying to keep ahead by shielding, a bigger bomb is just a lot cheaper than building defenses against it. There's some concern that any nuclear war will only last until the first few shots, as they will screw up the rest of the system, and any other missiles in the air. It kind of acts as a deterrent if you know that you only get one shot at it, and then you have to rebuild your arsenal from the chassis up. Tom Faller ------------------------------ Date: Wed, 11 Sep 91 19:52:16 PDT From: Pete Mellor Subject: Junk Mail -- In memoriam, Dave Sharp My apologies if this is of marginal relevance to the main subject matter of the lists to which I have mailed it. UK readers might be interested to watch the forthcoming edition of Equinox on Channel 4 this coming Sunday, entitled "Junk Mail". It was originally scheduled for 14th Oct., but was announced last week to be broadcast on 15th Sep. (I forget the time at which it will go out.) The blurb on the advertising postcard reads: "How much do direct marketers know about us and how do they get our names? Why would they want to put a brightly coloured fish in our mail?". (Photo on reverse of strange-looking man holding the fish in question over a glass of water.) The programme was produced by Orlando Television Productions Ltd., for WGBH Boston in association with Channel 4. Orlando was essentially Dave Sharp. As well as being a very good friend of mine, he was an extraordinarily talented film maker, and his one-man company established an excellent reputation for scientific (and other) documentary films. "Junk Mail" promises to be a very witty and thought-provoking piece of TV journalism. It is one of the last films Dave completed before his untimely death in the collision between a 737 and a private aircraft at Los Angeles in February this year. My thanks to those who responded to my e-mail request for information about the accident. Peter Mellor, Centre for Software Reliability, City University, Northampton Sq.,London EC1V 0HB +44(0)71-253-4399 Ext. 4162/3/1 p.mellor@uk.ac.city (JANET) ------------------------------ Date: 11 Sep 91 21:58:31 GMT From: fmsrl7!wreck@sharkey.cc.umich.edu (R. Cage) Subject: Risks of assumptions? (Re: Chase, RISKS-12.28) >People don't compute the crash-safety of new automobiles (well, I'm sure that >they do at some early stage), they run them into walls to see what happens. As it turns out, this is almost exactly backwards. Running a car, especially a hand-built prototype car, into a wall is horrendously expensive. Exercising a FEA model inside a Cray is very cheap in comparison, and it takes a lot less work to reconstruct a computer model after a crash, or modify it to work better. About the only crash-testing we do these days is to confirm the results of the computer models. The sanity-checking is done; we have no chance of GIGO resulting in bad products getting out. The effectiveness of the models is a result of a great deal of work in building and testing them. It's a good thing that the properties of sheet metal are not very difficult to determine. Having people just assume that climate models, or drug models, or population models are just as reliable is, IMHO, a big RISK. Russ Cage wreck@fmsrl7.srl.ford.com russ%rsi@sharkey.cc.umich.edu ------------------------------ Date: Wed, 11 Sep 91 20:33:05 PDT From: jgro@lia.com (Jeremy Grodberg) Subject: The seriousness of statistics mistakes RISKS-12.28 contained two instances of statistical fallacy, the less important of which was corrected in 12.29, and for which the moderator referred us back to earlier threads to which I had contributed. Lest you think I whine about people's misuse and misunderstanding of statistics just so I have something to complain about, I want to point out that the second statistics mistake was truly a life-or-death decision. In RISKS-12.28, Mark Fulk writes: >The Maternal Serum Alfa-fetoprotein (MSAFP) test is administered to pregnant >women in order to screen for a broad range of congenital defects of the fetus >[which I will simply call "the disease" -- JG][...] Let's presume Mr. Fulk's base data is correct, that the MSAFP has a 10% False Positive, is confirmed by amniocentesis which carries a 1% chance of inducing abortion, and let's also say that the chance that someone taking the test actually has the condition tested for is 1 in 10,000, which the high end of the risk range he gives. I believe he made the wrong decision about having the test based on an incorrect analysis of the data. He claims a .1% chance of the MSAFP leading to a inadvertent abortion of a healthy fetus. I can only guess that his reasoning was: 10% of people taking the test have healthy babies but will test positive, and 1% of that 10% will lose their babies because of the amnio, and 1% of 10% is .1%, so there is .1% chance of killing a healthy fetus. Unfortunately, this analysis is wrong, because of an important, less common error (which is becoming more common as people deliberately try to mislead with statistics): misunderstanding the definition of a statistic. Mr. Fulk made his mistake when he assumed a 10% False Positive rate meant that 10% of the people taking the test get positives that are really negative. However, it actually means that 10% *of the positive results* are really negative. Putting this together with the 1 in 10,000 chance for a True Positive, we come up with a 1 in 90,000 chance of taking the test and getting a False Positive (90,000 / 10,000 is 9 True Positives, which generates 1 False Positive), or a 1 in 9,000,000 chance of the MSAFP test leading to the death of a healthy fetus. Thus the test will detect 900 afflicted babies for every 1 healthy one it harms. This is the real decision making criterion, and speaks much more highly for the utility of the test. Let me quickly add that the above analysis is inaccurate (but close), because I don't have all the necessary data. False Negatives need to be factored in correctly (which can be tricky), and there may be other data which is a better basis for predicting the possibility that a specific individual (such as a 29 year old healthy woman) will have a false positive versus having the disease. Also, a True Positive refers to someone who has the disease and tests positive, which is a subset of the people that have the disease, although the above analysis assumes that they are one and the same (no False Negatives), which Mr. Fulk tells us is not correct. My point is that the above analysis brings us a lot closer to the best information than Mr. Fulk's did, because of one simple mistake he made. There are a number of other interesting aspects to this story which I want to point out, in no specific order. Medical professionals have difficulty with these statistics, too. I asked a few people who have been involved with clinical drug testing (where the data for such statistics is gathered and analyzed), and none of them were sure off the top of their head of which of the two versions of % False Positive was correct, although they all knew where to look it up, and most made the right guess. Clearly the people Mr. Fulk talked to were not conversant enough with the statistics to correct his mistake. What is worse, for some reason (which I leave to the reader to wonder about), Mr. Fulk did not find it unbelievable that his doctor would recommend a test which was 10 time more likely to kill his fetus than the disease was (.1% or 1 in 1,000 by Mr. Fulk's analysis, vs. 1 in 10,000 for the disease), and 1,000 times more likely to give an erroneously positive result than it was to detect the disease (10% or 1 in 10 vs. 1 in 10,000). I'm surprised and dismayed that he did not notice this and check further to find his mistake. Although we in the General Public have problems with statistics, our medical and scientific establishment, through researcher care, peer review, and governmental regulation have a very good record on handling the statistics carefully and correctly before the medical public policy decision is made. If the test was as bad as Mr. Fulk thought, standard practice would have been formulated to recommend against testing in his case. For example, because the prevalence of smallpox is so low, you are now more likely to get it from the vaccine than from anywhere else, so only people with higher-than-average risk factors (like people who work around smallpox-infected patients) are given the vaccine. If anything, public policy decisions are more likely to deprive you of beneficial tests because of the monetary cost (e.g. physicals for people in their 20s) than to suggest spending money on tests with high risk/reward ratios. So here is another lesson on the risks and dangers of innumeracy. This is why I'm on a mini-crusade about statistics. This stuff *is* hard, and we can't all be experts on it, but let us at least learn to know when and why we need to ask the experts, what we need to ask them, and what we can do to check on what they tell us. The life you save may be your own. Jeremy Grodberg jgro@lia.com ------------------------------ Date: Wed, 11 Sep 91 20:12:31 PDT From: Justine Roberts Subject: Risk Assessment: a specific experience (Wayner, RISKS-12.29) In RISKS-12.29, Peter Wayner writes that amniocentesis-caused abortions are "a violation of the Hippocratic Oath. The patient died because the doctor was curious..." This is a distortion. The amniocentesis procedure is NOT carried out because a doctor is curious. It is requested by parents and/or recommended by physicians because there is reason to believe that there may be a problem with the pregnancy or the fetus. Any halfway good doctor will inform parents of the abortion risk which accompanies the procedure, and the parents can then refuse the procedure if they wish. Wayner seems to assume that abortions are caused only by human intervention. The percentage of naturally occurring abortions is much higher than 1-2%. Justine Roberts, 152 Sycamore Ave., Mill Valley, CA 94941 jroberts@ucsfvm.bitnet jroberts@ucsfvm.ucsf.edu (415) 388 6814 ------------------------------ Date: Thu, 12 Sep 91 08:03:51 -0400 From: yodaiken%chelm@cs.umass.edu (victor yodaiken) Subject: Re: risk analysis At least some of the Post-Three-Mile-Island nuclear energy risk assessment literature has a, IMHO, properly humble tone. Here are 3 examples (transcription errors are mine, apologies to the authors): The formulation of societal risk as an expectation value runs into difficulties when the probability of the event is low, but the consequence is high if it occurs. In this case, there would be no consequence or a very large consequence. Therefore the use of expectation value does not adequately reflect the real societal risk because the numerical value does not reflect a consequence that would actually occur. [...] The criteria recommended in this article have no fundamental basis. Indeed, there is no fundamental approach to this issue and no way of proving whether any proposed criteria are right or wrong except by using them over a period of time and discovering whether the costs, risk, and other consequences of their use meet the requirements of society. D.J. Higson, Nuclear Safety Assessment Criteria, Nuclear Safety 31-32 April-June 1990 193-185 Finally, and perhaps the most important lesson learned, risk analysis helps recognize questions that can be posed in scientific terms but cannot be answered by science (page 102) Paolo F. Ricci in the Brookhaven/EPRI workshop on "Health and Environmental Risk Assessment" (Pergamon Press, 1985) [In reference to Probabilistic safety analysis methods] The modeling of dependent events, particularly human error and external events, is still less advanced. It should be noted that the qualitative aggregate results of PSAs, e.g. probability for core melt, for releases of radioactive materials or for health effects on the public should not be interpreted as frequencies in a statistical sense, although they are expressed in like units. Rather, probability is a numeral measure of a state of knowledge, a degree of belief, a state of confidence. L.V. Konstantinov "On the Safety of Nuclear Power Plants" Nuclear Engineering and Design 114 (1989) 2 Page 183 ------------------------------ Date: Thu, 12 Sep 91 10:16:34 EDT From: Jerry Leichter Subject: Averages and distributions A recent RISKS article repeated the old platitude that "by definition, half of all people have below average intelligence" (or are "below average drivers", or whatever). This led to the ritual replies, truncated by the editor, pointing out that, if by "average" you mean "mean" (the usual case), then this need not be true. In fact, it's easy to construct distributions that make it "as false as you like". That's all very true, but it's important not to replace one mantra by another. Many measures of the real world have normal distributions. Most deliberately constructed measures have normal distributions, essentially by construction. For a normal distribution, or anything at all close to it, it is a fact that half of all measured values will be below the mean. If you think the "average" in "average intelligence" really refers to "mean", then you need to have a numeric measurement of intelligence to make any sense of the remark. While it's been years since I looked at the literature in the field, all the various IQ scales I know of have very close to normal distributions. (They can't be EXACTLY normal since, if nothing else, an IQ can't be less than 0, and a normal distribution has infinite tails.) For IQ's, "by definition, half of all people have below average intelligence" is true. If by "intelligence" you mean some vague idea about how bright people are, then you can only interpret "average" as a qualitative English term. My Roget's Thesaurus has the following "cluster" under MEAN: mean, middle state, middle ground; golden mean, juste-milieu [F.]; medium, happy medium; average, balance, normal, rule, run, generality; middle term [logic.], mezzo terrine [It.]. Another cluster, under GENERALITY, lists: The generality, average, ruck, run, general ~, common ~, average or ordinary run. From this it's clear that English speakers use average for a cross between "mode" and "median", depending on context. Actually, I'll argue that when we say something is "average", we aren't just picking a sense of "mode" or "median" at random; we are assuming that the two are roughly the same. After all, the rough opposite of "average" is "extreme" or even "unusual". Think about exactly what you are saying when you describe something as of "average" quality. For a purely qualitative "average", a statement about how many items are above or below the average is difficult to interpret. In one way, it's pretty meaningless: Most things will be "average"; if we don't attempt to sub-divide those, then we're only talking about the outliers, which are presumably rare. Saying about half are above and half below the big central block means little. In fact, however, I suspect most people, if pushed to divide things up into, say, three groups - below average, average, and above average - will put more things in average than either of the others, but will put roughly equal numbers in the "above" and "below" groups. This seems fundamental to what we mean by "average". (This would make an interesting and easy experiment. Any social scientists or linguists want to follow up on it?) To the degree that my prediction is right, the statement that "half are below average" isn't quite true, since so many will turn out to BE average; but of the ones that AREN'T average, it WILL be true. If I remember right, the place this issue first came up was the statement that more than half of all drivers (particularly men) believe they are "above average" drivers. It would be quite reasonable for a large fraction of drivers to believe that they are "average or above" - that simply requires a broad, fuzzy middle ground, typical of qualitative measures. But it requires a very bizarre and unlikely measure of driving ability for a large fraction to actually be ABOVE average: It requires that some small number of drivers be EXTREMELY bad. Not only can I see no plausible evidence for this, I can instead see plausible evidence for the opposite: Race drivers and other professionals are clearly MUCH better than most drivers. Mathematics is all well and good, but the APPROPRIATE APPLICATION of mathematics is what's useful! -- Jerry ------------------------------ End of RISKS-FORUM Digest 12.31 ************************