Peter, Setting aside issues of bivalent vs. multivalent logic, let me try to respond to the question of how a Bayesian might reason. It seems to me that how the Bayesian reasoning would go depends on who is doing the reasoning. Take three possibilities:
(1) The Judge - a case comes before a Judge in which the defendant is accused of roller skating in the park on Sunday in violation of city ordinance. The defendant's attorney argues that roller skates are not motor vehicles so the ordinance doesn't apply. How should the Judge decide the case? Suppose there are no precedents and the ordinance was enacted so long ago that no one is really sure what the original purpose was, and there is no agreement today about what the purpose of the ordinance should be. The central concept in Bayesian analysis is _risk_. The Judge's responsibility is to determine to the best of his or her ability whether or not the defendant violated the "spirit of the law", and the Judge can't make exceptions for individual cases. There should be only one consitent interpretation of the ordinance that applies to everyone. So the Judge has two problems: decide what interpretation to give the law, and decide whether the defendant violated the ordinance according to that interpretation. Assume that the main problem is the former, and that the decision will be relatively straightforward once the interpretation is made. The Judge might then enumerate the possible interpretations, much as you have done, and assign (relative) risk values to each along with a likelihood of each risk. Then the Judge makes the decision with the least expected risk. (2) The Council - an item comes before the city council concerning a possible amendment to the "no motor vehicles in the park on Sunday" ordinance, given the many complaints the council has been receiving from persecuted roller skaters. Assume that the council reasons as a whole (through discussion) and in the interest of the city (personal risks and motivations aside). The council must determine the risk involved in allowing or diallowing roller skating in the park on Sunday. Possible risks in allowing skating might be: (i) people are disturbed by the noise (ii) religious people are upset by all the activity on Sunday (iii) people are injured by roller skaters bumping into them (the park is more crowded on Sunday). Possible risks in disallowing skating might be: (i) widespread depression sets in among the roller skaters (ii) a precedent is set that moves the city further down the slippery slope fascist conservatism. Again, risk values might be set for each of the identified risks, and probabilities assigned to them. Then the council decides to allow or disallow roller skating according to which decision gives the least expected risk. (3) The Cop - a police officer walking through the park is accosted by an elderly man who complains that people are roller skating, in explicit disobediance of the ordinance prohibiting the use of motor vehicles in the park on Sunday. The man expects the officer to tell the eject the skaters from the park with a warning, or arrest them if they refuse to comply. The officer knows of the ordinance, but he is not sure whether roller skating is included in the category of motor vehicles. He must decide whether or not to oblige the elderly complainant. If he doesn't, he risks failing to enforce the law. If he does, he risks improperly enforcing the law. Again, a calculation can be made as to which action has the least expected risk. ... One issue I have glossed over, especially in the case of the Judge, is the distinction between what might be called "rule-Bayesianism" and "act-Bayesianism", in analogy to corresponding types of utilitarianism. In evaluating the risk associated with a decision, should one evaluate the risk resulting from the outcome of this particular decision, or should one consider the risk involved in everyone making this same decision when faced with the same circumstances? But I think that gets too far off the point. I'm not proposing to give a definitive Bayesian treatment here, just to indicate what one might look like. I definitely _don't_ think that one ever needs to consider things like "to what degree is are roller skates motor vehicles?". Roller skates may have various characteristics in common with motor vehicles, along with various differences. But these don't combine to give a "net" value of motor-vehicleness. Rather, each characteristic is examined individually according to how it affects the question at hand. And what one ends up with is a _risk of classifying roller skates as motor vehicles_, rather than a value representing the extent to which roller skates are motor vehicles, or a probability or likelihood that roller skates are motor vehicles. Hope this is helpful. Regards, J.P. -----Original Message----- From: Peter Tillers [mailto:[EMAIL PROTECTED] Sent: Thursday, January 01, 2004 10:18 PM To: 'Jason Palmer'; [EMAIL PROTECTED] Subject: RE: [UAI] causal_ vs_ functional models The problem I posed was how one might or should talk about the uncertainty of the following proposition: roller skates are motor vehicles for purposes of an ordinance that prohibits the operation of a motor vehicle in a park on Sunday. Jason Palmer wrote (in part): >There was presumably a reason the ordinance was enacted, for example it might have been thought that motor vehicles disturb the peace that a park is supposed to possess. In that case to determine whether or not roller skates are motor vehicles, we should determine whether or not skating disturbs the peace. The difficulty in deciding the roller skate question presumably comes from the difficulty in deciding whether or not roller skating is a disturbing activity. < Alas, Jason Palmer's suggestion makes the business of interpretation of legal rules such as ordinances and statutes much more simple than it actually is. Consider: there is often only sparse "legislative history," the legislative history that exists often points in different directions, it is often not clear what sorts of phenomena count as evidence of "legislative intent," some observers believe that it is inappropriate or impossible to look behind the words of an ordinance or statute for the actual or true intent of the legislator or legislators, some observers believe that interpreters should assume that the legislator had reasonable intentions or would not have wished to produce invidious or harmful or irrational results, some observers believe that the common law background (in the U.S.) must be taken into account (at least sometimes) when the words of a statute or ordinance are construed, some observers simply assert that words in a statute or ordinance should be given a reasonable construction, etc., etc., .... And the validity of all of these and many other approaches to the interpretation of legal material such as ordinances and statutes is the subject of much debate ... and the empirical benchmarks (if any) that any one of these approaches (incoclusively!) suggests or implies are often or always inconclusive and, worse yet, they are often non-existent, unknown, or unavailable. *** To be a bit more concrete: imagine the possible interpretive complications & issues if any one of the following conditions holds: 1. Some city council members ("CCMs") on the city council that enacted the "motor vehicle in the park on Sunday" ordinance said (at one point, in any event) that the purpose of the ordinance was to keep noise levels down while some other CCMs said (at one point) that the purpose of the ordinance was to limit air pollution while other CCMs said that the purpose was to minimize the risk of physical harm to users of the park on Sunday whereas other CCMs entertained (at one point but not at anther point) rather catholic views of the purposes of the ordinance and said that the ordinance had all of the purposes mentioned at one time or another by other CCMs. 2. CCM-1 said in city council chambers that the purpose of the ordinance was to keep noise levels down in the park on Sunday but in a news conference CCM-1 said that she voted for the ordinance only because the religious sensibilities of her constituents are offended by motorized traffic in the park on Sundays. 3. Steel roller skates make much more noise than plastic roller skates but Honda Accords make less noise than a pair of either type of roller skate. Everyone agrees (let us suppose) that the operation of Honda Accords in the park on Sunday violates the ordinance -- unless, of course, a Honda Accord is operated by a police officer on duty, by an EMT, or, _possibly_, by an ordinary citizen rushing his pregnant wife to the hospital with the definite but mistaken belief that birth is imminent. Municipal garbage trucks can be operated in the park on Sundays. No city council member mentioned garbage trucks before the ordinance was enacted. No one knows if any city council members even thought about garbage removal in parks on Sunday. 4. Police offers have not ticketed users of motorized wheelchairs in the park on Sundays. The wheelchairs thus far operated in the park on Sundays have electric motors. It is not clear how police would react to wheelchairs powered by loud gasoline motors or to wheelchairs that can travel 35 miles per hour. 5. Police officers have not ticketed drivers of vehicles with "handicapped" plates who drive slowly through the park on Sunday. 6. Vehicles powered by electric motors emit almost no pollutants during their operation and some of them are extraordinarily quiet. But some vehicles powered by electric motors make loud clattering noises, some of them travel very quickly, and some of them -- for example, city buses -- are very large and occupy large swaths of space that might otherwise be used by pedestrians, prams, and pram pushers. (N.B. Is a pram a motor vehicle? Does it matter whether the pram has a motor? Does it matter whether a pram is carrying sand rather than a baby?) 7. The state's motor vehicle registration statute does not require the registration of any vehicle whose maximum motorized speed (on level ground) is below 20 m.p.h. (There are ambiguities here as well. Let me count the ways. No, let me not!) 8. The ordinance was enacted after newspaper articles reported that several small children were hit in the park on Sundays by Yellow Cabs. 9. When asked -- and even when not asked --, some citizens say, "I am disturbed by roller skaters in parks." Other citizens say, "Roller skaters? What they do makes no difference to me." Other citizens say, "Roller skaters make parks so romantic. I love them on any occasion and anywhere." Yet other citizens say other things about roller skating in response to various kinds of questions. Some (irascible? malevolent? demented?) citizens have been seen throwing gravel on the park paths that roller skaters use. 10. People over the age of 40 routinely frown and grimace at the sight or sound of skateboarders in the park on Sunday. 11. Etc., etc., ... Sincerely, Peter T ------- End of Forwarded Message
