Well, since the U.S. presidential primaries are now upon us, perhaps it's time to re-post this old item, which I originally posted to the "connectionists" mailing list in October of 1988. Some of the references may be a bit dated now. For younger readers: "Nixon" was a U.S. president of the mid-20th century who resigned to avoid impeachment over something called the "Watergate Affair". Of course, he is now a respected elder statesman, and is generally considered to be well above average as recent presidents go. "California" was a U.S. state that was prosperous and growing rapidly until it was destroyed by earthquake, flood, drought, fruit flies, and traffic gridlock. It is now largely uninhabited. - -- Scott =========================================================================== I was thinking about the upcoming U.S. election today, and it occurred to me that the seemingly useless electoral college mandated by the U.S. constitution might actually be of some value. A direct democratic election is basically a threshold decision function with lots of inputs and with fixed weights; add the electoral college and you've got a layered network with fifty hidden units, each with a non-linear threshold function. A direct election can only choose a winner based on some linearly separable function of voter opinions. You would expect to see complex issues forcibly projected onto some crude 1-D scale (e.g. "liberal" vs. "conservative" or "wimp" vs. "macho"). With a multi-layer decision network the system should be capable of performing a more complex separation of the feature space. Though they lacked the sophisticated mathematical theories available today, the designers of our constitution must have sensed the severe computational limitations of direct democracy and opted for the more complex decision system. Unfortunately, we do not seem to be getting the full benefit of this added flexibility. What the founding fathers left out of this multi-layer network is a mechanism for adjusting the weights in the network based on how well the decision ultimately turned out. Perhaps some form of back-propagation would work here. It might be hard to agree on a proper error measure, but the idea seems worth exploring. For example, everyone who voted for Nixon in 1972 should have the weight of his his future votes reduced by epsilon; a large momentum term would be added to the reduction for those people who had voted for Nixon previously. The reduction would be greater for voters in states where the decision was close (if any such states can be found). There is already a mechanism in place for altering the output weights of the hidden units: those states that correlate positively with the ultimate decision end up with more political "clout", then with more defense-related jobs. This leads to an influx of people and ultimately to more electoral votes for that state. Some sort of weight-decay term would be needed to prevent a runaway process in which all of the people end up in California. We might also want to add more cross-connections in the network. At present, each voter affects only one hidden unit, the state where he resides. This somewhat limits the flexibility of the learning process in assigning arbitrary functions to the hidden units. To fix this, we could allow voters to register in more than one state. George Bush has five or six home states; why not make this option available to all voters? More theoretical analysis of this complex system is needed. Perhaps NSF should fund a center for this kind of thinking. The picture is clouded by the observation that individual voters are not simple predicates: most of them have a rudimentary capacity for simple inference and in some cases they even exhibit a form of short-term learning. However, these minor perturbations probably cancel out on the average, and can be treated as noise in the decision units. Perhaps the amount of noise can be manipulated to give a crude approximation to simulated annealing. =========================================================================== Scott E. Fahlman School of Computer Science Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 Internet: sef+@cs.cmu.edu