A perennial challenge in cognitive science is framing an architecture powerful enough to be a credible support for human reasoning, yet simple enough to map to the known machinery of the human brain. Work done in the 1970s on systems such as Soar framed many of the problems, but the complex symbol processing in such systems is not a persuasive model for actual brain function. At the other extreme, models such as Braitenberg’s Vehicles  show how very simple circuits can produce surprisingly realistic movement behaviors from reasonable sensors, and models such as Minsky’s Society of Mind  suggest that collections of such reasoners might account for human cognition, but the details of this fusion remain obscure. This volume offers a coherent theory, together with a range of simulation experiments and modeling formalisms, for combining communities of simple reasoners into coherent higher-level systems.
Minsky’s fundamental insight, which can be traced back to Selfridge’s Pandemonium architecture for feature recognition in vision systems , is that competition among a community of reasoners can combine their agreements and cancel out their disagreements to yield a consensus view. But the devil is in the details. Simple combining methods such as having all reasons vote require an unrealistic global comparison that explodes combinatorically and is often unstable. One source of instability is that choices are often not binary. Individual reasoners may have an ordered list of preferences. A solution that takes into account only first choices may be the worst outcome for the defeated agents, leading to continuing revision, while a solution that gives them a highly ranked alternative that is still not their top one may converge rapidly. But adding preference orders to the comparison task over a large population of agents is not straightforward.
Richards draws on Condorcet’s insight that alternatives can be compared pairwise by each reasoner , making a decision in favor of the alternative that outranks all the others. This venerable (1785) concept has recently been shown to possess desirable optimality characteristics. To reduce the combinatorics further, Richards organizes the reasoners in a graph (an anigraf) showing the similarity relations among their desires. He explores a range of such graphical models, successively more complex.
The first set of models deals with individual anigrafs. First, he shows that certain graphs (though not all) can generate repetitive behavior by the emergence of a top-cycle, a series of preferences that form a cycle such that there is no ultimate winner. This consequence of the voting paradox, dating back to Condorcet, thus becomes the engine for generating self-sustaining activity among reasoners. Next, he exhibits graphs that exploit such cycles to swim (by oscillating a flagellum), and then to coordinate the movement of multiple limbs, and discusses how voting might be implemented in such a model.
The next set of models coordinates multiple anigrafs. The fundamental mechanism is the proxy reasoner, a reasoner incorporated in one anigraf that represents another, and thus models its beliefs about the other. He shows how his formalism supports planning through time, how anagrams can enrich their behavior by growing their graphs while running, and the behavior of societies of anigrafs of varying degrees of heterogeneity. The final chapter of the book explores metagrafs, or relations between different anigraf models. Throughout the book, he draws on phase plots that show the potential Condorcet winners for a given graph when all but two of the vertices in the graph have fixed weights. These plots allow the visualization of stable regions and also of regions where the agent represented by the graph enters a top-cycle, facilitating the study of the behavior of a given configuration.
This volume is a delightful exploration of an innovative approach to cognition and will be of interest both to cognitive theoreticians and to systems builders looking for new metaphors for composing simple parts into more complex structures.